125 physics projects - the eye
TRANSCRIPT
EvilGeniusSeries
Bike,Scooter,andChopperProjectsfortheEvilGenius
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ElectronicCircuitsfortheEvilGenius:57LessonswithProjects
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ProgrammingVideoGamesfortheEvilGenius
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25HomeAutomationProjectsfortheEvilGenius
3
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5
AbouttheAuthor
JerrySilver has developed components for terrestrial photovoltaic systems and designed solar arrays currently providing
power for more than 20 commercial and NASA satellites. He participated in the production of high-performance
semiconductormaterialsusedforcellphonetransistors,opticalcommunication,andmultijunctionsolarcells.Mr.Silverholds
aB.S.inEngineeringPhysicsfromCornellUniversityandanM.S.inPhysicsfromtheUniversityofMassachusetts.Mr.Silver
currentlyteachesintheNewJerseyarea.
6
Acknowledgments
The author would like to gratefully acknowledge SteveGrabowski, Dan Silver, Danielle Buggé, Tracey Jameson, MichaelDershowitz,theWallshes,BrookhavenLabs,JohnKenney,andthefolksatPASCOforassistancewiththeillustrationsinthis
book.Inaddition,specialthanksareofferedtoSteveGrabowski,ChisAleo,TiberiuDragoiu,RobinNolte,TomMisniak,and
KimFeltreforenablingmetobepartofaworldwherephysicsisappreciated,promoted,andsharedonadailybasis.
8
Contents
Introduction
Section1Motion
Project1Gettingstarted.Constantvelocity.Runningthegauntlet.
Project2Picturingmotion.Gettingamoveon.
Project3Thetortoiseandthehare.Playingcatch-up.
Project4Howdoesasailboatsailagainstthewind?Componentsofforce.
Project5Steppingonthegas.
Project6Rollingdownhill.Measuringacceleration.
Project7Independenceofhorizontalandverticalmotion.Basketballtossedfromarollingchair.
Project8Targetpractice.Horizontalprojectile—rollingoffatable.
Project9Takingaim.Shootingaprojectileatatarget.
Project10Mondaynightfootball.Trackingthetrajectory.
Project11Monkeyandcoconut.
Section2GoingAroundinCircles
Project12Whatisthedirectionofasatellite’svelocity?
Project13Centripetalforce.Whatisthestringthatkeepstheplanetsinorbit?
Project14Agravitywell.Followingacurvedpathinspace.
Project15Howfastcanyougoaroundacurve?Centripetalforceandfriction.
Project16Ping-pongballsracinginabeaker.Centripetalforce.
Project17Swingingapailofwateroveryourhead.
Section3Gravity
Project18Featherandcoin.
Project19Howfastdothingsfall?
Project20Thebuckstopshere(thefallingdollar).Usingametersticktomeasuretime.
Project21Weightlesswater.Losingweightinanelevator.
Project22Whatplanetareweon?Usingaswingingobjecttodeterminethegravitationalacceleration.
Section4ForceandNewton’sLaw
Project23Newton’sfirstlaw.WhattodoifyouspillgravyonthetableclothatThanksgivingdinner.
Project24Newton’sfirstlaw.Pokerchips,weightonastring,andafrictionlesspuck.
Project25Newton’ssecondlaw.Forcinganobjecttoaccelerate.
Project26Newton’sthirdlaw.Equalandoppositereactions.
Project27Newton’sthirdlaw.Bottlerockets.Whydotheyneedwater?(SirIsaacNewtoninthepassenger’sseat.)
Project28Pushingwater.Birdsflyinginsideatruck.
Project29Slippingandsliding.
Project30Springs.Pullingback.Thefurtheryougo,theharderitgets.
Project31Atwood’smachine.Averticaltugofwar.
Project32Terminalvelocity.Fallingslowly.
Project33Balancingact.Painteronascaffold.
Project34Hangingsign.
Project35Pressure.Implodingcans.
Project36Pressure.Supportingwaterinacup.
Project37Pressure.Sometimesthenewscanbeprettyheavy.
Project38Archimedes’sprinciple.Whatfloatsyourboat?
Project39Cartesiandiver.
Project40Anair-pressurefountain.
9
Project41Blowingupamarshmallow.Lessiss’more.Whyastronautsdonotuseshavingcreaminspace.
Project42Relaxingonabedofnails.
Project43Blowinghangingcansapart.WhatBernoullihadtosayaboutthis.
Project44Centerofmass.Howtobalanceabroom.
Project45Asimplechallenge.Moveyourfingerstothecenterofameterstick.
Project46Centerofgravity.Howfarcanastackofbooksextendbeyondtheedgeofatable?
Project47Centerofmass.Theleaningtowerofpizza.
Section5Energy/Momentum
Project48Thependulumandyourphysicsteacher’sMingdynastyvase.
Project49Twoslopes.Differentangle,sameheight.
Project50Racingballs.Thehighroadversusthelowroad.Whichwins?
Project51Linearmomentum.Wherecanyoufindaperfect90-degreeangleinnature?
Project52Elasticcollisions.
Project53Inelasticcollision.Stickingtogether.
Project54Impulseandmomentum.Eggstremephysics.
Project55Usinggravitytomoveacar.
Project56HowcanCSImeasuremuzzlevelocity?Theballisticpendulum.
Project57Angularmomentum.Ridingabike.
Project58Momentofinertia.Iceskatersanddumbbells.
Project59WhatcausedVoyagertopointinthewrongdirection?
Project60Momentofinertia.Thegreatsoupcanraceorthat’showIroll.
Project61Makingwaves.IthoughtInodethis.
Project62Rollinguphill.
Project63Gettingaroundtheloop.Fromhowfarabovethegrounddoestherollercoasterneedtostart?
Section6SoundandWaves
Project64Whatdoessoundlooklike?Oscilloscopewaveforms.
Project65Rippletank.
Project66Simpleharmonicmotion.Theswingingpendulum.
Project67Simpleharmonicmotion.Thespringpendulum.
Project68Generatingsinewaves.
Project69Naturalfrequency.
Project70Bunsenburnerpipeorgan.Resonantfrequency.
Project71Springsandelectromagnets.Resonance.
Project72Speedofsound.Timinganechooldschool.WhyGalileocouldn’tdothiswithlight.
Project73Speedofsound.Resonanceinacylinder.
Project74Racingagainstsound.Dopplereffect.
Project75Addingsounds.Beatfrequency.
Project76Pendulumwaves.
Project77Usingwavestomeasurethespeedofsound.
Section7Light
Project78Rayoptics.Tracingthepathoflightusingalaser.
Project79Twocandles,oneflame.
Project80Laserobstaclecourse.
Project81Lightintensity.Puttingdistancebetweenyourselfandasourceoflight.
Project82Howdoweknowthatlightisawave?ThomasYoung’sdoubleslitexperimentwithadiffractiongrating.
Project83Howtomeasurethesizeofalightwave.
Project84Thespeedoflightinyourkitchen.Visitingthelocalhotspots.
Project85Refraction.Howfastdoeslighttravelinairorwater?
Project86Polarization.Sunglassesandcalculatordisplays.
10
Project87Whatisthewireofafiber-opticnetwork?Totalinternalreflectionusingalaserandatankofwater.
Project88Thedisappearingbeaker.
Section8HotandCold
Project89HowmuchheatisneededtomeltGreenland?Heatoffusion.
Project90Awaterthermometer.
Project91Whatisthecoldestpossibletemperature?Estimatingabsolutezero.
Project92Liquidnitrogen.
Project93Boilingwaterinapapercup.
Project94Boilingwaterwithice.
Project95Seebeckeffect/Peltiereffect.Semiconductorheating.
Section9ElectricityandMagnetism
Project96Staticcharges.
Project97Makinglightning.ThevandeGraaffgenerator.
Project98TheWimshurstmachine.Separatingandstoringcharges.
Project99Runningintoresistance.Ohm’slaw.
Project100Circuits:Bulbsandbuzzers.
Project101Howdoesheataffectresistance?
Project102Resistivity.Canironconductelectricitybetterthancopper?
Project103Storingcharge.Capacitors.
Project104Isthemagneticforcemorepowerfulthangravity?
Project105Magneticlevitationusinginduction.Electromagneticringtosser.
Project106Magneticlevitationusingsuperconductivity.TheMeissnereffect.
Project107Movingelectronsproduceamagneticfield.Oersted’sexperiment.Themagneticfieldofacurrent-carryingwire.
Project108Faraday’sexperiment.Currentgeneratedbyamagnet.
Project109Ifcopperisnotmagnetic,howcanitaffectafallingmagnet?Lenz’slaw.
Project110Effectofamagnetonanelectronbeam.Theright-handruleformagneticforce.
Project111Whatistheshapeofamagneticfield?
Project112Whathappenstoacurrent-carryingwireinamagneticfield?
Project113Ano-frillsmotor.
Project114Magneticaccelerator.
Project115Alternatingcurrent.
Project116Thediode.Anelectronicone-wayvalve.
Section10TheEarth
Project117MeasuringtheEarth’smagneticfield.
Project118WeighingtheEarth.
Section11TheTwentiethCentury
Project119Whatisthesizeofaphoton?
Project120HowisahydrogenatomliketheNewJerseyTurnpike?SeeingtheenergylevelsoftheBohratom.
Project121Photoelectriceffect.
Project122Millikanoil-dropexperiment.Mysterymarbles.Understandinghowtheexperimentworked.
Project123Ping-pongballchainreaction.
Project124Thesodiumdoublet.Whydowethinktheelectronhasbothupanddownspins?
Project125Buildingacloudchamber.Whymuonsshouldnotbehere.Specialrelativity.
AppendixA
AppendixB
Index
11
Introduction
WhoThisBookIsWrittenFor
Thisbookhasbeenwrittenforanyonewhoisinterestedin,obsessedwith,orsimplymildlycuriousaboutexploringphysics.
Theexperiments in thisbookare intended toserveasa resource for teachersatall levels touse inplanning laboratory
activitiesfortheirclassesandtogetideasfordemonstrations.Thisbookcanalsoprovideawayforanyonenotnecessarily
directly involvedwith an academic physics class—including parents, scout leaders, and hobbyists—to pursue theworld of
physicsasfarastheirintereststakethem.Youngchildren—andthosefacilitatingtheireducation—willbeabletoappreciate
manyoftheseexperimentsonanintuitivelevel—perhapsonedaytorevisitthemingreaterdepth.
Ifyouarelookingforscienceproject ideas,youshouldbeabletofindsomethinginthesepagestoworkwith.Students
involvedinafirst-yearhighschoolorcollegephysicsclasswillfindtheoverallsequencefamiliarandhopefullywon’thave
toomuchtroublefindingtheirwayaround.
Iimaginethatreaderswithawiderangeofinterests,backgrounds,andavailableresourceswilllookthroughthesepages
forideasaboutphysicsexperiments.Forthisreason,Ihavewrittentheprojects/experimentstobeaccessibletoreadersina
numberofdifferentwaysandonavarietyoflevels.Mostoftheexperimentsincludeawaytogetstartedwithoutrequiring
elaborateequipment.
HowThisBookIsOrganized
Eachsectionstartswithalistofrequireditemsfollowedbystep-by-stepmethods.Becausethereisoftenmorethanoneway
to do a project, various options are given to accommodate varying experience, available resources, and interest levels
amongreaders.
Theexpectedoutcomefortheexperimentsisgiventohelpyouinterpretyourexperimentalresults.Firstyouwillfindthe
mostqualitativeandintuitiveinsights,followedbyincreasinglydetaileddescriptions.Forthosewhoareinterested(andonly
thosewhoareinterested)equationsareprovidedtocompletetheexplanationforwhytheexperimentswork.Thereaderis
invitedtopursueonlyasmuchoraslittledetailastheycareto.Thisbookisnotintendedtobeatextbookonphysicstheory.
Ihavetried,however,tohelpreadersconnectwiththenextsteptheymightbereadytotake.Justtobesure,eachproject
hasaconclusionthatspellsoutthepointoftheexperiment.
TheWorldofPhysics:DiscoveryandRediscovery
On more than one occasion in the history of physics, the greatest advances have taken place at a time when the
conventionalwisdomofthedaywasthateverythinghadalreadybeendiscoveredandallthatwaslefttoworkoutwerethe
details.Thehands-onapproachpresentedhere is tohelp the reader to (re-)discoverphysicsdirectly. (All Iask, is in your
acceptancespeechfortheNobelPrizeforphysics,youreserveafewkindwordsforthisbook.)
Thereistypicallymorethanonewaytodomanyoftheseexperiments.Atleastoneprocedurefromstarttofinishisgiven
foreachexperiment.Butalsoarangeofalternativeapproachesandextensionscanbefoundformostofthem.Hopefully
thisbookwillleaveyouwithideas,notonlyforhowtodotheseexperiments,butalsoforhowtocomeupwithexperimental
ideasofyourown.
WhatYouWillNeed:ToolBin/PartsList
TheBasics
Eachoftheprojectsinthisbookhasaspecificpartslist,called“Whatyouneed.”Becausedifferentreaderswillhaveaccess
12
todifferenttypesofequipment,alternativeapproachesarepresented.AlistofmajorsuppliersisgiveninAppendixAatthe
endofthisbook.
Thefollowingaresomeoftheitemsyoumaywanttohavehandy.Mostoftheseitemsareavailableintypicalphysicslabs
andmanycanbeimprovised.
stopwatch—aone-tenth-secondresolutionissufficientbecauseiteasilyexceedshumanreactiontime.
ring stands—many of the projects in this book involve supporting or holding other components of the apparatus.
Whilethiscanbeaccomplishedinotherways,havingabasicsetofringstandswithafewclampsgivesyoumore
timetofocusonsettinguptheexperiment.
meterstick—most metersticks have millimeter markings. Metersticks often serve multiple functions in addition to
measuring,suchasholdinglensesandmirrors.Thethinneronesusuallyfitbetterwiththesupportsusedinoptical
experiments.
tapemeasure—mostofyourworkwillbeinmeters.Itiseasyenoughtoconvertfeettometers,butgiventhechoice,
atapemeasurewithmetricdivisionsispreferable.
ruler—withmillimeterdivisions.
spring(s)—springswithvaryingdegreesofstiffnesstocompareareuseful.Thebestareonesthatcanbepartially
stretchedbyareasonableweight.
pulley—thelessfrictionandthelowestmass,thebetter.
stringandrope—variouskinds.Youwillwantatleastsomethinstrongstring.Weakerstringthatcanbreakplaysa
roleinProject24.
massset—arangeofmassesfrom10gto1kg(1000g).Theyshouldhaveanattachmentpointfromthetopand,
ideally,alsofromthebottom.
springscale—thesecomeinvariousranges,fromafullscalereadingof2.5newtons(255g)toafull-scalereading
of50newtons(5100g). Ifyouaredoingdemonstrationsbeforeagroup,alargecircularversionofthescalewith
oversize lettering is theway to go. (Not to quibble, butweight is a force that is read in newtonsandmass is a
measure of an object’s inertia, which is measured in grams. Physics purists definitely prefer weighing objects in
newtons.)MostofourworkwillbeintheSystemInternational(SI),which,tooversimplify,isafancynewnameforthe
metricsystem.Springscalesalsocomecalibrated inpounds (and if youmust, dynes,whichalmostnooneuses
today)—ifyouhappentohaveone,youcandothemath.ConversionfactorscanbefoundinAppenidixB.
balance—low-endelectronicbalanceshavebecomemuchmoreaffordableandcanbepurchasedforlessthan$50.
Otheroptionsincludeanalogtriple-beamscalesorthemoreelaboratedigitalbalances.
wire—severalmetersofinsulatedwire,suchasAmericanwiregauge(AWG)18,20,or22.
jumperwires—jumperwireswithvariouscombinationsofattachmentsmaketheelectricalprojectsgoalotsmoother.
Onetermination iscalledabananaplug,whicheasilyconnectsacircuit toameterorapowersupply.Another is
springloadedandgripsontoanelectricalconnectioncalledanalligatorclip.(IntheUK,somepeoplerefertothese
“croc”clips.Iamnotmakingthisup.)
DCpowersupply (orbatterieswithawireconnection)—someprojects require thecapability toadjust thevoltage.
Thisrequiresanadjustablepowersupply,whichcanbepurchasedasacomponent.Thepowersupplypictured in
FigureI-1(PASCO,partnumberSE-8828)costslessthan$150,andenablesyoutodoalltheprojectsinthisbook
thatcallforaDCpowersupply.ReasonablypricedDCpowersuppliescanalsobepurchasedfromSargent-Welch,
partnumberWLS-30972-81orFlinn,partnumberAP5375.
Somelabsalsohaveadjustablepowersuppliesbuiltintothelabbenches.IfyourDCpowersupplyconsistsofabattery,
thevoltagecanbemadevariablebyusingvariouscombinationsofresistors.Otheroptionsforapowersupplyincludea
hand-heldgenerator thatproducesaDCvoltagewhenacrank ismanually turned (suchasPASCO,partnumberEM-
13
8090orSE-8645,orSargent-Welch,partnumberWL2420).
FigureI-1Powersupply.CourtesyPASCO.
batteries—CorD cell battery and holder. Youwill not needa battery if you haveaDCpower supply except for
Project113.
electrical meters—the most useful and versatile meter is a multimeter. Multimeters perform the functions of
ammeters, voltmeters, ohmmeters, and many can also be used as a digital thermometer. Multimeters can be
acquiredforlessthan$50,whichinmanycasesislessexpensivethanstand-aloneammetersorvoltmeters.Some
projectsrequirebothanammeterandavoltmeter,soforthoseprojects,twomultimetersareneeded.Ifamultimeter
is not available, a separate ammeter and voltmeter are needed. Figure I-2 shows a multimeter available from
Sargent-Welch, part numberWLS-30712-60 (also fromPASCO, part numberSE9786A, or Frey, part number 15-
531978-21)thatworkswithalltheprojectsinthisbook.Onewordofcaution:themultimeterismuchmoreversatile
thanadedicatedammeterorvoltmeterformostpurposes.However,ifusedincorrectly,suchasbybeingplacedin
serieswithtoohighacurrent,youcaneitherblowafuse,orworse,damagethemeter.
14
FigureI-2Multimeter.CourtesyPASCO.
galvanometer—agalvanometerisaverysensitiveammeterthatdisplayssmallelectricalcurrents.
electroscope—thisisasimpledevicethatmeasuresthepresenceofstaticelectriccharges.Theyareinexpensive
andavailablecommercially.Homemadeversionsconsistofasmallballattachedbyawire.Thewireisconnectedto
twometalfoilleaves,whichareprotectedfromdischargeandaircurrentsbyaglassenclosure.
magnets—barandhorseshoemagnets
glassware—beakers,flasks
rubberstoppers—two-holeandno-holerubberstopperstofitflasks
hotplate—preferablyadjustablewithaceramictop
alcoholthermometer—mercurythermometersareno-no’sinmostlabstodaybecauseoftheenvironmentalproblems
creatediftheybreak.
hydrogentubewithhigh-voltagepowersupply
calculator—veryoftenthe ideasandkey insights inphysicsarerevealedanddiscoveredbydoingacalculation.A
simplescientificcalculator,suchasaTI-30orequivalent,canbehelpfulinmanyoftheprojectsinthisbook.
Computersareusedinmanyways,including:
–Collectingdatafrommotionsensorsandothermeasurementdevices(suchaslight,sound,force,current,andvoltage
sensor).
–Analyzingdatainaspreadsheet,suchasExcel,toidentifymathematicalmodels.
–Soundcardoscilloscope(seeProject64).
laserpointer—alaserpointerwithareplaceable(or,betteryet,rechargeable)AAbatteryisthemostversatileinthe
longrun.Thesimplelaserpointeravailableinmanydollarstoresworkswell,butislessreliable.
lenses—convex,concave,semicircular,rectangular,45-degree,60-degree,andright-angleprisms.Somelensesare
“smoky,”consistingofscatteringparticulatesintheglassthatmakethelightbeamsvisibleinthelens.Otherlenses
have a magnetic backing that makes them convenient to mount on a magnetic chalkboard or whiteboard. This
makesiteasytoenableraytracingonachalkboard.Itispossibletoglueastrongmagnettoalens,sotheycanbe
mountedonachalkboard.
mirrors—flat,concave,convex
tape—ducttape,maskingtape,electricaltape.Oneoften-overlookedprincipleofphysicsisthereisnosuchthingas
havingtoomuchtape.
Thingsthatarenicetohave
15
motionsensor—forlessthanthecostofavideogameconsole,youcangetamotionsensorthatconnectswithyour
computor.Motionsensors(suchasPASCO,partnumberPS-2103A)enablemeasurementofanobject’spositionfor
varioustimes.FigureI-3showsthemotionsensor.TheDataStudiosoftwarethatcomes(free)withPASCOmotion
sensors letsyougenerategraphsofdistanceversustime,velocityversustime,andaccelerationversustimewith
little prior experience with this equipment. The motion sensor requires a simple interface to the computer. The
simplestoftheseapproachesconnectstothecomputer’sUSBport(PS-2100A)andrequiresnoadditionalelectrical
power.ThreesensorscanbeconnectedtoacomputerusingthePS-2001.
FigureI-3Motionsensor.CourtesyPASCO.
Ahand-helddataloggersuchasPASCO’sXplorerGLX(partnumberPS-2002)functionsinasimilarwaywithvarious
sensors eliminating the need for a computer. This also enables measurements to be taken at more remote
locations.
oscilloscope—wave formsgenerated by soundpicked up by amicrophoneor electrical signals can be displayed
graphicallyonanoscilloscope. Ifyouhaveone,youcandoanumberof interestingthingswithascope.Because
eachoscilloscopeissomewhatdifferent,youalsoneedagoodmanualorapatientfriendtogetyoustarted.Ifyou
do not have a physical oscilloscope, you can inexpensively acquire software that can enable the sound card
commonlyavailableincomputerstoserveasasurprisinglyfunctionaloscilloscope.Detailsonhowtodothiscanbe
foundinProject64.
dry ice—the cloud chamber described in Project 125 uses dry ice, which can be obtained from welding supply
companies,scientificlabs,orchemicalspecialtycompanies.Ifyouareabletogetdryice,youmaywanttogeta
littleextratoexploreotherlow-temperaturephysicsexperiments.Becausedryice,whichisactuallysolidifiedcarbon
dioxide,issocold,youshouldtakeprecautionstoavoidprolongedcontactwiththebody.Useeyeprotectionwhen
workingwithdryice,especiallyifyouarebreakingitintosmallerpieces.
HoverPuck—somephysicslabsuseairtrackstoeliminatefriction.Alower-costoptionistouseaHoverPuckthat
floatsinanearlyfrictionlessmanneracrossthefloor.Thisiscalledoutasanoptioninafewoftheexperimentsin
thisbook.HoverPucksareavailablefromPASCO,partnumberSE-73358,andKick ItStick ItDiscfromSargent-
Welch,partnumberWLS-1764-09.
liquid nitrogen—liquid nitrogen is needed tomake the ceramicmaterial described in Project 106 cold enough to
becomesuperconducting.Aswithdryice,liquidnitrogenisamaterialthatisinterestinginitownrightandisexplored
inProject92.Itmaymakesensetoplanbothactivitiestogether.Justsoyouknow:dryicedoesnotgetcoldenough
todoProject106andliquidnitrogenisnotrecommendedforProject125becauseitistoocold.Liquidnitrogenmust
bestoredinaspeciallydesignedthermalcontainercalledaliquidnitrogendewar,whichsafelyhandlesthepressure
thatbuildsastheliquidnitrogenwarmsup.Aregularthermosbottlewithasealedcaporanyothertypeofsealed
containershouldnotbeused.Liquidnitrogenisdistributedinspeciallydesignedstoragecylinderstoorganizations
16
thatdo low-temperaturestudies, thermalcycling to testproduct reliability,andthatuse largevolumesofgaseous
nitrogen.
vacuumpump—avacuumpumpisusedinProjects18,41,and94.
Wish-list
Not so many years ago, some of the greatest physics experiments remained the province of obscure physics labs in
exclusiveuniversities.Today,theseexperimentsarewithinthereachofmanyphysicsdepartmentswithamoderatebudget.
Becausethepricetagfordoingtheseexperiments isthousands,ratherthanhundreds,ofdollars,formostofus,theyare
consideredheretobewish-listexperiments.Foreachofthese,asimpler,low-budgetoptionispresented.Thethreewish-list
experimentsreferredtointhisbookare:
Millikanoil-dropexperiment(PASCO,partnumberAP-8210,andFlinnScientific,partnumberAP5671)
photoelectriceffectapparatus,suchastheDaedelonEP-05(availablefromwww.daedelon.comorFlinnScientific,
partnumberAP5768).
Cavendishgravitationalconstant(PASCO,partnumberAP-8215)
Yardsalephysics
At the other end of the funding spectrum are items that can be adapted for use in physics experiments. As has been
demonstratedbymanyofthegreatscientistsofthepast,muchcanbeaccomplishedthroughresourcefulnessandingenuity.
Besidesthebargainhuntersandantiquedealers,physicsenthusiastscan,onoccasion,beobservedlookingforunnoticed
treasureatyardsaleswhereotherpeoplefailtoseethetruevalue.Herearesomeoftheitemsyoumightwanttoaddto
yourbagoftricks.
bowling ball—a bowling ball makes a good pendulum mass that can also give one of the most accurate
measurementsofgravitationalacceleration.AbowlingballcanbeusedinProjects19,22,26,or66, ifavailable.A
heavy-dutyscreweyecanbeanchoredbytapingintoapilotholesmallerthanthediameterofthescrew.Becareful
and thoroughly test your mechanical connection before experimenting. Bowling balls can also come in handy in
investigatingcollisions.
swivelchair—youwantonethatrotateswithaslittlefrictionaspossible.Thisisusefulintheconservationofangular
momentumstudies.Justthebottompartwithouttheseatcanbeusedforstudyingspinningobjects.
bathroomscale—thiscanbeusedtoexplorestaticequilibriumandtorque.
blowdryers—ablowdryerisahandywaytoproduceareasonablysteadyairflow.ThisisusedtoexploreBernoulli’s
principleinProject43.
fishtanks—theoneswithglassbottomsareespeciallyusefulforopticalprojectsusinglaserbeams.Afishtankcan
bemade into a cloud chamber in Project125 or used as the container of amousetrap-fission demonstration in
Project123.
slideprojectors—oldslideprojectorsormovingprojectscanbegoodsourcesoflight.
laser levels—thesecanbeusedlikea laserpointer.Thebeamsareangledtoproduceavisible linealongawall,
whichcanbeadvantageousforraytracing.Theoutputmaynotbethebest-focusedpointsourceoflight,sothisis
notthebestchoice,forinstance,tousewithadiffractiongrating.
turntables—turntablescanbeadaptedforrotationexperiments.(Thiscanalsobeusefulforthedigitalgenerationto
seewhatahistoricdevicelikethephonographlookedlike.)
airhockeygames—theseworkwellwithCDsaspucksandcanbeagoodwaytoinvestigateelasticcollisions.
skateboards,rollerblades—todemonstrateNewton’sthirdlaw.
leafblower—ifyouhavea leafblower,youhavemostofwhatyouneedtoput togetheraone-personhovercraft.
With just the right-shaped opening these can be used to levitate a beach ball in a demonstration of Bernoulli’s
principle(Project43).
bicycletires—thesemakegoodgyroscopesandcanbeusedforangularmomentumexperimentssuchasinProject
57.
17
Christmas tree lights—thesearean inexpensiveandeasyway to studyelectrical circuits suchas inProject100.
Theyusuallycomeinstrandsofseriesandparallelcombinations.
Youneverknowwhatelsemightcome inhandy,suchasbuckets, rope,wire,hotplates,clamps, lazysusans,golfballs,
varioustools,andmotors.Keepyoureyesopen.
18
Section1
Motion
Project1
Gettingstarted.Constantvelocity.Runningthegauntlet.
TheIdea
Withlittleornofrictiontostopit,amovingobjectwillkeepmovingataconstantvelocity.Thisexperimentexploresafew
simplewaysyoucantakefrictionoutofthepicture.
WhatYouNeed
HoverPuck
tapemeasure
5stopwatches
maskingtape
severalpeopletoserveastimers
Method
1. Setupacourse that ishorizontalandfreeofobstructions.Doa trial run tomakesure theHoverPuckdoesnot
moveunlessit’spushedandthatitfollowsareasonablystraightline.(Ifyoudon’thaveaHoverPuck,abasketballor
othersimilarobjectwilldo.)
2. Placedistancemarkers,suchasmaskingtapelabels,atregularintervals.(Typicallyinphysics,metersareusedfor
distance.However,forthisprojectanyconvenientunitcanworkaslongasyou’reconsistentthroughout.)
3. Eachofthetimersshouldbeassignedtomeasurethetimeataspecificdistancealongthepath.
4. Timersshouldsettheirstopwatchestoreadzeroandbepreparedtostartmeasuringthetimeassoonastheobject
startsmoving.
5. Pushthepuck(orbasketball)inthedesignateddirection.Startwithamediumpush.SeeFigure1-1.
6. Asthepuck(orbasketball)passeseachmark,eachtimershouldstopthestopwatchandnotethetime.
7. Repeatwithaslowpush.Aslowpushisdefinedasslowerthanthemediumpush,butfastenoughnottobepulled
offcourseorstoppedbyfriction.
8. Repeatwithamediumpush.
19
Figure1-1NearlyfrictionlessmotioncanbeachievedusingaHoverPuck.
9. Repeatwithafastpush.Thismaybethemostchallengingonetotime,especiallyforthefirstcoupleoftimers.
10. Thevelocityforeachoftherunnerswillbetheslopeofthegraphwheredistanceisonthey-axisandtimeisonthe
x-axis.
AlternateApproach
Runners
1. Placethepeoplewiththetimersonthe10,20,30,40,and50yardlinesofafootballfield.
2. Usearunnerorseveralrunnerstorunfromthegoallinetothe50yardline.
3. Asinnumber2,getthetimethateachrunnerpassesthedesignateddistancemarker,andthenplotandinterpret
theresults.
ExpectedResults
Withconstantvelocity,eachofthegraphsshouldbelinear(astraightline).Thefastestrunnerhasthehighestslope,followed
bythemediumrunner,withtheslowestrunnerbringinguptherear.
If,forsomereason,themotionwasnotperfectlyconstant,thepointsthatdifferedwillnotbeontheline.Forinstance,if
20
theassumptionthatfrictioncanbeignoredisnotcompletelyvalid,youmayseesomedeceleration.Inthatcase,theoverall
linearcurvemaybeseentotaperoffwithalowerslopethantheearlierpoints.Ifthesedatacomefromrunners,itcanbe
usedtodeterminehowsteadytherunnersactuallyare.Also, if therunnersstartfromzero,thefirst10yardswillshowan
upwardcurveindicatingacceleration.
Figure1-2showsexpectedresultsforthreerunsof0.5,1.0,and1.5meterspersecond(m/s).
Figure1-2Distanceversustimeforthreedifferentvelocities.
WhyItWorks
Average velocity can be thought of as the distance you go divided by the amount of time it took to get there. More
specifically,wecansayaveragevelocityisthechangeindistancedividedbythechangeintime.v=Δd/Δtistheslopeofthedistanceversustimegraph.(ΔistheGreekletterdelta,whichmeans“changein.”)
OtherThingstoTry
ThisexperimentcanbedoneusingapersonridinginstyleinaHovercraft,aspicturedinFigure1-3.Thiscanbedoneasan
interestingwaytodothepreviousexperimentorjustsimplyforthefunofdoingit.
Becauseofthenearlyfrictionlessmotion,thepersonmovesatconstantvelocityandmakesaperfectobjecttomeasure
atvariousspeeds.YoucanpurchaseaHovercraft(PASCO,partnumberME9838).
AHovercraftcanalsobebuiltbyfollowingthesebasicsteps:
1. Drillaholeinthecenterofa3-to-4footdiameterpieceofplywood.
2. Cutaholehalfwaybetweenthecenterandtheedgejustlargeenoughtofittheendofaleafblower.
21
Figure1-3Hovercraft.CourtesyPASCO.
3. StapleaplasticsheettothebottomoftheHovercraft.Trimofftheexcessplastic.
4. Insertabolt from theundersideof theHovercraft, throughaplasticspacer (made fromaplasticcoffee-can lid).
Attachtheboltthroughwashersonthetopandbottom,andthensecureitwithanut.
5. Tapeallthesealsbetweentheleafblowerandtheplywood,andtheplasticsheetandtheplywood,tomakethem
asairtightaspossible.
6. Cutseveralapproximately2-inchdiameterventholesintheplasticsheetafewinchesfromtheoutercircumference
oftheplasticspacer.
7. Withtheleafblowerturnedon,acushionofairshouldenableapersontomovewithaminimumoffriction.
Detailedplanscanbefoundathttp://amasci.com/amateur/hovercft.html.
The tendencyofamovingobject tokeepmoving iscalled inertia,which isaddressed inNewton’s first law.This is the
subjectofexperimentsthatfollow.
ThePoint
Constantvelocity is representedbyastraight lineonadistanceversus timegraph.Theslopeof the line isequal to the
averagevelocity.
22
Project2
Picturingmotion.Gettingamoveon.
TheIdea
Inthepreviousexperiment,weworkedwithconstantvelocityinonedirectionandfoundthatthemotionwasrepresentedby
simplegraphswhoseslopeswerestraight lines.Here,youstudythemotionofapersongoingforwardandback,fastand
slow.Youalsomeasure theeffectofspeedingupandslowingdown.Thesegraphswill takeonanewdimension. In this
experimentyouuseamotionsensorwithdisplaysoftwaretogetabetterfeelforwhatdifferenttypesofmotionlooklike.
Graphsareusedtoshowwhereanobjectisatvarioustimes.
WhatYouNeed
motionsensor
appropriatecomputerinterfaceforthemotionsensor
(roughly)8inchby10inchpieceofcardboard
Method
Motionsensor(PASCOEasyScreen)
1. Attach a motion sensor to your computer. If you have a PASCO motion sensor, it is connected through the
computer’s USB port by way of a computer interface. Follow the specific details provided by the sensor’s
manufacturer.
2. IfyouareusingthePASCOsensor,selecttheEasyScreentogetstarted.Fourmotionpatternswillcomeuponthe
screen.Selectonetostartwith.PressRun(whenyouareready).
3. Holdtheboardfacingthemotionsensor.(SeeFigure2-1.)
4. Positionyourselfsoyoustartatadistanceof1meterfromthescreen.Onthecomputerscreen,youseeavisual
indicatororyourpositionasafunctionoftime.
5. Adjustyourpositiontomatchthepatternonthescreen.(Note:youmightbetemptedtothinkthatmovingforwardis
positive,butthisisnotthecasehere.Movingbackwardresultsinincreasingthedistancebetweenyourselfandthe
motionsensor.Asaresult,forourpurposeshere,thisisthepositivedirection.)
6. RepeatforeachofthepatternsavailableontheEasyScreen.
23
Figure2-1Matchingapatternusingamotionsensor.CourtesyPASCO.
ExpectedResults
Figure2-2 shows the result of someonemovingbackwardand forward in suchaway that theymatch the targetmotion
pattern.Thisrepresentsholdingstillfortwosecondsat0.5metersdistance,thenmovingbackat2.2m/s,andthenholding
stillforanothertwosecondsatadistanceof1.8meters.Thepersondoingthematchingdoesnothavetothinkaboutthis,
butonlyneedstolookatthescreenandmovetofitthepattern.
Constantvelocityinthepositivedirection(whichinthiscaseisdefinedasawayfromthemotionsensor)isrepresentedby
astraightlineonadistanceversustimegraph.Thefasterthemotion,thesteepertheslope.
Figure2-2Motionmatchresults.CourtesyPASCO.
Zerovelocitymeansthedistancestaysthesameoveragiventimeinterval.Thisisrepresentedasahorizontallineonthe
distanceversustimegraph.
Acurvedlinewouldbeproducedbyacceleratedmotion(speedinguporslowingdown).
WhyItWorks
Thedistanceanobjectgoesinagiventimeinterval,t,isgivenbytheequation:
d=do+vt
24
From this equation, the slope of the distance versus time graph is given by v, the velocity of the motion. The initial
separationfromthemotionsensor,do,determineshowfarabovethebaselinethegraphstarts.
Each new phase of the motion contributes a separate segment to the graph. For instance, if the velocity stops, the
distanceremainsconstantforthatperiodoftime.Ifthemotionistowardthemotionsensorforanotherperiodoftime,that
motioncontributesasegmentofthegraphwithanegativeslopethatconnectstotheothersegments.
Table2-1summarizesthevariouspossibilities.
Table2-1
OtherThingstoTry
Atreasuremap
1. Onapieceofpaper,drawthefollowingmoves(ormakeupyourown):
Forward1meterinthreeseconds
Inplacefourseconds
Back0.5meterintwoseconds
Forward2.5metersinfourseconds
Inplacefourseconds
Back1meterinthreeseconds
2. Howfardidyouget?
Whatwasyourdisplacement?(Thisisthetotaldistanceyoutraveledfromyourstartingpoint.)
Whatwasyouraveragevelocity?This isthedisplacementdividedbythetotaltime (including the timestanding in
place).
Whatwas the totaldistanceyou traveled?Unlikedisplacement,every forwardandbackwardmovecontributes to
distance.
Whatisyouroverallspeed?Youroverallspeedisthedistancedividedbythetotaltime.Thetotaltimeisthesame
forbothofthese.
Theresultsofthetreasurehuntis:
Totaltime=20seconds
Displacementfromthestartingpoint=+1+0−0.5+2.5+0−1=2.0metersAveragevelocity=2meters/20seconds=0.1meterspersecond
Totaldistancetraveled=+1+0+0.5+1.5+0+1=4meters
Overallspeed=4meters/20seconds=0.2meterspersecond
Makeyourowndistanceversustimechallenges:
1. SelectanyoftheEasyScreenPatterns.
2. Usinga transparencymarker (erasable or not is your choice) and trace the rectangular shapedefining theEasy
25
ScreenGraph.
3. Drawyourownmotionpatternonthetransparency.
4. Tapethetransparencyonthescreen,sotherectanglealignswiththeoneyoutracedonthescreen.
5. Matchyourpatternbyadjustingyourdistanceasbefore.Thistime,youwillbeignoringtheEasyScreenPatternand
followingonlyyourown.
Once you get the hang of it, you can throw in accelerated motion. Acceleration (away from the motion sensor) is
representedbyanupwardslopingline,whichiscurvedupward.Acceleration(towardthemotionsensor)isrepresentedbya
downwardslopinglinethatiscurveddownward.
ThePoint
Constantvelocityisrepresentedbyastraightlineonthedistanceversustimegraph.Thevelocityisgivenbytheslopeofthe
line.
If thecurve is nota straight lineatanypoint this indicates thatacceleration hasoccurred.Accelerationcanbeeither
positive(speedingup)ornegative(calleddecelerationorslowingdown).
Anobjectmovinginaparticulardirection(forwardorbackward)canexperienceeitherpositiveornegativeacceleration.
26
Project3
Thetortoiseandthehare.Playingcatch-up.
TheIdea
Onecarisgoingfasterthantheother,buttheslowercarhasaheadstart.Wecanpredictwhereandwhenthefastercarwill
overtake the slower car. All we have to do is graph the movement of each car and see where the lines cross. This
experimentgivesyouamethodtomakethatprediction.
WhatYouNeed
2toycarswithadjustablespeeds
stopwatch
tapemeasure
Method
1.Setthespeedofeachofthetwocars,sooneisfasterthantheother.(Ifyoudon’tknowthespeedsbeforestarting,
youcanmeasuretheminthefollowingsteps.)
2.Determinetheaveragevelocityofeachofthecarsbymeasuringthedistanceitgoesinagivenamountoftime.The
equationisaveragevelocity=(distancetraveled)dividedby(timetogetthere).Inphysics,metersaretypicallyusedto
measure distance (to be consistent with the SI or System International unit system). This will result in velocity
measuredinmeterspersecond(m/s).However,youcanworkwithotherunitsfordistance(suchasfeetpersecond)
aslongasyouareconsistent.
3.Lineupthetwocarsinthesamedirectiononalevelfloorheadinginthesamedirection,asshowninFigure3-1.
4.Wearegoingtogivetheslowercaraheadstartofafewsecondsandtrytopredictwherethefastercarwillovertake
theslowercar.
5.Todothis:
Plotthespeedofthefastercaronagraphofdistanceversustimewiththelinestartingattheoriginandhavinga
slopeequaltothespeedofthefastercar.
Plotthespeedoftheslowercaronthesamegraph,butstartingatapointwherethedistanceiszeroandthetime
isequaltothechosentimedelay.
SeeFigure3-2,whichshowsaslowercargoingat0.25meterpersecondcargivena0.25meterheadstartinfront
ofafastercargoing0.4meterpersecond.(Noticetheslowercarispredictedtoovertakethefastercaratapoint
thatis0.68metersfromthestartingpointand1.8secondsaftertheracestarts.)
27
Figure3-1Whenwillthefastercarovertaketheslowerone?
Figure3-2Fastercarpassestheslowercarwhereandwhenlinescross.
6.Predictwherethefastercaryouareworkingwithwillovertaketheslowercar.
7.Starttheslowercarandgiveitaheadstart.
8.Comparewhereandwhenthefastercarwillovertaketheslowercarwithyourpredictions.
ExpectedResults
Thefastercarwillovertaketheslowercarwhenthetwolinesinthegraphcross.Thedistancethelinescrossatishowfar
fromthestartinglinethefastercarcatchestheslowercar.
Thetimewherethelinescrossishowmanysecondsfromthestartoftheracewhentheslowercarcatchesthefaster
car.
WhyItWorks
Thedistancethataobjectgoesisgivenbytheequation:
d=do+v(t−to)wheredoistheinitialdistancebetweenwheretheobjectstartsandthestartingline.(docanbeunderstoodastheheadstart
indistance)
visthevelocityofthecar
28
tisthetimeithasbeengoingfromthestartoftherace,andtoisthedelayortheheadstartinsecondsgiventotheother
car.
OtherThingstoTry
Herearesomealternativewaysofdoingthis:
1. If you have twomotion sensors, focusoneon the faster carand theother on the slower car.This generatesa
similarcurveasshowninFigure3-2.Ifthecarsaremovingawayfromyouasimilarcurvewillbeproduced,except
theslopewillbepositive.
2. Another way to establish two different velocities is to use objects rolling off two different slopes starting from
differentheights.Theobjectstartingfromthehigherstartingpointwillberollingonthetableorfloorwithahigher
velocity,withthevelocityproportionatetotheheightdifference.Ifthebottomsofeachoftherampsarethesame
distancefromthestartingline,theslowerrollingobjectcanbegivenafewsecondsheadstart.Asimilarprediction
andcomparisonofresultscanbemadeasintheprevioussection.
3. IfyouhappentobeassociatedwithaFIRSTroboticsteam,youmaywanttoconsiderusinglastyear’srobot(s)for
thisexperiment.
4. Anothervariationistopredictwhereandwhentwocarsmovingtowardeachotherwillmeet.
ThePoint
Twoobjects thatmove independently can be represented by separateequations that represent the relationship between
distanceandtime.Thesearetwosimultaneousequations,whichcanbesolvedgraphicallytofindthetimeanddistancethat
thefasterobjectovertakestheslowerobject.
29
Project4
Howdoesasailboatsailagainstthewind?Componentsofforce.
TheIdea
Itisnothardtounderstandhowagoodstiffwindblowingfrombehindasailboatcanmoveitalongatabriskpaceinthe
water.Butwhataboutgettingbackhome?Howcanasailboatmove(ortack)againstthewind?
Inthisproject,youdiscoverhowasailboatmovingagainstthewindcanresultinaforcethatpushesthesailboatforward.
Thisgetstotheideaofhowaforceinonedirectioncanbebrokendownintoseparatecomponentforces.Twomethodsare
shownhere.Thefirstmethodusesasailattachedtoapulleyonastring.Thesecondmethodusesanairtrackforthose
readerswhohaveaccesstoone.Afterlookingatthesemethods,youareencouragedtotryoneorbothofthese,ortocome
upwithyourownidea.
WhatYouNeed
Pulleyandstring:
stiffpieceoffoamboardorcardboardtouseasasail
(low-friction)pulley
smallmasswithanattachmenthook,approximately20g
1–2metersofthinstring
attachmentpoints(suchasringstandsclampedtoalabtable)toholdthestringhorizontally
blowdryerorothersourceofairflow
ducttape
Airtrack:
airtrack
glider
attachmentfor theglider thatcanholda“sail.”Abumper, for instance,canbeattachedto the topofaglider to
30
serveasa“mast.”
1CD(orastiffsheetofcardboard)
Method
Pulleyandstring
1. Attach thestringhorizontally to twoanchorpoints.Thestringshouldbe tautandable to supporta smallweight
withoutsagging.
2. Hangthepulleyonthestring.
3. Hangtheweightonthepulleysothepulleyisfreetoslideonthestring.
4. Tapethefoamboardorcardboardatanangleofabout20–30degreeswithrespecttothedirectionofthestring.
5. With thesailboatsupportedon thestring,direct theblowdryerat thesail.Theblowdryershouldbeataslightly
greaterangle(withrespecttothestring)thantheangleofthesail.Iftheairfromtheblowdryeristoostrong,the
sailmayvibrate. If theangle istoosmall, thesailwillbeforcedbackwardwiththewind.However,undertheright
conditions,theforceintheforwarddirectionwillbestrongenoughtopropelthepulleyagainstthewind,inasimilar
mannertoarealsailboat.SeeFigure4-1.
Airtrack
1. Level the air track. You can determine that the air track is level by observing the glider when the air track is
activated.Ifthegliderdoesnotmoveineitherdirectionundertheforceofgravity,thenthetrackcanbeconsidered
tobelevel.
2. Attachafixtureonthegliderthatcanholdaflatobject,suchasaCD.
3. PlacetheCDintheholderandsecureitatanangleofabout20–30degreeswithrespecttotheairtrack.
4. Direct the blow dryer at a slightly greater angle than the angle of the sail, and then observe its response. See
Figures4-2and4-3.
31
Figure4-1Atthecorrectangle,theblowdryerwilldrawthefoamboardsailintothewind.
ExpectedResults
Foreithermethod,theactionoftheblowdryerifpositionedproperlycausesthe“boat”tomovetowardtheblowdryer.The
boat isseen tomove“against thewind.”Theparallelcomponentof the forcewillcause thesailboat tomoveforwardor
tackingagainstthewind.
Using thepulley, ifconditionsare right, theperpendicularcomponentof the forcewillalsocause thesailboat to rotate
aroundthestring.This iscomparabletoasailboat listingundertheforceofastrongwind.Thekeelofanactualsailboat
servestocounteracttheeffectofthisperpendicularforce.Inthisexperiment,thisforceisnotconstrainedandcausesthe
pulleytorotate.
32
Figure4-2Sailboatsimulationusinganairtrackviewedfromtheside.PhotobyS.Grabowski.
Figure4-3Sailboatsimulationusinganairtrackviewedfromthetop.PhotobyS.Grabowski.
WhyItWorks
Thephysicalstructureofasailboatneedstodoatleastthreethings:
1.Itpicksuptheforceofthewind(roughly)perpendiculartothesail.
2.Thekeelof thesailboatmakesthesailboatfollowone-dimensionalmotionbypreventingthesailboatfromslipping
perpendiculartoitsforwardmovement.
33
Figure4-4Forcesonasailboat.
3.Itseparatestheforceofthewindintotwoparts:oneperpendiculartothemovementoftheboat,whichisresistedby
thekeel,andoneparalleltothemotionoftheboat,whichpropelsitforward.
Figure4-4showshowtheforcesareseparatedintotwocomponents.Theforceproducedonthesailbythewindblowing
getssplitupbythesailboatintotwootherforces.Onetriestopushtheboatsidewaysandisresistedbythekeel.Theother
force—iftheanglesareright—triestopushtheboatforward.Thishappensevenifthewindiscomingmorefrominfrontthan
frombehind.Quantitiesinphysicsthatcanbebrokendownintocomponentsasthisforceonasailboatarecalledvectors.
OtherThingstoTry
Attachingafoamboardorcardboardsail toatoycarwillwork.Thewheelsofthecarmustturnfreelyandthetiresmust
haveenoughfrictiontoserveasa“keel”torestrictsidewaysmotion.
Anotherway to do this is to usea (nearly) frictionless hockey puckwith a low-friction tube to constrainmotion in one
dimension.Aguidestring(suchasfishingline)isusedtokeepthemotioninonedimension.Youhavetokeepenoughtension
onthestringtopreventthepuckfromrotatingandbinding.Thepuckmustalsobeonanearlyperfectlyhorizontalsurface.
Tape a sail as in either of the two methods previously described. This approach also requires a reasonably horizontal
surfacetopreventthepuckfromdriftingonitsownbeforethebloweristurnedon.
ThePoint
Aforceinonedirectioncanbethoughtofasbeingequivalenttotwootherforcespushingincompletelydifferentdirections.
Thishappensbecauseforceisavectorquantityinphysics.Thisprojectillustrateshowaforceonthesailofasailboatisthe
sameasasidewaysforcepushingagainstthekeelandaforceintheforwarddirectionofthesailboat.Thisisanexampleof
theresolutionofaforceintotwoperpendicularcomponents.
34
Project5
Steppingonthegas.
TheIdea
Pressingdownwithyourfootontheacceleratorofacardoesnotnecessarilycauseyoutoaccelerate.Youmaybemoving
forwardwithconstantvelocity.Howcanyoutellifyouareaccelerating?Thisexperimentshowsyouafewwaystodetermine
whetheryouareacceleratingorjustmovingalongatconstantvelocity.
Inthisproject,youcanalsofindwaystodetectcentripetalacceleration,whichkeepsthingsmovinginacircle.
WhatYouNeed
Anyorallofthefollowing“accelerometers”canbeusedtodetectacceleration:
pendulum:anyweightonastring
floattiedtoastringheldunderwater
candle
partiallyfilledtankofliquid
accelerometer,suchasshowninFigure5-1
Figure5-1Accelerometer.CourtesyPASCO.
Method
Pendulum
1. Holdingthestringofthependulum,moveatassteadyapaceasyoucan.Observethependulumduringconstant
velocity.
2. Nowdothesamething,butobservewhathappenswhenyouspeedup(accelerate).
Skateboardaccelerometer
1. Attachapendulumtoaskateboard,asshowninFigure5-2.
2. Rollitdownarampthathasalargeenoughslopefortheskateboardtoincreaseitsspeed.Observetheanglethe
35
pendulummakeswiththeverticalposition.
3. Adjust theslopeof the ramp, so theskateboard is just heldon the rampby frictionwithout slidingdown.This is
calledtheangleofrepose.
4. Givetheskateboardaslightnudge.Itshouldmoveatafairlyconstantvelocity.Notetheangleofthependulum.
5. Whathappensiftheskateboardslowsorgoesuparamp?
Centripetalacceleration
Spinanapparatus,suchasshowninFigure5-3or5-4.Apairofcandlesateitherendofaspinningboardisanotherwayto
dothis.Thefloatingbobapparatus iscommerciallyavailableorcanbeassembledfromfishingbobs(orStyrofoamballs),
babyfoodjars,apieceofwoodwithaholeinthecenter,andametalpost.
Figure5-2“Skateboard”accelerometer.
ExpectedResults
Apendulumhangsverticallywhenmovingatconstantvelocity.Butitmovesintheoppositedirectionastheaccelerationitis
experiencing.Ifanobjectslowsdownordecelerates,itshowsupasabackwardmovementinthependulum.
Figure5-3Floatingbobaccelerometer.
Whentheapparatuswiththefloatingbobisspinning,thebobmovesinward.Thismaybetheoppositeofwhatyoumight
expect and is the opposite ofwhatwould happenwith a freely hanging pendulum.The reason for this is the centripetal
acceleration increasesthebuoyantforceonthebob,forcing it inward.Candlesmove intheoppositedirection.Theflame
36
movesoutward,asdoesliquidinacontainer.
WhyItWorks
Newton’ssecondlawrequiresthatforceandaccelerationarerelatedtoeachotherthroughF=ma.Ifthereisacceleration
(a),thereisaforce(F)onthemovingobject(ormass,m).Theforceisinthesamedirectionastheacceleration.
OtherThingstoTry
Anaccelerometer,suchasshowninFigure5-4,directlyindicatesaccelerationwithasetofLEDsthatlightinproportionto
the amount of acceleration. The greater the acceleration, the more LEDs will light. It can, for instance, indicate the
accelerationofacartpulledbyastring.Itcanalsobeusedtomonitorcentripetalacceleration.
ThePoint
Ahanging(orotherunconstrained)objectisaffectedbyacceleration,butisnotaffectedbyuniformsteadyvelocity.
Figure5-4Anappliedforcecausesanobjecttoaccelerate.CourtesyPASCO.
37
Project6
Rollingdownhill.Measuringacceleration.
TheIdea
Whenexposedtotheforceofgravity,objectsfallfasterandfaster.Thisiscalledgravitationalacceleration.Whenobjects
fallstraightdown,youhavetobeveryquickifyouwanttomeasurehowlonganobjectfallsagivendistance.WhenGalileo
Galileitriedtodothisduringthefifteenthcentury,heusedprimitivetimingdevices,suchasdrippingwaterandhisownpulse
tokeeptrackofobjectsdroppedfromtheLeaningTowerofPisa.Toovercomethedifficultyoftimingthesemeasurements,
Galileo had the brilliant insight of slowing down gravitational acceleration using a ramp. In this experiment, you follow in
Galileo’sfootsteps.However,youhavetheadvantageofbeingabletouseastopwatchorevenamotionsensortomore
accuratelymeasuretheobject’smovement.
WhatYouNeed
inclinedtrack(suchasasectionofwoodencornermolding,semi-roundvinylbullnosemolding,oraflatboardwith
two“gutters”createdbyattachingmetersticksasguides)
golfballsormarbles
stopwatchorothertimer
meterstick
optional:motionsensor,inclinedairtrack
Method
1.Settheinclinedtrackatamoderateanglewithrespecttothesurfaceonwhichitissupported.
2.Markdistanceintervalsfromthebottomofthetrackin10cmincrements.
3.Releasethegolfball(ormarble)fromeachofthedistancesmarkedandrecordthetimeinsecondsthatittakesto
reachtheendoftheramp.SeeFigure6-1.
Figure6-1Rampusedtomeasureeffectsofacceleration.
4.Ifyoumeasurethedistancetheballrollsandthetimeittakestoroll,youcaneasilyfindtheacceleration,a,atany
pointusinga=2d/t2,wheredisthedistanceitrollsandtisthetimeittakestorollthatdistance.
5.Whatistheeffectofchangingtheslopeoftheinclineontherateofacceleration?
ExpectedResults
Agraphofdistanceversustime,suchaspicturedinFigure6-2,showsthatthedistancetheobjectmovesinagivenamount
38
oftimeisincreasing.Thedistanceinthegraphisshowntoincreaseasthesquareofthetimewhichisacharacteristicof
constantacceleration.
WhyItWorks
Whenanobjectaccelerates,itsvelocitychangeswithtime.Forthecaseofconstantacceleration,thevelocityincreasesby
aconstantamounteverysecond.Thisresultsinthedistanceincreasingasthesquareofthetime.
OtherThingstoTry
A rolling golf ball or marble can be considered a falling object whose acceleration is slowed by the incline. This is
approximately,butnotcompletely,true.Anyrollingobjectdevelopsangularmomentumthattiesupsomeofitsenergyinthe
processofrolling.
Figure6-2Distanceversustimeforagolfballrollingdownanincline.
Figure6-3Anairtrackwithamotionsensorattachedtotheend.CourtesyPASCO.
Betterprecisioncanbeachievedbyusinganairtrack.Thisreducesthe impactoffrictionandrotationalkineticenergy.
Incorporatingamotionsensortomeasurevelocityandaccelerationaddsanotherdimension,asFigure6-3shows.
DataStudiosoftwaredisplaysthedistancemeasuredbythemotionsensor,asshowninFigure6-4.
ThePoint
Whenanobjectaccelerates,itsvelocitychangeswithtime.Ifthataccelerationisconstant,distanceincreasesasthesquare
oftime.
39
Project7
Independenceofhorizontalandverticalmotion.Basketballtossedfromarollingchair.
TheIdea
Whichwillhit thegroundfirst:abulletdroppedstraightdownfromaheightof5feetorabulletfiredhorizontallyoverflat
groundat300m/sfromthesameheight?Manypeopleguessthatthegreatermomentumofthemovingbulletwouldkeepit
intheairlonger.Thisexperimentaddressesthisquestion.
Aprojectile isanobjectthathasbothhorizontalandverticalmotion.Althoughmotion intwodimensionsmayseemvery
complicated,itcanbeenormouslysimplifiedbasedontheresultsofthissection.Youdiscoverthatthehorizontalmotionofa
projectileiscompletelyindependentofitsverticalmotion.Itdoesnotmatterhowfastanobjectisfalling.Inthisexperiment,
youprovethisinseveralways.
WhatYouNeed
chair
basketball
someonewillingtositinachair
independenceofhorizontalandverticalmotionapparatus
ballisticcar
Method
Rollingchair
Thisissimpletodo,butithasasignificantresult.
1. Havethepersonsitinthechairholdingthebasketball.
2. Rollthechair(withthepersonsitting).Thepersoncanalternativelybeonaskateboardorrollerblades.
3. Havethepersontossthebasketballupandobserveitstrajectory.
Coins
1. Placeacoinattheedgeofatable.
2. Flickasecondcointowardthefirstsothatthefirstisjustpushedovertheedgeandthesecondcoinfliesoffthe
table.
3. Bothcoinsshouldstartfallingatthesametime.Onewithahorizontalvelocityandonewithout.
4. Listen to seewhich, if any of the coins, strikes the floor first. Repeat this enough times until you get consistent
results.
Apparatus
Useacommerciallyavailableapparatus,suchaspicturedinFigures7-1and7-2.TheapparatusshowninFigure7-1ismuch
easiertouse.TheballisticscarshowninFigure7-2mayrequirealevelsurfaceandsomepractice.Amorereliableversion
ofthisisavailableasanaccessoryforanairtrack.
41
Figure7-1Bothballshittheflooratthesametime.
ExpectedResults
Thebasketballshouldgoupandcomedowntobecaughtbythepassengerintherollingchair.Thisworksbestiftheballis
thrownstraightupintheverticaldirection.Similarly,thecoinswillhitthegroundatthesametime.Itiseasiertocomparethe
soundofthecoinsstrikingthefloorthantomakethatcomparisonvisually.Whenusingacommercialapparatus,agreater
distancefromthefloorgivesamoredefinitiveresult.
WhyItWorks
Theforceofgravityanditsassociatedaccelerationisentirelyintheverticaldirection.Gravitydoesnotinanywayinfluence
thehorizontalvelocity.
Figure7-2Ballisticscarshowingthesteelballhasthesamehorizontalvelocityasthecar.
OtherThingstoTry
42
1. Placeacoinattheedgeofatable.
2. Slideasimilarcointowardthefirstone,sothemovingcoinjustknocksthestationarycoinoffthetableandbothfall
tothefloor.Thiswilloccurifthemovingcoinstrikesthestationarycoinatalargeenoughangle.
3. Ifaproperangle ischosen,thestationarycoin isnudgedoffthetableandfallsnearlystraightdown.Themoving
coinwillfallatagreaterdistancethanthestationarycoin.
ThePoint
Horizontalmotionandverticalmotionarecompletely independent.Excluding theeffectsofair resistance, thehorizontally
firedbulletwillfalltothegroundatexactlythesametimeasthedroppedbullet.Thisformsthebasisforanunderstandingof
projectilemotionthatisgreatlysimplifiedbytreatingtheverticalandhorizontalmotionseparately,asiftheotherdidnoteven
exist.
43
Project8
Targetpractice.Horizontalprojectile—rollingoffatable.
TheIdea
Inthisexperiment,youwilltrytohitatarget.But,toimproveyourodds,youcanusethelawsofphysicstopredictwherea
projectilewill land.Yourprojectilewillbeasteelballoramarble.Thephysicalsituation isverymuchsimplifiedwhen the
projectile isshot (or launched) in thehorizontaldirectiononly. In thisproject,weseehowcloseyoucanget to the target
usingthelawsofphysicsthatdescribehowhorizontalobjectsmoveundertheforceofgravity.
WhatYouNeed
steelballormarble(toserveasaprojectile)
inclinedtracktogetthemarblerolling(Thiscanbeapieceofgroovedwoodenmoldingorarulerwithagroove)
flat,smooth,horizontaltable
stopwatchorothertimer(wristwatch,cellphone)
cup(yourtarget)
meterstick
optional:motionsensor(tomeasurevelocity)
Method
Part1:Findthevelocityofthemarblecomingofftheramp
Youwillneedthisinformationtomakeyourpredictions.
1. Setuptherampinsuchawaythatitspositionremainsfixed.
2. Placeamarbleatthetop(oranotherarbitrarilymark)oftheramp.
3. Releasethemarblefromthemarkandmeasurethetimeittakestogotothebottomoftheramp.
4. Repeatafewtimesuntilyougetaconsistentreading.Then,taketheaverage.(Iftherampistooshortortheslope
istoogreat,itismoredifficulttomeasurethetimetogodowntheramp.)
5. Findthefinalvelocityatthebottomoftherampusingtheequation:
Part2
1.AswefoundinProject5,theverticalmotionisindependentofthehorizontal,sowecandeterminethetimeittakes
themarbletofallfromthetablejustfromtheheight,h,ofthetable.Thisisgivenbytheequation:
2.NowmakeyourpredictionforhowfarthemarblewillgousingR=vt.ThedistancetheballwillgoisnowgivenbyR=
vt.UsethevyoufiguredinStep5aboveandtfromthepreviousstep.
3.Setthe(centerofthe)cupatthedistanceyoupredictedandtryitout.Nocheating.Itismorefuntocallyourshotfirst,
andthenseeifitworks.Linethecupupvisually,soitisonastraightlinewiththemotionofthemarble,asshownin
44
Figure8-1.
ExpectedResults
Clearlytheexpectedresultisforyoutohavethemarblerollintothecup.Ifthemarblehitsataboutthedistanceofthecup,
buttotheleftorright,thatshouldcountasahit.Hittingthetargetrequiresaccuratemeasurementofthemarble’svelocityon
thetable.Itisreasonabletoassumethatthemarbledoesnothaveanysignificantvelocitylossfortheshorttimeitisrolling
onthetable.
(Asimplerwayofdoingthis—appropriateforyounger readers—istoqualitativelycompare thedistancethemarblegoes
withtheheightoftherampandskippingthemath.Thehighertheramp,thefasterthemarbleandthefartheritgoes.)
Thetimeittakestofallfromagivendistanceisprovidedbytheequation:
Tousethisequation,thedistancetheprojectilefallsmustbecompatiblewiththeunitsforgravitationalacceleration,g. If
youuse9.8m/s2forg,hmustbeinmeters.ThetimetofallagivendistanceisshowninthefollowingTable8-1:
Table8-1
Usingthistable,thedistancetheprojectilegoesissimplyitsvelocitymultipliedbythetimeitisintheair(fromthetableor
equation).
WhyItWorks
Thehorizontalvelocityofthemarbleisconstantandunaffectedbythefactthatthemarbleisfalling.Thedistanceitmoves
issimplythehorizontalvelocitymultipliedbythetime.
Thetimeittakestofallagivendistanceisdependentonlyontheverticaldistance.
Findthevelocityatthebottomofarampusingthefactthatthefinalvelocityistwicetheaveragevelocitydividedbythe
time.
45
Figure8-1Horizontalprojectile.
Thehorizontaldistancethemarblegoesissimplythehorizontalvelocitytimesthetime.
OtherThingstoTry
Anotherwaytodothisistouseahorizontalprojectilelauncherandcalibratethevelocity.
ThePoint
Horizontalmotionandverticalmotionarecompletelyindependent.Thismeanswhenanobjectismovingwithonlyaninitial
horizontalvelocity,thetimeitisintheaircanbedeterminedbyhowlongittakestofall.
46
Project9
Takingaim.Shootingaprojectileatatarget.
TheIdea
Inthisexperiment,yougettoshootthingsaroundtheroom.Youcanuseatoybow-and-arrow,atoyping-pongballshooter,a
Nerfgun,amarble launcher,oraprecisionprojectile launchermade for thispurpose.You learn tomakepredictions that
accuratelyguidetheprojectiletothetarget.Inthiscase,usingthelawsofphysicsisnotcheating.Itdoes,however,giveyou
adefiniteadvantagecomparedwithsomeonewhoisnotarmedwiththisknowledge.
First,youmeasurewhatisthebestangletoaimsomethingforittotravelthegreatestdistance.
Then,youmakeandtestpredictions.Tohitatarget,youneedtoknowonlytwothings:thevelocityoftheprojectileandthe
angleatwhichitisshot.That’sall.Knowingonlythosetwoconditions,youcandeterminehowfartheprojectilewillgo,and
howhighitwillgo.Theangleiseasytomeasuredirectly,sowewillfirstworkonasimplewaytodeterminethevelocity.
WhatYouNeed
projectileandlauncher
–Aprojectilelauncher,suchasshowninFigure9-1.Plasticratherthansteelballsaresafer.
–Or,atoygun,atoybow-and-arrow,aping-pongballshooter,Nerfgun,oramarblelauncher.
tapemeasure
protractor
target—horizontal:panorcup;vertical:ringonaringstand
stool(s)orothermoveableobjecttoholdthetargetattheheightofthelauncher
Method
Whatisthebestangle?
Westartherebecausethispartdoesnotinvolveanynumbercrunching.
1.Youwillbeshootingyourprojectilefromground-to-groundorfromtabletoptoraisedsurfaceatthesameheightas
thetabletop.Theprojectileshouldbelaunchedandlandatthesameheight.
2.Selectasettingforyourlauncherthatwillfireaprojectilefromagivenheightandreturntothatsameheightwithout
hittingtheceiling,awall,orbreakinganything.
47
Figure9-1Projectilelauncher.CourtesyPASCO.
3.Forevery test in thispart, youwillbeusing thesamevelocity.Pickanangle toshoot theprojectileat.Launch the
projectile andmeasure the distance. Increaseor decrease the launchangle until you find theangle that gives the
greatestdistance.(Remember,forthispart,wearemeasuringthedistancetheobjectgoesafterreturningtothesame
heightfromwhichitwaslaunched.)
Determinethevelocityofthelauncher(tomakepredictions).
Forthispart,wearegoingtousethemethodoftheprevioussectiontodeterminehowfasttheprojectileismovingasit
leavesthelauncher.Forthispartonly,weshoottheprojectilehorizontally,sowecanfindthisvelocity.
1. Firehorizontallyseveraltimesandrecordthedistance,R,thattheprojectiletravels(inm).Taketheaverage.
2. Measuretheheightwhentheprojectileleavesthetable.
3. Aswedidinthepreviousexperiment,wewillusethetrickoffindingthetimetheprojectileisinflightbydetermining
howlong it takestofall.Thiscanbesimplyfound justknowingtheheight (inmeters)andusingtheequation, t=
(2d/g)½,wheregis9.8m/s2.Table8-1intheprevioussectiongivesthetime,t,forvariousheights.
4. Now, it isasimplemattertofindthevelocityusing the techniqueof theprevioussection.Divide thedistance the
objectgoesalongthefloor,R(inmeters),bythetimeitwasinflight,t(seconds).Thisisgivenbytheformula:
v=R/t
Hittingthetarget
1.Selectanangle,θ,atwhichyouwillshoottheprojectile.2.Predicttherange,orhowfartheprojectilegoesalongthefloor,usingtheequation
R=(v2/g)sin2θwherevisthevelocityyoujustfoundinnumber4,gis9.8m/s2,andθistheangleyouselected.3.Predicttheheightusingh=(vsinθ)2/2g,withthevariablesasdefinedinthepreviousequation.4.SetacupadistanceRhorizontallyalongthegroundlocatedatthesameheightasthelauncher.
5.Setaringontopofaringstandataheight,h,abovethelevelofthelauncher.Thecircularopeningoftheringshould
befacingthelauncher.Useafewstools(stackedontopofeachother,ifnecessary)tosettheringstandtoestablish
theheighttarget.
6.Visuallyalignthetargets,sotheyareinlinewiththeprojectile.
7.Afteryousetthetargetstowhereyoupredictedtheyshouldbe,firethelauncherandseehowcloseyouget.
ExpectedResults
48
Figure9-2showstypicalresultsforaprojectilefiredatavelocityof10meterspersecond.Noticethatthe45-degreeangle
resultsinthelongestrange.Noticealsothatthe60-degreeand30-degreeangleswindupinthesameplace.Theprojectile
firedat75degreesstaysintheairlonger,butithasalowerhorizontalvelocitythantheonefiredat30degrees.
Figure9-2Projectileshotat10m/s,returningtothesameheightitwasshotfrom.
WhyItWorks
Accordingtotherangeequation:
a45-degreeanglegivesthegreatestdistanceanobjectmoveshorizontallyalongtheground.Foragivenlaunchvelocityand
achosenangle,therangeaprojectilewillgocanbedetermined.
Similarly,theheightequation
determinesthemaximumheightofaprojectile,giventhelaunchvelocityandthechosenangle.
OtherThingstoTry
Combiningprojectilemotionwith“thermodynamics:”OK.Thejustificationfordoingthis,otherthanforfun,isastretch.Butit
doesaddabitofextraexcitementtothisexperiment.Todothis,firstofall,findaverysafeplaceawayfromceilings,loose
paper,oranyflammableobject.Nothingflammableshouldbeunderneaththeringincaseofdrips.Wraptheringwithasmall
amountof tissuepaperandsoak it ina littlealcohol.Bycarefully igniting the ring,youcanshoot theprojectile througha
flamingring.Carefulmeans:wearsafetyglasses,usealongwoodenmatch,andmakesurethatneitheryounoranyviewers
comeincontactwiththeflameortheringimmediatelyafteritburnsbecauseitcanremainhotforashortwhile.Thiscanbe
madeevenmoredramaticinaverycornywaybyplayingarecordingofJohnnyCash’s“RingofFire.”Thismustbedoneina
safeplaceandunderthesupervisionofanadult(ifyouarenotyetanadult).Bytheway,thisexperimentdoesworkperfectly
wellwithanonflamingring.
49
Figure9-3T.Dragoiushowsthe“ringoffire”top-of-trajectorytargetforaprojectileshotatanangle.
Anothermuchsimplerbutlessaccuratewaytolaunchaprojectilewithaknownvelocityatapredictableangleistodropa
bouncyballfromaconsistentheightfromanincline.Theballwillcomeoffatvariousangles,dependingontheslopeofthe
board.Asa result of conservationofmechanical energy, if released from thesameheightabove theboard, theballwill
bounceoffatthesamevelocity.Thismaynotgoasfar,butitprovidesalowercostoptiontoproduceareasonablyconstant
velocityatvariousangles.
ThePoint
Therangeandheightofaprojectilecanbedeterminedfromknowingonlythefollowingtwothings:velocityoftheprojectile
andtheanglethatitislaunchedfrom.
50
Project10
Mondaynightfootball.Trackingthetrajectory.
TheIdea
Thisexperimentwilltakeyououtsidetomakethesemeasurements.YoucanalsocollectdatafromMondaynightfootball.
Themeasurementpartisverysimple.Allyouneedtomeasureisthetotaltimeaballorotherprojectileisintheairandthe
total distancealong theground that the projectile travels. If wemeasure only those two thingswe can figure just about
everythingelse:launchangle,velocity,andheight.
Howhighdidthepuntgo?Howhardwastheballhit?Whatanglediditgo?Youkickasoccerball,hitagolfball,andpunt
afootball.Whichhasthegreatervelocity?Withoutresortingtoahigh-techsolution,suchasaradargun,thereisasimple
waytoanswerthatquestionusingonlythelawsofmotion.
Todothis,youeitherworkthecalculationsorusethetablesasaguide—yourchoice.
WhatYouNeed
stopwatch
footballfield
TVtunedtoafootballorbaseballgame
assortedprojectilesandlaunchers:soccerballorfootball;tennisballandracket;golfclubandball
Method
Projectile
1. Launchtheprojectileand,attheexactsametime,startthestopwatch.
2. Recordhowfartheobjectgoesandhowlongitwasintheair.
Calculation
Ifthissectioncontainsmoremaththanyoucaretodo,fastforwarddirectlytothetablesinthenextsection.
Figure10-1showsapuntedfootballfromtheeyesofaphysicist.
1.Findthehorizontalvelocity(inm/s),vx,bydividingtheoveralldistance,R,bythetotaltime(hangtime,t).
vx=R/t
51
Figure10-1Distance,height,velocity,andangleforafootball.
2. Find the vertical velocity (inm/s) bymultiplying one half of the hang time (or the time to reach the peak) by the
gravitationalconstant:
wheregis9.8m/s2.
3.Findthevelocity(inm/s)using:
4.Findtheangleusing:
(Incaseyoudon’tknowwhattan−1isyoucanjustusethekeyonyourcalculatorwiththatidentification.Thefunction,tan−1,alsocalledthearctan,givestheangleifyouhavethetangentofthatangle.Youcangetthetangentbydividingvybyvx.)
Find(orlookup)thevelocity,heightreached,andanglelaunched.
ExpectedResults
SeeTables10-1to10-3.
Table10-1
Howfastitgoes(inm/s)
52
Table10-2
Howhighitgets(inm)
Table10-3
Whatangleitgoesoffat(indegrees).Calculationsarebasedonθ=tan−1(vy/vx)
WhyItWorks
Thisworksforthesamereasonsasthepreviousexperiment.Becausehorizontalandverticalmotionareindependent,the
rangeandtimeintheaircanuniquelybedeterminedbythevelocity,height,andlaunchangle.
OtherThingstoTry
Determinethevelocity,maximumheight,andangleforthefollowingcases:
53
Theresultsareshowninthefollowingtable:
ThePoint
Knowingonlythetimeaprojectileisintheairandthedistancealongthegroundthatittravels,itispossibletodeterminethe
velocity,maximumheight,andangleoftheprojectile.
54
Project11
Monkeyandcoconut.
TheIdea
Amonkeyishangingfromabranchinatree.Themonkeylookshungryandyouwanttothrowacoconuttohim.However,the
monkeyisnervousand,assoonasheseessomethingbeingthrownathim,heletsgoofthebranch.(Themonkeyapparently
knows that in previous versions of this problem, a hunter was trying to shoot it, so themonkey is understandably a bit
nervous.)Knowingthemonkeywillletgoassoonasthecoconutisthrown,whereshouldyouaim?a)Abovethemonkeyb)At
themonkeyc)Belowthemonkey.
WhatYouNeed
“monkey”—(representedbyapiepanorlidofametalcontainer).SeeFigure11-1.
“coconut”—(representedbyaprojectilefromProject8)
DCpowersupply
electromagnet
insulatedwire—about25feet
switch that opens the circuit at the precise moment the projectile is launched. This can be accomplished by
assemblingtwopiecesofmetalfoilinfrontofthelauncher.Attheinstanttheprojectileemerges,itpushesthefoil
apart,openingthecircuit.SeeFigure11-2forasimplewaytosetthisup.Therearealsoopticaltechniquestodo
this,someofwhicharecommerciallyavailable.
55
Figure11-2The“coconut”isshotbyaPASCOlauncherwithanaluminum-foilswitchtapedinfront.
laserpointer
varioustypesofthemonkeyandcoconutapparatusarealsoavailablecommercially
Method
1. Setuptheapparatus,asshowninFigure11-3.
2. ApplytheDCvoltagetotheelectromagnetcircuit.
3. Armthelauncher(bypushingtheballinwiththeplungerinthecaseofthePASCOlauncher).
4. Closetheswitch.
5. Aimthelauncherdirectlyatthetarget,eithervisuallyoraidedbythelaserpointer.
6. Shoottheprojectile.Astheprojectileemergesfromthelauncher,itcausestheswitchtoopenanddeactivatesthe
electromagnet.Thisreleasesthemetallid(monkey)astheprojectileisshotatit.
57
Figure11-3Electricalconnectionsforthemonkey-and-coconutapparatus.
ExpectedResults
Theanswertothequestionposedpreviouslyis:b)firingatthemonkey.Aslongasthemonkeyisinrange,firingdirectlyat
themonkeywillcauseadirecthiteverytime.
WhyItWorks
Boththemonkeyandthecoconutaresubjectedtothesamegravitationalacceleration.Ifthecoconutisaimeddirectlyatthe
monkey in the tree, thecoconutwill fall fromthatstraight linepathand follow thecurved (parabolic)path thatprojectiles
normallytake.SeeFigure11-4.Asaresult,thecoconutfallsawayfromthatstraight-linepathatpreciselythesamerateas
themonkeyfallsdownward.Thiscausesthemonkeyandthecoconuttobeinthesameplacebeforethemonkeyhitsthe
ground.
OtherThingstoTry
Supposeourmonkeygetstiredofhavingcoconutsthrownathim.Whereshouldheaimacoconutofhisownthathethrows
to deflect the one that is thrown at him? This can be set up using two projectile launchers, but it requiresmuchmore
precisionbecausetheballshaveasmalldiameter.Theanswer isthesameasthepreviousone.Themonkeyshouldaim
directlyatthehunter.
58
Figure11-4Youaimdirectlyatthemonkey.Hewillfallasfastasthecoconutandwillcatchitonthewaydown.
ThePoint
This project illustrates one of the underlying concepts of projectiles, which is the idea that the horizontal and vertical
componentsofmotionarecompletelyindependentanddonotinfluenceeachother.Themonkeydoesnothavehorizontal
motion,butthecoconutdoes.Theybothhaveverticalmotion,whichexperiencesthesamerateofacceleration,regardless
ofthehorizontalmotion.
59
Section2
GoingAroundinCircles
Project12
Whatisthedirectionofasatellite’svelocity?
TheIdea
What is thedirectionofanobjectmoving inacircle?Acommonmisconception is that thevelocity,atanygiven time, is
pointedinacircle.Thissimpleexperimentillustratesthatthedirectionofanobjectmovinginacircularpathisinastraight
line,asshowninFigure12-1.
WhatYouNeed
1marble
rollofmaskingtape
Figure12-1Thevelocityofanobjectincircularmotionatanygiventimeisastraightlinetangenttothecircle.
Method
Marbleandtapering
1. Placethemarbleinthecenterofataperoll.
2. Getthemarblespinningrapidlyinacircularpath,asshowninFigure12-2.
3. Quicklyliftthemaskingtaperollandobservethepaththemarbletakeswhenit’snolongerconstrainedbythetape,
asFigure12-3shows.
ExpectedResults
Themarblestravelinastraightpathassoonastheyarereleasedfromtherolloftape.
60
Figure12-2Marblekeptinacircularpathbycentripetalforcefromataperoll.
WhyItWorks
Circularmotionistheresultofacentripetalforcethatchangesthedirectionofmotionfromastraightlinepathtoacircular
path.Thecentripetalforceisprovidedbythestringinthecaseoftheball,bytheinteriorwallofthemaskingtapeinthecase
oftherotatingmarble,andbygravityinthecaseofsatellitesandplanets.Objectstravelinginacircleatanygiventimehave
an instantaneous velocity that heads in a perfectly straight line. This is actually a consequence of Newton’s first law of
motion,whichweexplore later:anobject inmotion tends tostay inmotion inastraight line,unless it’sacteduponbyan
externalforce.
Figure12-3Freemarblemovingalongastraightpath.
OtherThingstoTry
Attachastringtoaballandspintheballinacircle.Cutthestringorletthestringgoandobservethepathoftheballafterit
isreleased.Withoutthecentripetalforceprovidedbythestring,theballmovesinastraightline.
ThePoint
Anobjectmovinginacirclehasavelocitythattakesitinastraightlineatanygivenpointintime.Acentripetalforcethat
continuouslychangesthedirectionisneededtoformthecircularpath.
61
Project13
Centripetalforce.Whatisthestringthatkeepstheplanetsinorbit?
TheIdea
Inthisexperiment,youinvestigatehowobjectsmoveinacircle.Gravitationalforcekeepstheplanetsandsatellitesintheir
orbits.Thesamephysicallawsdeterminehowarubberstopperonastringmovesinacircle.
WhatYouNeed
1.5meteroflight,strongstring
1rubberstopper(1or2holes)
glass,plastic,orsmoothcardboardtube—about5inchesin lengthwithasmalldiameter,but largeenoughforthe
stringtomovethroughfreely
springscale—10N
clamptoattachthespringbalancetothetable
hookedmasses:10,20,50,100g
meterstick
markerpen
safetygoggles—(youwillbeswirlinganobjectinacircle,sosafetygogglesshouldbeworntopreventthepossibility
ofeyeinjury)
Method
SetuptheapparatusasshowninFigure13-1.
1. Tiethestringsecurelytotherubberstopper.
2. Feedthestringthroughtheglassorcardboardtube.
3. Withabout1meterofstringlengthbetweenthetubeandtherubberstopper,cutthestring,soabout25centimeters
ofstringisbelowthetube.
Makingmeasurements
Eachoftheseexperimentsusesthesamebasictechnique.Gettingthehangofitmaytakealittlepractice.
1.Putonyoursafetyglasses.(Thespinningwasherposesapotentialeyehazard.)
2.Youhavetwowaystomeasurethecentripetalforcerequiredtokeepthewashermovinginacircleunderagivenset
ofconditions.
62
Figure13-1Apparatusforexploringcentripetalforce.CourtesyPASCO.
–Oneway is tohangaknownweight from thestring, Figure13-1 shows this approach.The force is theweight (in
newtons)whichisdeterminedbymultiplyingthemass(inkg)bygravitationalacceleration(9.8m/s2).Thistechniqueis
simpleenough,butitrequiresacertaindegreeofskilltokeeptheradiusfixedforagivenmeasurement.
–Theotherapproachistomeasuretheforcedirectlyusingaspringscale,asindicatedinFigure13-2.Inthiscase,you
needtocoordinateyourmovements,sotheforcestaysnearlyconstantforagivenmeasurement.(Note:Holdingthe
stringatanangleslightlyoff verticalcan introduce justenough friction tostabilize the readingwhile introducingan
errorofonlyafewpercent.)
3.Holdingthetubeinonehand,swingtherubberstopperinasmooth,horizontalcircle.
63
Figure13-2Usingaspringscaletomeasurecentripetalacceleration.
4.Measurehowmanysecondsittakestomaketenrotations,andthendividebytentogettheperiodforonerotation.
Becarefultocountthefirstrotationattheend,ratherthanatthebeginning,oftherotation.Itmayhelptocount“zero”
whenyoustart,andthentocount“one”whenthefirstrotationiscompleted.
5.Usingthemarker,placeaseriesofmarksat1centimeterintervals,startingattheloopforthehangingmass.
6.Usingthemeterstick, identifythedistancebetweenthetopofthetubeandtherubberstopperassociatedwiththe
markclosesttothehangingweight.Youcannoweasilymeasuretheradiusbysubtracting1centimeterforeverymark
belowthetubethatyoucancount.(Youcanalsodeterminetheradiusbymeasuringthelengthofstringbelowthetube
andsubtracting from the total lengthof thestring.) Youcanalsouseapieceof tapeorapaperclip tomark the
positionof thestring togivea radius thatyoumeasurebeforespinning.Howeveryoudo it,makesure thatnothing
restrictsthefreemovementofthestringthroughthetube.
Firstinvestigation:Forceversusvelocity(forfixedradiusandfixedrotatingmass)
1. Setthespringbalancetozero.(It’spreferablethatthespringbalancereadsdirectlyinnewtons.Ifitreadsingrams,
multiplyby0.0098toconverttonewtons.)
2. Attachthebottomofthespringbalancetoaclamponthetableandtheotherendtothestringcomingfromthe
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tube.SeethepreviousFigure13-2.
3. Starttherubberstoppergoinginacircle.
4. Measure the radius from thecenterof thecircle to the rubberstopper (inmeters).Thisshould remainnearly the
sameforallthesemeasurements.
5. Measuretheperiodorthenumberofsecondsittakestogotencompleterotations.
6. Calculatethevelocity(inmeterspersecond)byusingv=2πr/T,whereristheradius(inmeters)andTistheperiod(inseconds).
7. Measuretheforceonthespringscalewhilethewasherisspinning.Ifyouareusingamasshangingfromthestring,
theforce(innewtons)isequaltotheweightofthemass(massinkgtimes9.8ormassingtimes0.098).
8. Increaseordecreasethevelocitywhilemaintainingafixedradius.Foreachnewvelocity,measuretheforceonthe
spring scale. Repeat for several velocity and forcemeasurementsat (nearly) the same radius, and then plot the
results.
Radiusforalltrials=____meters
Secondinvestigation:Forceversustherotatingobject’smass(forfixedradiusandfixedperiod)
1. Withthespringbalancesettozeroandattachedtothetableasdonepreviously,starttherubberstopperspinningat
amedium-pacedperiod.
2. Measuretheforceandrecordthemassoftherubberstopper.
3. Tieasecondstopper(todoublethemass)attheendofthestring.
4. Repeatbyaddingathirdandthenafourthrubberstopper.
5. Completethedatatable,plotyour results,anddescribetherelationshipbetweenforceandmassfor fixedradius
andperiodfromyourdata.
Radiusforalltrials=(constant)____meters
Periodforalltrials=(constant)____seconds
Thirdinvestigation:Forceversusorbitalradius(forfixedperiodandfixedrotatingmass)
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Thispartismorecomplicatedthantheprevioustwoinvestigationsandwillrequireagreaterdegreeofskillandpatience.
1. Zerothespringbalanceandclamptothetable,asdonepreviously.
2. Starttherubberstoppergoinginacircle.
3. Measuretheradius,measuretheforceonthespringscale,andthenmeasuretheperiodaspreviouslydescribed.
(Throughout thispartof theexperiment, thevelocityneeds tostayasconstantaspossible,so theonlyvariables
being studied are forceand radius.Measure the period and from that determine the velocity. As the radius gets
larger, it will be necessary to allow the period to decrease to maintain a constant velocity. If the velocity is
reasonablyclosetothefirstreading,recordtheradiusandtheforce,aswellasthespringscale.Otherwise,adjust
therateofturningandtryagainuntilthevelocityisreasonablyclose.)
4. Adjusttheradius(eitherlongerorshorter)whilecontinuingtoturnatthesamerate.Foreachnewradius,measure
theforceonthespringscale.
5. Repeatforseveralradiusandforcemeasurementsat(nearly)thesameperiod.
6. Completethefollowingdatatableandplottheresults.
Periodforalltrials=____seconds
ExpectedResults
Thisprojectleadstothefollowingconclusions:
1.The faster the rotation (or theshorter theperiodof rotation), thegreater thecentripetal forceneeded tomaintain
circularmotion.
Fora12-gramrubberstopper,theexpectedresultsareshowninFigure13-3.Thisshowstherelationshipisnot linear,
butthatitincreasesmorerapidlyasthevelocityincreases.
2.Thegreaterthemass,thegreatertheforceneededtokeeptherubberstoppergoingatagivenspeedataparticular
radius.Thisresultisexpectedtobelinear.
3.Foragivenrotationalspeed,theshorterthestring,thegreatertheforceneeded.
For a 12-gram rubber stopper, the expected results are shown in Figure 13-4, which shows an inverse relationship
betweenforceandstringlength.
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Figure13-3Centripetalforceversusvelocity.
Figure13-4Forceversusstringlength.
WhyItWorks
The“string”thatkeepsanobjectgoingaroundinacircleisprovidedbyacentripetalforce.Inthiscase,itisliterallyastring.
Inthecaseofasatelliteorplanet,the“string”isthegravitationalforce.
Thefastertheobjectgoes(foragivenradius),thegreatertheforce,accordingtotheequation:
whereFc is thecentripetal force,m is themassof the spinning object (thewasher in our case), v is the velocity of the
washer,andristheradiusofthecircle.
OtherThingstoTry
Findingthemathematicalmodel
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GiventhedatashowninFigure13-3,wecandeterminethatforceincreaseswiththesquareoftherubberstopper’svelocity
inoneoftwoways:
1.Useacurve-fittingprogram,suchasExcel.Fromascatterplot,withthedataselected,gototheChartmenu,select
AddTrendline,andthenselectapowerfitoption.SelectAddEquationtotheChartfromtheOptionstab.Thisdisplays
themathematicalmodelforyourdata.Theexpectedresultisforthistobetheformy=x2orclosetoit.
Figure13-5Centripetalforceversusvelocitysquared.
2.EitherusingExcelorplottingbyhandmakesagraphofforceversusvelocitysquared.Iftherelationshipisoftheform
expected,thatgraphshouldbeastraightline.ThisisshowninFigure13-5.
Given the data previously shown in Figure13-4, we can determine that force varies inversely with the radius (string
length)usingthesametechniques.
1.HaveExceldeterminethetrendlinefortheexpecteddata,asshownonthegraphforthepreviousFigure13-4.
2.Plottingforceversusthereciprocalofradius(1/r)resultsinastraightline,asshowninFigure13-6.
Figure13-6Centripetalforceversusreciprocalofradius.
Sourcesoferror
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Thisprojectworksreasonablywellandenablesyoutofindthemodelforcentripetalforceusingverysimpleequipment.The
followingarepotentialsourcesoferrorsthatmayimpactyourresults:
1. Frictionbetweenthestingandthetubeoverstatestherequiredforce.
2. Airresistanceresultsinaslightlyslowervalueofvelocity.
3. Atslowerspeeds,thecirclemaynotbeperfectlyhorizontalandmayhaveacomplicatingeffectfromgravity.
Determiningtheaccuracyofthemodelyoufound
Foranyofthepointsyoumeasured,comparetheforceyoumeasured(byeitherthespringscaleorthehangingmass)with
theexpectedvalueforthecentripetalforcegivenby:
ThePoint
Centripetalforcekeepsanobjectrotatinginacircle.Thecentripetalforceequalsthemassoftheobjecttimesthevelocity
squareddividedbytheradius.
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Project14
Agravitywell.Followingacurvedpathinspace.
TheIdea
Inthisproject,youbuildasimplemodelofaplanetgoingaroundthesun.Thismodelexhibitsmanyofthephysicalproperties
foundthroughoutthesolarsystem.YoucandiscoverforyourselfthebasicprinciplesofplanetarymotionasdidCopernicus
andKepler,exceptyouwon’thavetospendyearssquintingthroughatelescopeoncoldwinternights inthemiddleofthe
nighttodothis.Thismodelalsoprovidesan intuitivewaytovisualizeEinstein’stheorythatgravity istheresultofamass
curvingspace.
WhatYouNeed
bucketorothercircularframe
sheetofLatex,largeenoughtocovertheopeningofthebucket
mass(roughly50g)—a1-inchdiametersphericalsteelballwouldbeidealbecauseitcanpositionitselfinthecenter
ofthesheet
marbles,smallsteelballs
Method
1. StretchtheLatexonthebucket.Removethewrinkles.
2. Rollthemarbleacrossthesheetandobservethepathittakes.
3. Now,placethemassinthecenterofthesheet.Thisshouldcausethesheettobecomenoticeablydistorted.Ifthis
isnot thecase, itmaybenecessary to increasethemass,butavoid tearing thesheet.Thecentralmassshould
maintainafixedposition,whichcanbefacilitated,ifnecessary,byalittletape.
4. Rollamarbleinacircularpatharoundthecentralmass.
5. Observethemotionofthemarble.SeeFigure14-1.
6. Observewhathappensifthemarbleisrolledfasterorslowerinagivenpath.Whathappensifthemarbleiscloser
orfartherfromthecentralmass?
ExpectedResults
Thekeyobservationisthatthepathfollowedbythemarbleisanellipse.Thepathmayappearcircular,butellipticalpaths
arecertainlypossible.ThisiscomparabletooneofKepler’sobservationsconcerningplanetarymotion.
Kepleralsoobservedthatthecloseraplanetgetstothesun,thefasteritgoes.Themarblesinthisexperimentexhibitthe
sameproperty.
Ifthemarbleisgivenavelocitythatistoohigh,itwillnotfollowthetypeofellipticalorbitfollowedbytheplanetsaround
thesunbut,rather,theopenhyperbolicorbitfollowedbymeteors.
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Figure14-1
WhyItWorks
Kepler’s law can be derived by equating the centripetal force that keeps a planet in orbit to the gravitational attraction
betweentheplanetandthesun.Thedepressioncreatedbythecentralmassexertsaforceonthecirculatingmarblethat
varieswith position. Although this force does not exactly decreasewith the inverse square of the distance, as does the
gravitationalattractionbetweenaplanetandthesun,itdoesprovideagoodapproximation.
OtherThingstoTry
ThisexperimentalsoprovidesananalogyforunderstandinganaspectofEinstein’stheoryofgeneralrelativity.Theideais
thatwhatwecallgravityisreallyadistortioninspacecausedbythepresenceofamass.Thedistortionofthesheetcanbe
thoughttorepresentthedistortioninspace,whichguidesthepathofaplanetgoingaroundthesun.Asfar-fetchedasthis
mayseematfirst, lightfromstarsemergingfrombehindthesunhasbeenobservedbyastronomerstofollowabentpath
causedbythesun’smass,confirmingEinstein’sprediction.
ThePoint
Objectsinmotionaroundacentralmassfollowanellipticalpath.Theclosertheygettothecentralmass,thefastertheygo.
Gravitationalattractioncanbethoughtofasadistortionofspacecausedbythepresenceofthemass.
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Project15
Howfastcanyougoaroundacurve?Centripetalforceandfriction.
TheIdea
Whatdetermineshowfastacarcansafelygoaroundacurveandnotskidontheroad?Thisprojectexploresturningand
friction,andhowthetwoarerelated.
WhatYouNeed
board (approximately) 36 inches by 4 inches by¾ inch (Other shapes, including a circularly shaped board or a
turntable,canalsobeused.)
verticalpole,suchasaringstand,toserveasapivotpoint
afewcloselymatchedtoycars,suchasMatchboxcars
Figure15-1Positionofcarsbeforerotation.
Method
1. Drillaholeinthecenteroftheboard.Theholeshouldbelargeenoughtoallowtheboardtofreelyrotateonthe
post.
2. Placeeachofthecarsalongalinerunningfromthecentertotheouteredgeoftheboardatapproximately6-inch
intervals,asshowninFigure15-1.(Youcanalsodothiswithpenniesorotherobjectsinsteadofcars.)
3. Predictwhatyouthinkwillhappentothecarsasyoustarttorotatetheboardaroundthepivotpoint.
4. Rotatetheboard,veryslowlyasfirst,butthenpickupspeed.Whathappenstothecars?
ExpectedResults
Carsfurthestfromthecenterbegintomovefirst.Asthecarsstarttomove,theymoveawayfromthecenter,asshownin
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Figure15-2.
WhyItWorks
Thecarsremainontheboardaslongasthefrictionalforceisgreaterthanthecentripetalforceneededtokeepthecars
movinginacircularpath.Thefurtheryouarefromthecenterofrotation,morecentripetalforceisneeded.Forthisreason,
thecarsfurthestfromthecenterarethefirsttomove.
Figure15-2Carsfurtherawayfromthecenterofrotationrequiremorefrictiontoremainstationary.
OtherThingstoTry
Thiscanalsobedoneusingpenniesonarotatingsurface,suchasaturntable.
ThePoint
Frictioncanprovidethecentripetalforceneededtokeepanobjectmovingalongacircularpath.Iftheforceoffrictionisnot
sufficienttoprovidethecentripetalforceforagivenradius,theobjectwilldepartfromitscircularpath.
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Project16
Ping-pongballsracinginabeaker.Centripetalforce.
TheIdea
Inthisproject,yougetapairofping-pongballscirculatingrapidlyinabeakerwithablowdryer.Theballscontinueracingina
frantic high-speed circular path long after the blow dryer is removed. This is a fun, attention-getting demonstration that
exploresvariousaspectsofcircularmotion,includingangularvelocity,centripetalforce,andtheeffectoffriction.
WhatYouNeed
250mLglassbeakerorplasticcontainerroughly5inches(12cm)indiameter
2ping-pongballs
blowdryer
Method
1.Placetheping-pongballsinthebeaker.
2.Withonehand,holdthebottomofthebeaker.Theotherhandholdstheblowdryer.(Noheatisneeded.)
Figure16-1PhotobyS.Grabowski.
3.Directtheairfromtheblowdryertorapidlycirculatetheairflowinacircularhorizontalpatterninsidethebeaker.
Figure16-2PhotobyS.Grabowski.
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4.Theblowdryershouldgettheping-pongballstorapidlyspininsidetheglasscontainer.
Figure16-3PhotobyS.Grabowski.
5.Assoonastheping-pongballsarespinningrapidly,quicklyturnthebeakerupsidedownand(carefully)placeitonthe
table.
Figure16-4PhotobyS.Grabowski.
ExpectedResults
Theping-pongballscontinuetorevolvearoundtheinnerwallsofthecontainer.Whilespinning,theyappeartodefygravity.
Theyalsotendtomoveasfarawayfromeachotherastheycan,especiallyastheyslowdown.
WhyItWorks
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Therapidlymovingairgivestheping-pongballskineticenergy.Theinnerwallsofthebeakerprovidecentripetalforcethat
keepstheballsmoving inacircularpath.Theforcebetweentherotatingballsandthesidewallofthebeakerresults ina
frictional force that is large enough to hold the balls suspended above the table as they rotate. The balls have enough
angularmomentumtokeepgoinguntilfrictionalforcesbetweentheballandthewallsofthecontainercausethemtoslow
down,resultingintheballscontinuingtorotatemoreslowlyanddroptothesurfaceofthetable.
Figure16-5PhotobyS.Grabowski.
The rapid rotationcauses frictionbetween theballsand thesideof thebeaker.Thiscancause thepingpong-balls to
becomecharged,resultingin(minor)attractiontothewallsofthecontainerandrepulsionfromeachother.
OtherThingstoTry
Asimilareffectcanbeachievedbyvigorouslyrotatingapairofmarblesinaninvertedglassorbeaker.
ThePoint
The ping-pong balls are given kinetic energy by the blow dryer. Likeall rotating objects, their inertia tends to keep them
moving inastraight line.The insidewallsofthebeakerapplycentripetalforce,whichcausesthepathtobecircular.The
ballscontinuetomoveuntilthekineticenergyisconvertedintofriction.
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Project17
Swingingapailofwateroveryourhead.
TheIdea
Ifyoufillabucketwithwaterandturnitupsidedown,thewaterwill(ofcourse)spillout.But,ifyouspinthebucketoveryour
headfastenough,youmayavoidgettingwet.Howfastdoyouhavetoswingapailfilledwithwateroveryourheadsoasto
notgetwet?Inthisproject,youexplorewhatittakesnottogetsoakedor,inotherwords,howfastisfastenough?
WhatYouNeed
smallbucketwithahandleorstringattached
water
stopwatch
meterstick
personwillingtogetwet
anotherpersonwillingtogetthefirstpersonwet
optional:papertowelsoramoptowipeupspills
optional:raincoatorumbrella
Method
1. Putsomewaterinthebucket.
2. Predicthowfastyouthinkyouneedtospinthebuckettoavoidspillingitscontents.Thiscanbedonequalitativelyby
spinning at a relatively fast rotation and pushing your luck by going progressively slower.One simple refinement
would be to do this in terms of time (in seconds). Amore quantitative prediction can be based on the linear or
angularvelocity,anditcanbemeasuredbasedontheperson’sarmlength.)
3. Spinthebucket,asshowninFigure17-1,andevaluateintermsofthepredictions.
ExpectedResults
Theslower yougo, thegreater the riskof soaking thespinner foragiven radius. If yourarm is shorter, youwill have to
completethecircleinlesstime.
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Figure17-1Spinningabucketfilledwithwateroveryourhead.
The maximum time to go around a vertical circle of a given radius without spilling is shown in the table below. The
maximumtimetospinthebucketoverheadisabouthalfthattime.Keepinmindthesetimesarebasedonuniformvelocity.
Themostcriticalpointofcourseisatthetopofthecircle.(Ifyouslowdownthere,youmayneedthatraincoatidentifiedin
thewhat-you-needlist.)
WhyItWorks
Thepersonspinningthebucketwillbesparedasoakingaslongasthebucketmovesfastenoughsothecentripetalforceis
greaterthantheforceofgravity.
Theconditionforthisis:
Note,thisresultindicatesitdoesn’tmatterhowmuchwaterisinthebucketaslongasthespinnermovesatasufficient
speed.Thelargertheradius,thefasteryouhavetogo.Toomuchwater,however,maycausethespinnertoslowdown.
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OtherThingstoTry
Thiscanalsobedoneusingconfettiinsteadofwater.
Physicsalert:thereisreallynosuchthingasacentrifugalforce.Thewaterisgivenavelocityandisforcedintoacircular
pathby thecentripetal forceexertedby thebottomof thebucketon thewater. If thebucket ismoving fastenough, the
centripetalforceofthebucketisneededtokeepitgoinginacircle.Ifthebucketisnotgoingfastenough,gravitywouldbe
greatenoughtocausethewatertospillout.
ThePoint
Thecentripetalforceonthewaterisprovidedbythebottomofthebucket.Thehandleofthebucketprovidesacentripetal
forceonthebucketitself.Thewaterwillnotfalliftherateofrotationishighenoughthatthecentripetalforceisatleastas
greatasgravity.
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Section3
Gravity
Project18
Featherandcoin.
TheIdea
Doesanobjectwithagreatermassfallfasterthananobjectwithalowermass?
This isa fundamental issue thatwasaddressedbyGalileo,aswellasApolloastronautson themoon.Afterdoing this
experiment,youcanweighinonthisquestion.
WhatYouNeed
feather
coin
clearcylindricalplastictube
capstofittheendofthetube—oneclosedandonewithavacuumfitting
vacuumpump
Method
1. Putthecoinandthefeatherinthetube.
2. Inserttheendcapsineachoftheendsofthetube.
3. Withbothobjectsonthebottomendcap,invertthetubeandletthefeatherandthecoinfallinthetube.Makesure
bothareabletofallfreelywithoutinterference.
4. Attachthevacuumpumptothetubeandevacuatetheairfrominsidethetube,asshowninFigure18-1.
5. Invertthetubeandobservetheresultsagain.
Figure18-1Clearplastictubeattachedtovacuumpump.
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ExpectedResults
Withairinthetube,thecoinwillfallfaster,asshowninFigure18-2.
Figure18-2Withairpresentinthetube,thecoinfallfaster.
Withairremovedfromthetube,bothobjectsfallatthesamerate,asshowninFigure18-3.
(Twothingscouldresultinanunintendedoutcome,whichshouldbeavoidedifpossible:Withairinthetube,thecoinmight
pushthefeathertowardthebottomatafasterratethanitwouldfallonitsown.Also,someelectrostaticdragmightdevelop
betweenthefeatherandtheplastic,whichslowsthedescentofthefeatherinavacuum.)
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Figure18-3Withairremovedfromthetube,bothobjectsfallatthesamespeed.
WhyItWorks
ThereisnodoubtthatthegravityoftheEarthexertsagreaterforceonamoremassiveobject.However,themoremassive
objectrequirespreciselythatsameamountof largerforcetocauseittoaccelerate.Theupshot isthatallobjectsonthe
surfaceoftheEarthaccelerateatthesameconstantrate.
OtherThingstoTry
Thisexperimenthasanumberofvariations,including:
Comparethedescentofacrumpledsheetofpaperwithanunfoldedsheetofpaper(bothofthesamemass).
Comparethedescentofasinglepencilwithseveralpencilsbundledtogether.
Tieaweight(suchasalargestainlesssteelnut)toastringatthefollowingintervals:125cm,80cm,45cm,20cm,
5cm.Holdthestringvertically.Whendropped,eachweighthitsthefloorinthesametimeinterval.Thisisbecause
thedistanceeachweightfallsisproportionaltothesquareofthetimethatitisfalling.Theseintervalsarebuiltinto
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thespacingoftheweights,sotheyshouldhitatthesametimeinterval.
Whichfallsfaster(inair):abookoradollarbill?Certainly,ifthey’redroppedsidebyside,thebookwillfallfastest.
However, if the dollar bill is placed on top of the book or below the book, the effect of air resistance will be
eliminatedandtheywillfalltogether.
ThePoint
Gravitationalacceleration(inavacuum)isaconstant.Specifically,itdoesnotdependonthemassofthefallingobject.
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Project19
Howfastdothingsfall?
TheIdea
Objectsexposedtotheforceofgravityaccelerateatthesamerate.Weprovedthat inthepreviousexperiment.Here,we
measuretherateofgravitationalaccelerationforallobjectsontheearth.
Youmeasureaccelerationtwodifferentwaysinthisexperiment.Inthefirstmethod,youuseastopwatch.Wecallthisa
ballparkexperiment,whichmeansweexpectittogivearoughapproximationratherthanaveryaccurateresult.
Thesecondmethodinvolvestheuseofamotionsensor,whichoffersagreaterdegreeofprecision.
WhatYouNeed
Stopwatchmethod
variousobjects:baseballs,golfballs,bowlingballs,yourphysicstextbook
stopwatch
tapemeasure
Motionsensormethod
motionsensorwithDataStudiosoftware
ringstandorothersupporttoorientthemotionsensorvertically,lookingdownward
basketball,softball
Method
Stopwatchmethod
1. Usethetapemeasuretoidentifythedistancetheobjectwillbedropped.
2. Onepersondropstheobjectandtheotherpersontimesthetripdown.
3. Start the timer just as the object is released and stop it at the precise time it hits the ground. Try to avoid
anticipating the release that will give too large a time measurement and an understated value for gravitational
acceleration.
4. Calculatethegravitationalaccelerationusingtheequationg=2d/t2,wheredisthedistanceinmetersandtisthe
time inseconds.Gravitationalacceleration ismeasured inm/s2,which is readasmetersper secondsquaredor
meterspersecondpersecond.
Motionsensormethod
1.Setupamotiondetectormountedonatablewithanunobstructedviewofthefloor,asshowninFigure19-1.
2. Set up themotion detector to read distance versus time and velocity versus time. This can be accomplished by
selectingthe“velocity”filethatcomeswiththeDataStudiosoftwarepackage.
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Figure19-1Motionsensoralignedtomeasureverticalmotion.CourtesyPASCO.
3. This measurement works best by increasing the frequency of the motion sensor measurement by increasing the
samplingfrom10persecondto50persecond.
4.Alignthemotionsensorintheverticaldirection.
5.Hold theball justunder themotionsensor,asshown inFigure19-2.Start the readingsand release theball.Try to
avoidimpartinganyverticalmomentumtotheballbylettingitdropwithoutaninitialpushordelayedrelease.
6.Capturethemotionoftheballthroughseveralbounces.
7.Measure the slope of the velocity versus time graph. Use either the initial descent or the first bounce. The initial
descenthastheadvantageofhavingthelargeststatisticalsample.Thefirstbouncehastheadvantageofbeingfree
oferrorsassociatedwiththerelease.
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Figure19-2CourtesyPASCO.
ExpectedResults
Foreithermethod,theacceptedvalueforgravitationalaccelerationisabout9.81m/s2.Thismayvaryslightlywithlocation
andelevation.
Stopwatchmethod
Foratypicaloutdoorhigh-schoolathleticbleacherabout15feetabovetheground(about4.6meters),anobjectwill take
about1secondtofall.Welearninthenextprojectthataperson’sreactiontimecaneasilybeasmuchas¼second.Asa
result,anygivenmeasurementmayhaveanerrorofasmuchasabout25percent.(Thiscanbeevengreaterbecausethere
canbenon-offsettingerrorsforthestartandstoptimeofthemeasurement.)Thisisnotveryprecise,butitputsusinthe
ballpark.Itishardtoimproveonthisbecauseofthelimitationinmeasuringtimeinherentintheuseofastopwatch.Some
peoplefindthatlisteningfortheballtohitthegroundiseasiertotimethantryingtoobserveitvisually.Agreaterdistanceto
fallalsoreduceserrorsbecausethereactiontimeisasmallerpercentageoftheoveralltimemeasured.
The following chart summarizes expected times for various distances. Timesmeasured in this range gives reasonable
valuesforgravitationalacceleration,g.
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Another resultexpected is that,within theaccuracyof thisexperiment,allobjects fallat thesamerateofacceleration,
regardlessoftheirmass.
Noticehowsensitivetheresultsareonthetimemeasurement.Forinstance,supposeyoudropabowlingballfroma4.6
meterheightandmeasure1.1secondsinsteadof1.0seconds.That0.1seconderrorwouldresultinacalculatedvaluefor
gravitationalaccelerationof7.6m/s2insteadoftheexpectedvalueof9.8m/s2ora22percenterror.A0.1seconderroris
lessthanthereactiontimeofmostpeoplesoitisagoodthingthatwehaveanotherwaytomakethismeasurement.
Motionsensormethod
Withamotionsensor,therangeofmeasurementsismuchtighter.ThepositionversustimegraphisshowninFigure19-3.
Notice thisshowsacurved line typicalofacceleration.As theball falls, theposition increases,s theportionof thecurve
sloping up to the right represents the falling motion. After the ball bounces off the floor, the distance increases, which
generatesthecurvedlinethatslopesdowntotheright.Thisgraphshowsaninitialreleaseandthentwobounces.Thedata
collectionstopsjustbeforeathirdbounce.
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Figure19-3Positionversustimeforafallingballshowingtwofullbounces.CourtesyPASCO.
A velocity versus timegraphgeneratedbyamotion sensor is shown inFigure19-4.Gravitational acceleration is given
directlybytheslopeof the line.Thiscanbedeterminedbydividingtherise(change invelocity)by therun (corresponding
changeintime).TheslopecanalsobefoundbyusingtheslopetoollocatedintheDataStudiopull-downmenu.Thisgraph
showsthesamedropfollowedby twobounces,asyousaw inFigure19-3.Noticethefirstbounceoccurs justbefore1.2
seconds.Theballreachesitsfirstpeakat1.5secondsandbeginstofallagain.InFigure19-4,thevelocityrapidlychanges
frompositive(abovetheline)tonegative(belowtheline).
Alsonoticeoneinterestingaspectofthephysicsoffree-fall,illustratedbyFigure19-4.Aftereachbounce,theslopeisthe
samebelowthezero line(bouncingup),atthezero line(atthehighestpoint)andabovethezero line(fallingbackdown).
Whatthismeansisgravitationalaccelerationisconstantandaffectsanobjectinfree-fall,regardlessofwhetheritismoving
upordown.
Figure19-4Velocity versus time for a falling ball. The slope of each line gives the acceleration of the ball in free fall.
CourtesyPASCO.
WhyItWorks
Part1isadirectmeasurementandapplicationofthebasicmotionformula:
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a=2d/t2
wherewefindtheaccelerationduetotheforceofgravity.
Part2measuresthesamething,butitusesamuchmoreprecisemeasurementofthedistancetraveledinagiventime.
WeknowfromProjects1and2thattheslopeofthedistanceversusthetimegraphgivesameasureofvelocity.Similarly,
theslopeofthevelocityversusthetimegraphgivesacceleration.Eachbounceprovidesareplicationofthisexperimentthat
canprovideaseparatedatapoint.
OtherThingstoTry
Amotionsensorrevealsthebrief timethataballencountersthegroundas itcompresses,decompresses,andeventually
reversesdirection.Someballsdothismorequicklythanothers.Thiscanbeseenintime-lapsephotographybutcanalsobe
noticeableinthedistanceversustimegraphsgeneratedbymotionsensor.
ThereisanothermethodformeasuringtheEarth’sgravitationalaccelerationusingapendulum.SeeProject22.Compare
thiswiththeresultsyougetwiththemotionsensor.
ThePoint
ThisexperimentgivestwowaystomeasuretheaccelerationonanyobjectcausedbythegravitationalforceoftheEarth.
Thefirstwayisadirectmeasurementlimitedbythereactiontimetorecordhowlongittakesanobjecttofall.Thesecond
methodusesamotionsensorthatcapturesthisdatawithgreaterresolutionandprecision,andwheninterpretedgraphically
givesamoreaccuratevalueforgravitationalacceleration.Ineithercase,thecorrectvalueis9.8m/s2or32ft/s2.
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Project20
Thebuckstopshere(thefallingdollar).Usingametersticktomeasuretime.
TheIdea
Thisexperimentexplores thenatureof free-fall: the longeranobject falls, thegreater thedistance it falls.Measuring the
distanceanobjectfallscangiveanindicationofthetime.Thiscanbeusedtoestimateaperson’sreactiontime.Youuse
bothadollarbillandametersticktoprovethispoint.
WhatYouNeed
meterstick
Method
1. Thisrequirestwopeople.Thefirstpersonholdsameterstickupsidedown,sotheendthatreads0cmisdirected
downward.
2. Thesecondpersonholds their fingersat thebottomof themeterstick ready tograb themeterstick,asshown in
Figure20-1.
3. Themeterstickisdropped,andthencaughtasshowninFigure20-2.
4. Thedistance themeterstick falls is an indication of the person’s reaction time. Under gravitational acceleration,
distanceisrelatedtotimeaccordingtotheequationd=½gt2whereg isthegravitationalaccelerationconstant,
9.8m/s2,andtimeismeasuredinseconds.Thisequationgivesthedistanceinmeters.Thisrelationshipistabulated
inTable20-1:
Figure20-1Readytocatchthemeterstick.
90
Figure20-2Thepositionwherethemeterstickiscaughtisanindicationofthetimeitwasfalling.
Table20-1
ExpectedResults
The reaction time can be determined by the distance that themeterstick falls before being caught. Themeterstick will
typicallyfallabout10–20centimetersbeforebeingcaught,butthiswillvarywiththeindividual.
WhyItWorks
91
Thedistanceanobjectfallsincreaseswiththesquareofthetimeitfalls.Similarly,thetimeittakestofallisproportionalto
thesquarerootofthedistance.
OtherThingstoTry
Adollarbillisabout15.2cm(6inches)inlength.Accordingtothepreviouschart,itwilltakeadollarbillnearly0.18seconds
tofall.Challengesomeonetocatchthedollar.Unlessthepersonanticipatesthatrelease,thebillwillfall(almosteverytime).
Figure20-3Moneyoftenseemstofall throughourhands. Itfallsthroughitsownlength inatimelessthanmostpeople’s
reactiontime.
Typical human reaction time is about ¼ second. Most of the time, people are unable to catch the bill. Occasionally,
someonecangetluckyandanticipatethefallingdollar.Ifyouareofferingtoletthepersonkeepthebilliftheycatchit,you
maywanttoconsiderasmallerdenomination.
ThePoint
Thedistanceanobjecttakestofallisrelatedtothetimeittakestofallthatdistance.Knowingthetimeletsyoupredictthe
distance.Similarly,knowingthedistanceletsyoupredictthetime.
92
Project21
Weightlesswater.Losingweightinanelevator.
TheIdea
Whenthingsfall,theynolongerseemtohaveweight.Objects,includingpeople,floatintheSpaceShuttleasiftherewereno
gravity.Theshuttleorbitisnotthathighabovetheearth’ssurfaceforthegravitationalattractiontotheEarthtodisappear
and,iftheshuttlewerenotmovingsorapidlyinorbit,itwouldbepulledstraightdowntotheearth.So,wheredoestheforce
of gravity go to make the shuttle astronauts seem weightless? It has to do with the forces on falling objects. In this
experiment,youinvestigatewhathappenstotheweightoffallingobjectsusingafallingcupofwaterandbyholdingaweight
onascaleinanelevator.
WhatYouNeed
cupwithafewholesinit
water
springscale
mass
optional:anelevator
Method
Cup
1. Fillthecupwithwater.Observewhathappens.
2. Dropthecup(overasinkorbucket).Observewhathappens.
Elevator
1. Hangthemassonthespringscale.
2. Withthemassheldstationary,notetheweightoftheobject.
3. Whileholdingthescale,letthescaleandmassdroptowardthefloor.Stopbothjustbeforetheyhitthefloor.
4. Youdon’thavemuchtimetodothis,butobservethescalereadingasitfirststartstofallandthereadingasitis
slowedpriortohittingthefloor.
5. Again,whileholdingthescale,raisethescaleandmassfromthefloor.Bringittoastopwhileyou’restillholdingit.
6. Ifyoucangettoarealelevator,observethescalereadingwiththemasssuspendedastheelevatorgoesupandas
the elevator goes down. Even in a real elevator, you will find the period of acceleration for you tomake these
observationsisshortbecauseelevatorsreachasteadyvelocityfairlyquickly.
ExpectedResults
Thewaterdripsoutfromtheholeswhenthecupisfilledwithwaterandheldstationary.Thewaterstopsdrippingwhenthe
cupisinfree-fall.
93
Thescalereadsagreaterweightwhenyouliftthemass.Withyourarmfullyextendedasthescaleandmassslows,the
scalereadsalowerreadingthanwhilestationary.
Thescalereadsalowerweightwhenyoudropthemass.Asyouslowthescaleandmassasitnearsthefloor,thescale
readsahigherreadingthanwhilestationary.
Withtheelevator,thescalereadsahigherweightwhenitfirststartstogoupandalowerweightastheelevatorslowsto
thenextstop.Goingdown,thescalereadsloweratfirst,andthenhigheratthenextstop.
If the starting-up and slowing-down phase is uniformly spread over about 1 second, the change in apparent weight
measuredbythescaleshouldchange(verybriefly)bynotquite50percent.Thesechangesare illustrated inthefollowing
Figures21-1,21-2,and21-3.
Figure21-1Objectatrest.
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Figure21-2Upwardacceleration.
Figure21-3Downwardacceleration.
WhyItWorks
With thecupheld, thewater isdrawnthroughtheopeningsbygravity.However,whenthecup is in free-fall, it fallsat the
samerateas thewater.While falling, thewater is (apparently) “weightless,”similar toastronauts in theshuttle. If thecup
wasn’t falling, thebottomof thecupwould resist thatpull, leaving thewaternoother resort than to falloutof theholes.
However, with the cup falling, the water does not experience a force from the cup opposing its downward movement.
Becausethecupwasfalling,thewaterinthecupseemedweightless.
Wehaveallseenimagesofastronautsfloatingintheshuttleandspacestation,asiftheywere“weightless.”Asatubeof
scrambledeggsfloatsbyanastronaut, itcertainlyappearsthatway.However,weight is theforcecausedbygravityona
massand,althoughthatattractiondropsoffastheinversesquarerootofthedistance,itneverbecomeszero.Infact,atthe
shuttleorbitof200km,theforceoftheEarth’sgravitationalattractionisonlyabout6percentlowerthanwhatitisonthe
surfaceoftheearth.
Objects inorbitareessentially fallingataspeedconsistentwithmaintaining theorbit.Theapparentweightlessnessof
objectsinspaceistheresultoftheobjectsintheshuttlefallingtoEarthatthesamespeedastheshuttleitself isfalling.
Becausethewaterisfallingatthesamespeedasourcup,it,too,appearsweightless.Whenweholdthecup,webalance
theforceofgravityonthecuponly,butnotonthewater.Inthatcase,thewaterhasweightthatspillsoutoftheholesinthe
95
cup.
The weight measured on the scale is a combination of the actual weight decreased or increased by the effect of
accelerating theweight. It does notmatter how fast theweight ismoving.Once a high-speed elevator gets going at its
cruisingvelocity,themeasuredweightshouldexactlyequalthestationaryweight.Itisonlytheaccelerationexperienceduring
thestoppingandstartingthataffecttheforceontheobjectduringthattime.
OtherThingstoTry
Avisualaccelerometercanbeusedtoindicatethedirectionandrelativemagnitudeoftheaccelerationsthataccompanythe
weightchangesencounteredhere.
Figure21-4CourtesyPASCO.
Usingamotionsensortomeasureanobjectmovingupandthendownaninclineprovidesacloserlookattheacceleration
ofanobjectsubjectedtogravity.Figure21-4showstheaccelerationversustimedisplayedinDataStudio.Thisshowsthat
accelerationisdownward(slightlymorethan−2m/s2)forboththeuphillanddownhillsegmentsofthegraph.
ThePoint
Thesensationofweight iscausedbyaforce(suchastheground)holdingyouup.Thisupward(ornormal)force,whether
exerted from below (as in the cup) or above (as with the scale and weight), is howwe experienceweight. If the object
supportingusisalsofalling,wearenolongerexposedtotheforceweexperienceasweight.
96
Project22
Whatplanetareweon?Usingaswingingobjecttodeterminethegravitational
acceleration.
TheIdea
ThisprojectexploresanindirectwayofmeasuringthegravitationalaccelerationoftheEarth(oranyotherplanetyoumaydo
thisexperimenton).Becausegravitationalaccelerationaffectshowfastapendulumswings,wecantakeadvantageofthat
tofindthegravitationalaccelerationprovidedbymeasuringtwothings:howlongthependulumisandhowmuchtimeittakes
toswingbackand forth. (If youare less thaneighteenyearsold,pleasebesure toget yourparents’permission forany
interplanetarytravelforthisproject.)
WhatYouNeed
pendulumconsistingofamasssupportedbyastringattachedtoasupport
pendulumwithalongstringandalargemasssuchasabowlingballsupported(safelyandsecurely!)fromtheceiling
stopwatch
Method
1. Measuretheperiodofapendulumbymeasuringhowlongittakesforthependulummasstoswingbackandforth
onetime.Sincethismaybelessthanasecond,moreaccuratemeasurementscanbemadebycountingthetimefor
10back-and-forthexcursion,andthendividingby10.Rememberthatincountingthecycles,thefirstcycleiscounted
whenthemassreturnstothepointfromwhichitwasreleasedandnotatthepointwhenitisfirstreleased.
2. Measurethelengthofthependulum.Thisisthedistanceinmetersfromthecenterofthehangingmasstothepoint
ofattachment.
3. Try to minimize vibration of the ring stand or other support structure. Also keep the pendulum moving in two
dimensions.Somepeopleliketouseadoublestring—oneoneithersideofthemass—tokeepthependulumfrom
wobbling.
4. Calculatethegravitationalacceleration,g(inmeterspersecondpersecond),usingtheequation:
whereLisstringlengthinmetersandTistimeinseconds.(ThiswillalsoworkifyoumeasureLinfeetbutyouwillget
ananswerinfeetpersecondpersecond.)Trythismultipletimesandtaketheaveragetogetthemostaccurateresult.
SeeFigure22-1.
ExpectedResults
Gravitationalaccelerationshouldbeclose to theacceptedvalueof9.81m/s2.Resultswithin2percentof this valueare
easilyachievable. Ifyouareworkingwithfeet,gravitationalacceleration is32feet/s2.Longerpendulumlengthsencounter
lessfrictionallossandareeasiertogetanaccurateperiodmeasurement.Remember,100centimetersisequalto1meter
whendeterminingthelengthofthependulum.
97
Figure22-1Usingapendulumtofindg.
Thefollowingsetofvaluesresultsinthe9.81m/s2targetvalueforgravitationalacceleration:
WhyItWorks
98
Itstands to reason that thegreater thepullofgravity, thefaster thependulummotionand theshorter theperiod.This is
givenbytheequationfortheperiodofapendulum:
whereL is the length (in meters) and the period is one cycle back and forth (in seconds). Solving this for gravitational
accelerationgivesus:
Thedefinitionoftheperiodofapendulumisthenumberofsecondsforittoswingbackandforthonetime.
OtherThingstoTry
Youhavebeencapturedbyalienabductorsandtakentoanunknownplanet(wheretherearenovideogamesandnocable
TV).Youareabletoremoveyourshoe,whichhasa15cm(0.15m)shoelace.Youfindthatwhenyouletyourshoeswing
freelyinashortarc,itreturnstothepointfromwhichitwasreleasedin1.26seconds.Towhichplanetshouldyoudirectthe
interplanetaryrescueteam?Thegravitationalaccelerationonthevariousplanetsis:Venus8.93m/s2,Earth9.81m/s2,Mars
3.73m/s2, Jupiter924.9m/s2,andSaturn10.6m/s2. Try it. (Hint: theanswer is this planet is oneofEarth’s neighbors in
spacepossessingaverythinatmosphere,icecaps,andareddishclay-likesurface.)
ThePoint
For a given string length, the period of the pendulum depends on the gravitational acceleration. This provides a fairly
accuratemethodformeasuringthelocalgravitationalacceleration.
99
Section4
ForceandNewton’sLaw
Project23
Newton’sfirstlaw.WhattodoifyouspillgravyonthetableclothatThanksgivingdinner.
TheIdea
Anobjectatrest(includinganobjectatrestontopofatablecloth)tendstostayatrestunlessactedonbyanexternalforce.
Onewaytoprovethisistopullaclothoutfromundertheobject.Thiscanbedonemoresimplyatfirstormoreelaborately
asyoubuildyourconfidenceinthelawofphysics.
WhatYouNeed
tablecloth (one with low friction is best—tweedy fabrics, gravy spots, and spilled soda can increase friction and
compromisetheintendedresults)
table
objectstoplaceonthetableclothsuchasbowls,bottles,litcandles,andyourphysicstextbook
spareroastturkey,stuffing,andcranberrysauce,ifyouactuallyattempttodothisatyourThanksgivingdinner
Method
1.Placetheclothonthetable,soatleastseveralinchesextendbeyondtheedgeofthetable.
2.Carefullyplacetheobjectsonthecloth.Iftheobjectsareclosertotheedgeofthetablethisiseasier,butallowforat
leastafewinchesfortheobjectstoslide.
Figure23-1Don’thesitate!
3.Atthispoint,allyouneedtodoispullthetableclothoutfromundertheobjectsonthetable.Aswithaband-aid,the
fasterthebetter.Don’thesitateandbetentativewithyourpullbecausethatincreasesthechancesfortheobjectsto
topple.(Itdoesn’thurttocreatesuspensebypretendingyouneverdidthisbeforeandhaveeveryreasontoexpectit
tofail.Themoreyoudothis,thegreaterlevelofactingskillsthismayrequire.)
100
Figure23-2Afastpullworksbetterthanatentativepull.
4.Youcanalsodothiswithjustonebeakerandacloth.Perhapsthisisaless-dramaticstart,butitstillprovesthesame
point.
Note:Thisworksbestwhenobjectsplacedonthetableclothhavesmoothbottomsurfaces.Bowlswithacircularliptendto
catchonthetablecloth.Potterywithafeltbottomormountedsiliconrubberrestingpointscanalsoleadtohumiliationand
ridiculeiftheyhangupduringthisdemonstration.Theobjectsshouldhaveashortvertical“momentarm,”whichmeansbowls
are safer than bottles and partially filled bottles are safer than empty bottles. Bottles with liquid should be at room
temperaturetoavoidcondensationontheoutsideofthebottle,whichcanincreasefriction.
ExpectedResults
Theclothisremovedandtheobjects-at-restsittingonthetableclothtendtostayatrestinapproximatelythesameposition
theywereoriginallyplaced.Mostlikely,therewillbesomeslidingandeventeeteringbeforetheobjectscometorest.
Thecriterion forstability is that theheight todiameter ratio forcylindricalobjectsbe less than thecoefficientofstatic
frictionbetweentheclothandtheobject.
WhyItWorks
Thisisbasicallyafunexperiment,butthereisagoodbitofphysicstolearnhere.Theobjectsretaintheirpositionsonthe
table due to Newton’s first law, which states that an object in motion tends to stay in motion unless acted upon by an
externalforce. (Anobjectat rest tendstostayat restunlessacteduponbyanexternalforce.) Ifexcessivefrictionexists
betweentheclothandthebottomoftheobjects,therewillbeanexternalforceandtheobjectswillmove.Thetablemust
havelowenoughfrictionsothetableclothcanbepulledoutsmoothly,butenoughfrictionsotheobjectsdon’tslidetoofar
aftertheclothisremoved.Thesmallfrictionalforcethatoccurswhentheclothispulledoutexertsatorquethatcanrotate
theobject,especiallyonewhosecenterofmassisrelativelyhighabovethetable.Thefrictionalforceexertedbythetableon
the bottom surface of the objects opposes this rotational motion and helps stabilize tall objects, such as bottles and
candlesticks.
OtherThingstoTry
Asaway toget in touchwith your inner nerd, youcandrawdiagrams, called free-body-diagrams, showingall the forces
101
presentinthisproject.Youcanlearnalotofphysicsbydoingthis.
ThePoint
OneaspectofNewton’sfirst lawisthatanobjectatresttendstostayatrest.Thiscanbeseeninthereluctanceofthe
objectsonthetabletobemovedastheclothispulledoutfromunderthem.Somefrictionalforceexistsbetweenthecloth
andtheobjects,whichexertsatorquethat,ifstrongenough,willrotateandtoppletheobject.
102
Project24
Newton’sfirstlaw.Pokerchips,weightonastring,andafrictionlesspuck.
TheIdea
ThisexperimentfurtherexploresNewton’sfirstlawinboththehorizontalandverticaldirections.
WhatYouNeed
5to10pokerchips(orcoins)
table
string—strongenoughtosupportthemass,butweakenoughtobreakwhenpulled
1weightwithattachmentpointsonboththetopandbottom
1supporttohangtheweight
Method
Chips
1. Placethechipsinaverticalstackonthetable.
2. Thetableshouldbesmoothenoughforthechipstoslidefreelyacrossitssurface.
3. Takeonechipanddirectittowardthestackbyflickingitwithyourfingersorpushingitrapidlytowardthestack.
Weightonastring
1. Youaregoingtodothistwice(twodifferentways),soifyouhaveenoughmaterials,itworksbestifyouduplicatethe
set-upside-by-side.
2. Usethestringtohangtheweightfromthesupport.
3. Attachastringonthebottomoftheweight.
4. Predictwhatwillhappenwhenyoupullthestring.
5. Firsttime—pullthestringslowly.
6. Secondtime—pullthestringquickly.
ExpectedResults
Theslidingchipshouldknockoutthebottomchipandtakeitsplaceinthestack(Figure24-1).
103
Figure24-1Inertiakeepstheupperchipsinplacewhiletheloweroneisremoved.
Figure24-2Wherethestringbreaksdependsuponhowfastyoupull.
Pullingthestringslowlycausesonlytheupperstringtobreak.
Pullingthestringquicklycausesonlythebottomstringtobreak.
WhyItWorks
ThesearesimpledemonstrationsofNewton’sfirst law.Thestackofpokerchipsremainsarerest.Themomentumofthe
movingchipistransferredtothechipitreplaces.MomentumisexploredinSection5inthisbook.
When the string is pulled slowly, the force from pulling is added to the weight pulling down on the upper string. The
combinedtensionisgreaterontheupperstringandthatisthestringthatbreaks.
Whenthebottomstringispulledrapidly,themass,whichisatrest,tendstostayatrestandthetensionisappliedtothe
bottomstring,whichbreaks.
OtherThingstoTry
YoucanexploreNewton’sfirstlawinanumberofotherways.Theseinclude:
1.Cutorteararectangularsheetofpapernearlyinthirds,leavingjustashort⅛inch(1mm)pieceofpaperremainingtoholdthesectionstogether.Challengesomeonetopullsidewaysatbothends(perpendiculartothetears)tocausethe
centersectiontodrop.BecauseofNewton’sfirstlaw,thisisvirtuallyimpossible.
104
Figure24-3Itisjustaboutimpossibletomakethecenterpieceofpaperfallbypullingtheothertwopiecessideways.
2.Placeahandfulofcoinsonyourinnerarmwhileit’sbent.Inonequickmotion,swingyourarmforwardandcatchthe
coinsinmidair.Inthefirstone-tenthofasecond,thecoinsfallonlyabout2inches(or5centimeters),soifyouare
quick,youstandagoodchanceatcatchingthem.Thistakespractice.Makesurenoonegetshit,eitherbythecoins
oryourarm.
3.Placeacoinonacardplaceddirectlyoverthebottle.Flickthecardawayandthecoindropsintothebottle.
4. Support a coin or sugar cube on the edge of an embroidery hoop balanced on the opening of a jar (or bottle).
Smoothlypullingthehoopwillresultinthecoinorcubefallingintothejarbelow.
5.Slideanairpuckoraslideronanair track. (Anairhockey tablecanalsowork.)Without friction,anobjectkeeps
moving inastraight lineuntila force interactswith it, justasanobject inspace.Thisdemonstrates theaspectof
Newton’sfirstlawthatreferstoabodyinmotionstayinginmotion.
ThePoint
ThisprojectexploresNewton’sfirstlaw,whichisalsoknownasthelawofinertia:abodyatresttendstostayatrestunless
acteduponbyanexternalforce.Abodyinmotiontendstostayinmotioninastraightlineunlessacteduponbyanexternal
force.
105
Project25
Newton’ssecondlaw.Forcinganobjecttoaccelerate.
TheIdea
This classic experiment explores the connection between an object’s acceleration and the force applied to it. This
fundamentalprincipleofphysicswasfirstformulatedbySirIsaacNewtoninthefamoussecondlawofmotionthatbearshis
name.Tomeasureacceleration, youuseeither thestopwatchor themotionsensor techniqueofmeasuringacceleration,
whichweusedinpreviousexperiments.TheforcewillbeprovidedcourtesyoftheEarth,intheformofthegravitationforce
onamasshangingfromastring.
WhatYouNeed
low-frictioncart(oranairtrackandglider,ifavailable)
springscale
massset(including50g,100g,200g)
tape
string
pulley(lowmassandlowfrictionispreferable)
clamptoattachthepulleytothetable
tabletop(atleast1meterinlength)
stopwatchandmeterstickormotionsensor
Method
1. Determinethemassofthecartingrams.Divideby1000togetkilograms.
2. Placea100g(0.1kg)massinthecart.Secureitwithtape,ifnecessary.
3. Setthecartatoneendofthetable,andattachthepulleytotheotherend.
4. Attachthestringtothecart,runitoverthepulley,andtiealoopthatextendsafewinchesbelowtheedgeofthe
table,intheotherend,asshowninFigure25-1.
5. Whileholdingthecartinpositionatthefarendofthetable,hangamassontheloopontheothersideofthestring.
6. Next,youreleasethecartandlettheweightofthehangingmasspullthecartacrossthetable.Asyoudothis,you
measuretheaccelerationofthecartusingeitherofthepreviousmethods:
–Stopwatch:measurethetime(inseconds)forthecarttobepulledameasureddistance(inmeters).Theacceleration
(inm/s2)isdeterminedbya=2d/t2,wheredisthedistancethattheobjectispulledacrossthetable(inm)duringtime,
t(inseconds).
106
Figure25-1Newton’ssecondlawapparatus.CourtesyPASCO.
–Motionsensor:recordthepositionofthecartasit isdrawnacrossthetable.Displaythevelocityversustimegraph
anddeterminetheaccelerationofthecartbyfindingtheslopeofthatgraph.ThiscanbedoneeitherusingtheSlope
toolfromtheDataStudiomenuormoresimplybyobtainingtheaccelerationasthechangeinvelocitydividedbythe
changeintime.
7.Repeatthismeasurement,butmakethefollowingchanges:
–Varythemassinthecart,butkeeptheappliedforceconstant,asindicatedinFigures25-2and25-3.
–Varytheappliedforcebyaddingorremovingsomeofthehangingweight,butkeepthemassinthecartconstant,as
showninFigure25-4.
Figure25-2Findingaccelerationasafunctionofmass,whilekeepingtheforceconstant.CourtesyPASCO.
Figure25-3Addingmasstothecartwhilekeepingtheforceconstant.CourtesyPASCO.
Figure25-4Accelerationasafunctionofthehangingmass.CourtesyPASCO.
ProvingNewton’ssecondlaw
Newton’ssecondlaw,whichstatesthatF=ma,orasNewtonoriginallyputit,a=F/m.
mrepresentstheentiremassofthesystemandincludesthemassofthecart(mc),plusthemassinthecart(m1)
plusthehangingmass(m2).
Fistheappliedforcethatpullsthecartandisgivenbythehangingmass,m2(inkilograms,notingrams)timesthe
gravitationalacceleration(9.8m/s2).(Togetkilogramsfromgrams,dividethenumberofgramsby1000.)
aistheacceleration(inm/s2)oftheentiresystem,includingthecart,itscontents,andthehangingmass.
Youcanusethefollowingtoorganizeyourdata:
107
ExpectedResults
Theeffectofforceonacceleration
For a fixedmass in the cart (m1), the greater the applied force, the greater the acceleration. The expected relationship
betweenaccelerationand force isshown inFigure25-4,which (forsimplicity)shows theeffectof increasing thehanging
massonacceleration.(Theactualdrivingforceisgiveninnewtons,whichissimply9.8timesthemassinkilograms.)Without
friction(andtotheextentthatfrictioniseliminatedfromthisexperiment),thisshouldbealinearrelationshipasindicatedin
Figure25-5.
Figure25-5Predictedaccelerationversusappliedforcefordifferentvaluesof(total)mass.
Theeffectofmassonacceleration
Foragivenappliedforce,theheaviertheload,thesmallertherateofacceleration.Thisisaninverserelationship,asshown
inFigure25-6.
Experimental results for acceleration for a given mass and applied force come close to the predicted results if the
frictionalforcesarenotsignificant.Evenwithfriction,itcanstillbeshownthataccelerationdependsonappliedforceandis
inverselyproportionaltothemass.Frictionincreaseswhentoomuchmassisplacedinthecart.However,ifthemassistoo
small,theaccelerationcanbesohigh,itbecomesmoredifficulttomeasureaccurately.
Useoflow-frictiontracksreducestheamountoffriction.Motionsensorsprovideanicewaytodeterminetheacceleration.
Figure25-7showstheresultofmotionsensordatafortwodifferenttotalacceleratedmasses.
108
Figure25-6Predictedaccelerationversustotalmass.
Figure25-7Velocityversustimefortwodifferentmassesacceleratedbyaconstantforce.Theslopeofthev-tcurvegives
theacceleration.CourtesyPASCO.
WhyItWorks
Newton’ssecondlawstatesthatF=maora=F/m.Moreforceleadstogreateracceleration,butmoremasslowerstherate
ofacceleration.
OtherThingstoTry
YoumaywanttoconsiderdoingthisusingaHoverPuckdrawnacrossthefloorbyamasshungfromapulley,asshownin
Figure25-8.Asbefore,remembertoincludethemassoftheHoverPuckaspartofthetotalsystemmassbeingaccelerated.
Thehigherthepulley issupportedabovethefloor,thelongertherunyoucanhaveacrossthefloor.Aqualitativebutvery
intuitivewayofshowingtherelationshipbetweenaforceandaccelerationcanbeshownusinganLEDaccelerometer.The
constantforcefromthefanresults inanaccelerationindicatedbytheLEDsasshowninFigure25.9.Thedirectionofthe
forcevectorisinthesamedirectionastheaccelerationvector.
109
Figure25-8UsingaHoverPucktoproveNewton’ssecondlaw.
Figure 25.9 The fan exerts a force which accelerates the cart. The LEDs on the accelerometer show how the cart
accelerates.CourtesyPASCO.
ThePoint
The result here is one of the most significant results in physics: a force causes acceleration. For a given mass, the
accelerationofanobjectisproportionaltotheappliedforce.Foragivenforce,theaccelerationisinverselyproportionalto
theamountofmass.
110
Project26
Newton’sthirdlaw.Equalandoppositereactions.
TheIdea
IfSirIsaacNewtonhadaskateboard,itmighthavesavedhimsometimeindiscoveringhisthirdlaw,althoughNewtonmight
havehadsomuchfundoingit,hewouldn’thavehadtimetoinventcalculus.Thelawsofphysicsapplytoallobjects.Sports,
inparticular,canbethoughtofasintuitiveapplicationsoftheprinciplesofphysics.Thisexperimenttakesadvantageofthe
factthatallobjectsintheuniversefollowthelawsofphysics.WefocusparticularlyonNewton’sthirdlawandconservation
oflinearmomentum.
WhatYouNeed
2rollingchairs
or2peoplecapableofkeepingtheirbalanceonskateboards(eachwithhelmets);rollerbladeswillalsowork
medicineballoraseveralpoundmass,suchasabowlingball
safeplacetodothis
Method
1. Twopeoplefaceeachothersittinginthechairsonrollers,afewfeetapart.
2. Onepersontossesthemedicineballtotheother(bothareseatedinchairs).Feetshouldbekeptoffthefloor,so
thechairsarefreetomove.
3. Thetwopeopleagainfaceeachother.Onetriestopushtheother.Whathappens?
ExpectedResults
Thepersonwhocatchestheball,aswellasthepersonwhothrowstheball,willmovebackward.Similarly,thepersondoing
thepushing,aswellasthepersongettingpushed,willrecoilbackwards.
WhyItWorks
Momentumismasstimesvelocity.
Atthestartofthis,thetwoskateboardershavezeromomentum(theyhavemass,butnovelocity,sotheirmomentumis
zero).
Thevelocityoftheballtransfersmomentumfromthefirsttothesecondperson.Thefirstpersonrecoilsbackward.The
secondpersonalsomovesbackwardintheoppositedirection.
Another principle illustrated here is Newton’s third law: For every action (movement of the ball), there is an equal and
oppositereaction(recoilofthepersoninthechair).
OtherThingstoTry
Thepreviousdemonstrationscanbedonebyskateboardersorrollerbladers.(Pleaseremember,althoughweareinterested
inhorizontalactionandreactionhere,gravityisstillactiveintheverticaldirection,sokeepyourbalance.)
111
Mousetrapandtennisball
Conservationof linearmomentumandNewton’sthird lawcanbedemonstratedbyattachingamousetraptoa low-friction
cart.Thetrapissetandatennisballispositionedinplaceofthecheese.Whenthemousetrapisreleased,theprocessof
tossingtheballresultsintheequalandoppositereactionofthemousetraprecoilinginabackwardmotion.Thisisshownin
Figure26-1.Boththemousetrapandtheball initiallyhavezeromomentum.Themomentumoftheballgoingtothe left is
equalbutoppositetothemomentumofthemousetrapandcartmovingtotheright.
Figure26-1Equalandoppositereactions.
Fancar
Puttingapropelleronacartwithwheels,asshowninFigure26-2,propelsthecartforward(orbackwardifturningtheother
way).
Whatwouldyouexpecttohappenifasailisputinfrontofthepropellertocatchtheair,asshowninFigure26-3?Some
peoplewouldsaythecartwillmovefasterbecausetheforcefromthefanwill“push”thecart.However,whatwefindisthis:
withthesailinplace,thecartdoesnotmoveasitdidwithoutthesail.Thisisasurprisingresultformanypeopleseeingthis
forthefirsttime.Thereasonforthisis,withoutthesail,theequalandoppositereactionofthepropellercausesthecartto
moveforward.However,withthesailinplace,theforceofthepropellerbalancesthereactionforce.Asaresult,thereisno
netforceandthecartdoesnotmove.
Figure26-2Withouta“sail”thefanpushesthecart.
112
Figure26-3Witha“sail”thecartdoesnotmove.
ThePoint
Linearmomentumisconservedintheabsenceofexternalforces.Foreveryaction,thereisanequalandoppositereaction.
113
Project27
Newton’sthirdlaw.Bottlerockets.Whydotheyneedwater?(SirIsaacNewtoninthe
passenger’sseat.)
TheIdea
Inthisexperiment,youlauncha2-litersodabottleintotheair.Yourfueliswater,whichispropelleddownwardbyairpressure
forcing the rocket upward. This experiment is a good illustration of Newton’s third law and the law of conservation of
momentum,anditlendsitselftoanice,friendly,competitive“spacerace.”
WhatYouNeed
2-litersodabottle(waterbottlesarenotnecessarilycapableofsustaininginternalpressure,assodabottlesare)
noseconefabricatedfromacardboardpartyhatoraconeformedfromposterboardandtape
cardboardforfins
gluegunortape
water
hardrubberstopperthatjustfitsthetopofthebottle(thestoppershouldbesnugenoughtosealthebottlewhileit
isbeingpressurized,butnotoversizedtotheextentthatitpreventsthebottlefromlaunching)
bicyclepumpwithaone-wayvalve(oranelectricpumporcompressor)
optional: support toserveasa “launchpad” for thebottle (for instance,made froma tripodbuilt fromPVCpipe
sections).SeeFigure27-1.
Method
Buildtherocket
1.Slidetheopenendofthebottleovertheverticalrodofaringstandforeasierassembly.
2.Usetheglueguntoattachfinstotherocket(rememberingthattheflatsideofthebottleisthetopoftherocket).Be
carefulnottoapplyexcessiveheat,whichcouldmeltaholeinthebottle.
3.Attachanoseconetomakethebottlemoreaerodynamic.Useposterboardoraconeshapedpartyhat.
114
Figure27-1Bottlerocketreadyforlaunch.
4.Fillthebottlefromaboutone-quartertoone-thirdfull.
Assemblethelauncher
Youcandothisinseveralways.Ifyouareplanningmanylaunches,youmaywanttogoforsomethingmoreelaborate.The
basicpartsare:
1.Anairpumporcompressor.
2.Aone-wayvalve:Thesimplestwaytodothisistoinsertaneedle(availableatanysporting-goodssupplystore)used
toinflatefootballsandbasketballsthroughthestopper.Withthismethod,noreleasemechanismisneededbecause
therocketwilltakeoffassoonasenoughpressurebuildsuptoovercometheforceholdingthestopperinthebottle.
3.Areleasemechanism:Ametal“claw,”whichholdsthebottleinplaceuntilthepressurebuildstoacertainlevel,allows
agreaterpressuretobuildupinthebottle.ThiscanbemountedonawoodenorPVCtripodstructure.Youcanalso
holdthisinyourhand,butbepreparedtogetwetasthe“fuel”surgesdownwardfromthebottomoftherocket.
Launchtherocket
1. Insertthestopperintothebottle.
2. Securethebottleontothelauncher.Movetheholdingmechanismintoplace(orholditifthatiswhatyouaredoing).
3. Pressurize thebottle.Themaximumairpressureshouldnotgoabove80 to100psi (poundspersquare inch) to
avoidburstingthebottles.
4. Useastringtoremotelyreleasethereleasemechanism.
ExpectedResults
Therocketwillascendvertically.Theupwardlegpathcantakeaslongasabout4secondscorrespondingtoamaximum
heightofmorethan75meters(over250feet).
WhyItWorks
115
Theair pressure forces thewaterdownwardwithahigh velocity.Themassof thewater times the velocityof thewater
representsthedownwardmomentumofthewater.Conservationofmomentumrequiresanequalmomentumupwardthatis
appliedtothemassofthebottle,whichacquiresavelocitytotakeitupward.Anotherwaytosaythisistheactionofthe
downwardforceofthewateriscounterbalancedbyanequalandoppositereactionthatdrivesthebottleupward.
OtherThingstoTry
Bottlerocketscanbemademoreelaboratebyaddingfins.Aparachute,madeoftheclearplasticusedbydrycleaners,can
beaddedtokeeptherocketintheairforalongertimeortoreleaseapayloadconsistingofatennisballorotherobject.
YoumaywanttoseetheMythbustersepisode,wheretheyexploretheuseofbottlerocketstopropelaperson.Note,for
safetyreasons,theyconfinedtheireffortstodummies.
ThePoint
ThisisanotherexampleofconservationoflinearmomentumandNewton’sthirdlaw.
Figure27-2SirIsaacNewton’slawsofmotiondescribethemotionofbottlerockets,satellitesandplanets.
116
Project28
Pushingwater.Birdsflyinginsideatruck.
TheIdea
Newton’sthirdlawstatesthatforeveryaction(force),thereisanequalbutoppositereaction(force).Thisprojectillustrates
howthisconceptcanbeapplied toaparticularphysicalsituation.Theoutcomemaybedifferent thanwhatmanypeople
expect.
WhatYouNeed
1ping-pongballattachedtoastring
2beakers(orjars)filledwithenoughwatertoimmersetheping-pongball
balancescale
counterweights
Method
1.Seteachofthebeakersontheopposingpansofthescaleandestablishabalance,asshowninFigure28-1.
2.Predictwhatwillhappenwhentheping-pongballisloweredintothebeakerofwater.Willthesidewiththepingpong
ball
a.Rise?
b.Fall?
c.Remainbalanced?
3.Lowertheping-pongballintothebeakerandobservewhathappens.
4.Removetheping-pongball.Whatistheeffectonthebalance?
ExpectedResults
Loweringtheping-pongballintothebeakerforcesthatsideofthebalancedown,asshowninFigure28-2.
Whentheping-pongballiswithdrawn,thebalanceisrestored.
WhyItWorks
Thereisabuoyantforceonanyobjectimmersedinwater(orpartiallyimmersedinwatersuchasafloatingping-pongball).
Foreveryactionthereisanequalandoppositereaction.Inthiscaseiftheaction(thebuoyantforce)isup,thereactionmust
bedown,causingtheobservedeffect.
117
Figure28-1Whatwillbetheeffectofafloatingobject?Willittipthebalance?
Figure28-2Newton’sthirdlaw:Thebouyantforcepushesup.Theoppositereactionpushesthescaledown.
OtherThingstoTry
Thisissimilartotheenigma:ifbirdsareinatruck,willthetruckweighlessifthebirdsareflying,insteadofatrestonthe
floorofthetruckbed?Itturnsoutthattheforceexertedbythebirds’wingsexertsthesamedownwardpressureonthetruck
bedastheweightofthebirdsatrest.(Aswiththepreviousexperiment,thisisalsoaddressedbyaMythbustersepisode.)
ThePoint
ThisexperimentshowshowareactionforceisestablishedbyNewton’sthirdlaw.
118
Project29
Slippingandsliding.
TheIdea
This project compares the amount of friction developed by various common substances. It also shows a simple way to
measuretheamountoffriction.
WhatYouNeed
book
coin
icecube
rubbereraser
protractor
Method
1. Lineallthreeobjectsupinastraightlineonthebook.
2. Slowlyliftthebook.
3. Asyouraisethebook,notetheanglewhereeachoftheobjectsjustbeginstoslide.
4. Breaktherubbereraserintovariouspiecesofdifferentareas.
5. Lineuptheeraserpiecesanddeterminethesequenceinwhichtheyslide.
6. Breaktheicecubeintovarioussizedpiecesindifferentareas.
7. Linetheeraserpiecesupanddeterminethesequenceinwhichtheyslide.
ExpectedResults
Theicegoesfirst,thenthecoin,andthen,finally,theeraser.
Foragivenmaterial,thecontactareabetweentheslidingsurfacesdoesnotsignificantlyaffecttheforceoffriction.
WhyItWorks
The surface of each material is characterized by a different amount of friction. It would be nice if this was called the
surface’s“slipperiness.”However,itgoesunderthemoreprestigiousnameofcoefficientoffriction,whichistheamountof
frictionalforceasurfaceimposesonanobjectcomparedtoitsweight(onahorizontalsurface).Thereisafrictionalforceto
getsomethinggoing(staticfriction)andaforcetokeepsomethinggoing(kineticfriction).Thefrictionalforcedependson
thecoefficientoffrictionandthe(horizontal)weightoftheobject.Itdoesnot(tofirstorder)dependonthecontactarea.
Theconditionfortheobjecttoslideisthatthetangentoftheangleequalthecoefficientof(static)friction.Byfindingthe
anglewheretheobjectjustbeginstoslide,youcanfindthecoefficientofstaticfrictionbysimplytakingtheinversetangent.
(Thisisthekeyonyourcalculatorthatsaystan−1,arctanoratan.)SeeFigure29-1.
119
Figure29-1Forcesonanincline.
OtherThingstoTry
Frictionappliesa force thatputs thebrakesonmotion.Theamountof frictionbetween twosurfaces ischaracterizedby
something called the coefficient of friction, which is represented by the Greek letter μ (mu pronounced “myoo”). On ahorizontalsurface,theforceexertedbyfrictionisequaltotheweightoftheobject,multipliedbythecoefficientoffriction.
Thereare two types—static friction,whichmust beovercome toget somethinggoing,andkinetic friction,whichmust be
overcometokeepsomethinggoing.
Inthisproject,theobjectsslidedowntherampifthetangentoftheangleisgreaterthanthecoefficientofstaticfriction
forthatobjectonthebook.Thisconditioncanbeturnedaroundand,iftheslidingangleisfound,thecoefficientoffriction
canbeeasilyandsimplydetermined.
Afollow-upalongasimilarthemeistopredictwhetheranobjectcanslidealongasurfacewithouttoppling.Abooksliding
frontsidedownonasmoothtablewillnothavestabilityproblems.Butacanoftomatojuiceslidinguprightacrossarough
woodenfloormaybeanotherstory.Trythiswithseveralcylinderswiththesamediameter,butwithdifferentheights.Sections
of cardboard tubes or plastic pipe sections are good to test this. The condition for sliding without tipping is that the
coefficientof(kinetic)frictionbelessthantheratioofthediameterofthecylindertoitslength.
Youcouldalsodesignanexperimenttostudytheeffectofincreasingtheweight,surfacearea,andvelocityofmotion.You
willfindtheweightoftheobjectistheonlysignificantvariableand(surprisingly,formanypeople)thecontactareais(almost
entirely)insignificant.
ThePoint
Frictionisaforcethatopposesmotion.Onahorizontalsurface,theamountoffrictiondependsontheweightofanobject
pressingitincontactwiththatsurface,andthecoefficientoffriction.
120
Project30
Springs.Pullingback.Thefurtheryougo,theharderitgets.
TheIdea
Theforceexertedbyaspring,unlikeanyoftheforceswehaveencounteredsofar, isnotconstant.Itcontinuouslyvaries.
Thefurtheryoupullthespring,theharderitpullsback.ThisrelationshipisknownasHooke’slaw.Becauseofthis,springs
havethecapabilitytokeepgoingbackandforthuntilfriction(eventually)slowsthemdown.
WhatYouNeed
varioussprings
massset(oraspringscale)
metricruler
Method
Measurethespringconstantofaspringbyfollowingthesesteps:
1. Suspendthespringfromthesupport.
2. Locatethedistancefromthebottomofthespringjusthangingunderitsownweight.Thisiscalledtheequilibrium
point.
3. Hangamassfromthespring.Themassshouldbechosensoitincreasesthelengthofthespringbynogreaterthan
about50percent.
4. Measurethedistance(incentimeters)thebottomofthespringispulledbelowtheequilibriumpoint.SeeFigure30-1.
5. Find the force. If your reading is in grams, convert it to newtons by dividing themass in grams by 1000 to get
kilograms,andmultiplyingby9.8togetforceinnewtons.Itmaybeeasiertodothisusingaspringbalancetoget
theforce topull thespringacertaindistance.Manyspringbalancesarecalibrateddirectly innewtons,so in that
case,thereisnoneedtoconverttheforceintonewtons.
6. Thespringconstantcanbedeterminedbydividingtheforcebythedistanceaccordingtotheequation:k=−F/x.(Note:thenegativesignaccountsforthefactthattheforceandtheextensionareinoppositedirections.Ifyoupull
up, thedistance ispositive,but the force isnegative.Regardlessofhowyoudo it, thespringconstant isalways
positive.)
121
Figure30-1Determininghowstiffaspringisbymeasuringthespringconstant.
ExpectedResults
Thestifferthespring,thehigherthespringconstant.Asanexample,ifittakes10newtonsofforcetostretchaspringby1
centimeter,thespringconstantwouldbek=10N/1cm=10N/cm.Itwouldtake20newtonstostretchthatsamespringby2
centimeters. The spring constant should prove to be constant and establish a linear relationship between force (F) and
extension(x).RealspringshavealinearrangeoverwhichHooke’slawisareasonableapproximation.Ifyoustretchtoofar,
however,youwillgooutofthelinearrangeanditusuallytakesaninitialforcetobringthespringintoitslinearrange.
WhyItWorks
Overmostofitsrange,theforceexertedbyaspringisdirectlyproportionaltotheamountitisdisplacedfromitsequilibrium
position.Thespringconstant isaway tocharacterizehowmuchaparticularspringexerts foragivendisplacement from
equilibrium.
OtherThingstoTry
A more accurate value for the spring constant can be determined by taking several readings and plotting force versus
displacement,andthenfindingtheslopeoftheline.
ThePoint
The forceexertedbyaspring isproportional to thedistance thespring isstretched.The furtheryoupull, thegreater the
forcethespringexertsintheoppositedirection.
122
Project31
Atwood’smachine.Averticaltugofwar.
TheIdea
The Atwood machine illustrates some aspects of force and acceleration. Like an incline, the Atwood machine slows
accelerationdowntoameasurableandobservableamount.ThisprojectshowshowtheAtwoodapparatuscanbeusedto
studyacceleration.
WhatYouNeed
pulley
supportforpulley,suchasaringstand
string
variousmasses
Method
1. Setuptheapparatuswitheachoftwomassesattachedtostringandsuspendedoverapulley,asshowninFigure
31-1.
2. Releasethemassesandobserve/measuretheirmotion.
3. Asinpreviousexperiments,theaccelerationofthemassescanbemeasuredusingthestopwatchmethod(usinga
=2d/t2) or determining the acceleration using a motion sensor. (Different combinations of masses can also be
comparedandrankedvisuallywithoutdetailedmeasurements.)
ExpectedResults
Thegreaterthedifferencebetweenthetwomasses,thegreatertheacceleration.
Thegreaterthecombinedmasses,thesmallertheacceleration.
Theaccelerationforthetwomassesis:
123
Figure31-1Atwood’smachine.
Ifm1isthelargermass,theaccelerationisinthedirectionofthelargermassgoingdown.
WhyItWorks
The force on the system is F = g(m1− m2). According to Newton’s second law, this equals the total mass times theacceleration.Becausethetotalmassis(m1+m2),wecanderivethepreviousexpressionforacceleration.
OtherThingstoTry
Onceyougettheideaofthis,tryitatanincline,asshowninFigure31-2.
Predictwhatangleorcombinationofmasseswillresultinequilibrium.
Because frictionhelpsestablishstability,awindow isaround thepredictedconditions thatwillalso result inequilibrium.
Thiscanalsobedonewitheachofthetwomassesslidingonanincline.
ThePoint
AnAtwoodmachinedemonstrates theprinciplesofNewton’ssecond law.Thenet forceon themassescauses the total
massofthesystemtoaccelerate.
124
Project32
Terminalvelocity.Fallingslowly.
TheIdea
Shortlyafterjumpingfromanairplane,skydiversreachasteadyvelocityinsteadofconstantlyacceleratingasdoothermore
streamlinedobjectssubjected toEarth’sgravity.When thishappens, theskydiver fallsata terminal velocity that isnearly
constant.Thisisfortunatebecause,oncetheparachuteopens,itismucheasiertoslowtheskydiver’sfall.Hadtheskydiver
beenarockinavacuumwithoutthebenefitofairresistance,itwouldreachamuchhighervelocity.
WhatYouNeed
coffeefilter
meterstick
stopwatch
coin,book,oranothercompactobject
optional:motionsensor
Method
1. Dropacoffeefilterfromameasureddistance.
2. Comparethetimeittakestofallwithacoinorabook.
3. Comparethedistanceversusthetimegraphgeneratedbyamotionsensorforeachofthetwoobjects.
ExpectedResults
Notonlywillthecoffeefiltertakelongertodescend,butmoresignificantly,itfallsatasteadyvelocity.Thecoin,typicalof
other objects in free-fall, accelerates as it falls and will have an ever-increasing velocity. The following shows distance
versustimeandvelocityversustimegraphsforthesetwoobjects.Noticethefallingbookcontinuestoaccelerateasitfalls.
Thisisindicatedbythecurvedshapeoftheposition-timegraphandthepositiveslopeforthevelocity-timegraph.
126
Figure32-2Fallingcoffeefilter.
The coffee filter falls with constant velocity. The position-time graph is a straight line and the velocity-time graph is
essentiallyahorizontalline,indicatingaconstantvelocityduringthedescent.
WhyItWorks
When a falling object encounters significant air resistance, the faster the object falls, the greater the force opposing its
descent.So,themoregravitytriestopulltheobjectdown,themoredeterminedtheairresistanceistoopposegravity.Asa
result,equilibriumisestablishedwiththeobjectfallingataconstantterminalvelocity.
OtherThingstoTry
Comparethedescentofbottlerockets(describedinProject27)withandwithoutparachutes.
ThePoint
Free-fallisdifferentthananobjectsubjectedtodragforces.
Anobjectinfree-fallaccelerateswithaconstantrateof9.8m/s2.Anobjectsubjecttoadragforcedoesnotaccelerate,
butreachesasteadyconstantvelocity,calledtheterminalvelocity.
128
Project33
Balancingact.Painteronascaffold.
TheIdea
Ascaffoldisbuiltfromaboardplacedacrossabasewithoutanythingholdingitdown.Howfarfromtheedgeoftheboard
canapainterstandwithouttippingtheboard?Thisexperimentinvestigatestheconditionforstabilitycalledstaticequilibrium.
WhatYouNeed
sectionofa2″×4″blockabout6″longmeterstick
20gmass
Method
1. Settheblockonthetable.Thiscanbeeitherwiththe2”edgeparalleltothetableorthe2”edgeperpendicularto
thetable.Eachcasegivesadifferentresult.
2. Measurethemassofthemeterstick.
3. Laythemeterstickovertheblock,asshowninFigure33-1,withthe50-centimetermarkofthemeterstickcentered
overthemiddleoftheblock.
4. Predicthowfarthe20-grammass(the“painter”)canbeplacedfromthecenterwithouttippingthemeterstick,asis
thecaseshowninFigure33-2.
5. Theprincipletouseisthatthetorquetryingtotipthe“scaffold”mustnotbegreaterthanthetorquethatholdsitin
place.Herearetheformulas:
Tippingtorque
1w1
2w2
d1=distancefromedgeofblocktocenterof20gmass
w1=weightofblock
d2=distancefromedgeofblocktothe50cmmarkofthemeterstick
w2=weightofthemeterstick
A2″×4″blockhasactualmeasurementsof1½″×3½″(or3.8cm×8.9cm).(The3.8cmsideistheheightandthe8.9cmsideisthewidthoftheblock.)Thedistance,d2,isone-halfthesupportingedge.Thiswouldbe4.45cm(withthe
widthoftheblockalongthetable)or1.6cm(withtheheightoftheblockonthetable).
6.Tryitwithothermasses.
129
Figure33-1Howfarcanthe“painter”movetowardtheedgeoftheboard?
Figure33-2Herethe“painter”hasgonetoofar.
ExpectedResults
For a 90-grammassmeterstick balanced on top of a nominally 2”× 4” block, the following table shows themaximumdistancethepainter,m2,cangowithouttopplingthemeterstick.
WhyItWorks
Theamountofmasscarriedatapointofsupportistheresultofatorquegeneratedaroundthepivotpoint.Inthiscase,the
springscalesformapivotpoint.Thegreaterthemasssupported,andthefurtherfromthepivotpoint,thegreaterthetorque.
OtherThingstoTry
130
Howweightisdistributed
Placetwobathroomscalesonthefloorseparatedbythelengthoftheboard.Setastiffboardabout8feetlongovereach
scale.Adjust thescalestoreadzero, toeliminatetheeffectof theweightof theboard.Predictandmeasurethereading
directlyoverthescales,inthemiddle,andatarbitrarypositionsinbetween.
Figure33-3
Verticalstaticequilibrium
AssembletheapparatusshowninFigure33-3.Basedonbalancingclockwiseandcounter-clockwisetorque,developother
combinations that establish equilibrium. This is based on a demonstration found on the U.C. Berkley Physics Lecture
Demonstrationwebsitehttp://www.mip.berkeley.edu/physics/noteindex.html(item:A+60+0).
ThePoint
Staticequilibrium reflectsabalanceof forces that results inacollectionofobjects remainingstableandstationary.The
conditionforstaticequilibriumisthatthesumoftheforceandthesumofthetorquesonanobjectiszero.
131
Project34
Hangingsign.
TheIdea
Youarehangingasignforyourcaféthatweighs50pounds.Youhaveonecablethatis4feetlongandanothercablethatis5feetlong.Whichonesupportsmoreoftheweight?
Anglescomplicatehowforcesaredistributed.Thisprojectexploresasimplesituationsimilartohangingasignwithtwo
differentlengthcables.
WhatYouNeed
2springscales
mass—(shouldgiveclosetoafull-scalereadingintheverticalpositiononyourspringscales)
string
2ringstandswithclampsorcomparablesupport
keyring
protractor
Method
Symmetricalsign
1. Placetheringstandsabout18inchesapart.
2. Cuttwoequal-lengthsectionsofstring.Thestringsshouldbe8inches,leavingacoupleofinchesoneachsidefor
attachingtothesupportandtheweight.
3. Setthespringscalestoreadzero(inthepositiontheyarebeingused),withnoweighthangingfromthem.
4. Hookbothofthespringscalestoeachoftheringstands.
5. Attacheachstring—onesidetothekeyringandtheothersidetotheclampontheringstrand.
6. TheapparatusshouldbeasshowninFigure34-1.
7. Hangthemassonthekeyring.
8. Recordthereadingoneachofthespringscales.
9. Repeat,usingdifferentmassesanddifferentstringlengths.
Asymmetricsign
1. Repeattheprevioussteps,usingdifferentstringlengths.
2. Basedonyourevaluation,canyouanswerthequestionposedatthebeginningofthissection?
132
Figure34-1
ExpectedResults
Inthecaseofthesymmetricsupports,thetwoscaleswillreadthesame.
Ifthestringsaredifferentlengths,theshorterofthetwostringswillbearmoreoftheweight.
WhyItWorks
Theforceinacableisthecombinationofthevariousforcespresent.Theoverallforcedependsonhowlargeeachofthe
forcesisanditsdirection.Themethodofcombiningtheseforcesiscalledvectoraddition.
OtherThingstoTry
Tensionistheforceinaropeorcablethatcanchangedirectionwithoutlossesbygoingaroundapulley.Howdoyouthink
theforceineachofthecasesinFigure34-2compares?Testitoutwithweightsandpulleys.
Eachspringscaleshouldread9.8newtons,whichistheamountofforceexertedbygravityona1kgmass.
Tugofwar.Itisalmostimpossibletopullaropesupportingamoderateweighttightenoughtobeperfectlyhorizontal.The
experimentalsetupisshowninFigure34-3.Agallonmilkcontainerfilledwithwatermakesagood4kgmasstotrythiswith.
133
Figure34-2Howmuchforceismeasuredbyeachofthespringscales:A,B,andC?
Figure34-3Witha4kgmass,itisalmostimpossibletopulltheropeperfectlyhorizontal.
Tobringtheropetowithin5degreesofhorizontalwitha4kgweightinthemiddle,youneedtopullwithaforceof560
newtons(orover125pounds).Tobringtheropetowithin1degreeofhorizontal,youneedtoapplyaforceofabout2300
newtons(orover500pounds).
ThePoint
Thisexerciseshowshowaforcecanbebrokendownintoorresolvedintoapairofcomponentforces.Thedownwardforce
from the suspended sign is supported by cables of various lengths in various directions.This is the typeof thinking civil
engineersapplyonadailybasis—tooversimplify,howstrongsomething(likeabridgecable)needstobetosupportaload
(liketheroadsurfacewithcars).
134
Project35
Pressure.Implodingcans.
TheIdea
Howpowerfulisairpressure?Wecananswerthisbyobservingwhathappenswhenweremoveairfromwhereitisnormally
found.
WhatYouNeed
emptysodacans
oralargerrectangularcanwithascrew-oncap,ifyoucangetone.(Theseareusedforcookingoilorpaintthinner,
andtheycanbepurchasedtodothisexperiment.)
hotplate
beaker
water
ovenmittorbeakertongs
pailofcoldwater
Method
1.Rinsethecan,soitisreasonablyclean.
2.Putasmallquantityofwater(2tablespoons)inthecan.
3.Placethecanonthehotplateandkeepitthereuntilthewaterboilsandsteamcomesoutofthecan(Figure35-1).
4.Carefullyremovethecanfromthehotplateusingthemittortongs.
5.Quicklyimmersethesodacan,withsteamstillevolving,topsidedowninthewater.Observewhathappens(Figure35-
2).
Figure35-1Asmallamountofwaterinthecanisheated.
135
Figure35-2Lowerairpressureinthecancausesittobecrushed.
6.Removetherectangularcanfromthehotplate.Withsteamstillcomingoutofthecan,screwonthecap.Waituntilit
cools intheairorfacilitatethecoolingwithwateror ice. (Ifyouaredoingthisasademonstration,thismaytakea
while and a sense of drama can be created by pretending that nothing is happening and going on to the next
experiment.)
ExpectedResults
Thesodacanwillbecrushedalmostinstantaneously.Therectangularcanmaytakeafewminutes; itgetscrushedslowly
(asifbyaprotégéofDarthVaderusingtheForce).
WhyItWorks
Airexertsapressureof14.7poundsoneverysquareinch.Asthesteaminthecanscondenses,theairpressureinsidethe
candropsandthereisadifferenceinpressurebetweentheinsideandoutsideofthecan.Thisisprimarilytheresultofthe
changeinstatefromvaportoliquidandtoalesserdegreefromthecontractionofthegasinthecanasitcools.Thismeans
asodacan(6.5incheshighand3inchesindiameter)hasaforceofover900poundspressingdownonitssides!
OtherThingstoTry
Trythiswitha55-gallondrumasshowninFigure53-3.Useavacuumpumpconnectedtothedrumthroughavalvetocreate
thepressuredifference.Thismaytakesometime,butitwillbeworththewait.Youmaywanttowarnthepeopleyouwork
withthattheboomtheyareabouttoheardoesnotrequiretheemergencyresponseteamtobesentin.
ThePoint
Airpressureissubstantial,exertingaforceofnearly15poundsforeverysquareinchthatitisincontactwith.
136
Project36
Pressure.Supportingwaterinacup.
TheIdea
Whichweighsmore:anemptycuporafullcup?Obviously,thefullcup.So,ifyouturnacupupsidedownwithaflatcover,
which has the better chance of being supported: the (lighter) empty cup or the (heavier) full cup?Many people find the
outcomesurprising.
WhatYouNeed
cuporbeakerwithaflat,circular,smoothtop.(Ifthebeakerhasaspout,itshouldbeflatenoughsoitcanmake
contactwithacardatallpointsalongitstopsurface.)
watertofillthecup
flat,stiff,lightweightsquare,largeenoughtocovertheentiretopsurfaceofthecup.Thesquareshouldnotbecome
waterlogged.Cardboardisnotthebestchoice.Foamboardstandsuptowaterbetter.Indexcardscanwork,butyou
mustbecarefulnottoletthemflexandbreakthesealwiththecup.
Method
1. Startwith theempty cup.Cover theempty cupwith the square.Turn it upside downandobservewhat happens
(Figure36-1).
2. Withthecupstillempty,moistenthetopsurfaceofthecuptomakeitmoresticky.Coverthecupandturnitupside
down.Whathappens?
3. Nowfill thecupwithwater to thebrim. Itwon’thurt tohave itgoabovethesurfaceof thecupor toallowsome
watertospillout.Coverthecupwiththesquare.Invertandobservewhathappens.
ExpectedResults
The squarewill fall off with the empty cup, evenwith the benefit of the surface being sticky. Thewater in the full cup,
however,willbeheldinplacebythesquare(Figure36-2).
WhyItWorks
Thewaterinabeaker5centimetersindiameterand12.7inchestallhasamassof250g(0.25kg)andweighs0.55pounds
(or2.5newtons).Theairpressureonthe5centimeter(roughly2inch)diametercircleisover3pounds.Theairpressureis
fargreaterthantheweightofthewaterinthebeaker.Theemptybeakerhasthesamepressureinsideandoutsidethecup,
sotheairpressureisbalancedandtheweightofthecupcausesittofall.Theadhesionofthesquaretothecupisclearly
notenoughtomakeupthedifference.
138
Figure36-1Withthecupempty,thereisnothingtoholdthesquareontothecup.
Figure36-2Theforceextertedbyairpressureisgreaterthantheweightofthewater.
OtherThingstoTry
Calculatehow tall theglasscanbewith thecardsupportedbyairpressure. (Thedensityofwater is1g foreverycubic
centimeterand1000gistheequivalentof2.2pounds.)Atmosphericpressurewillsupportacolumnofwater34feethigh.
Sincemercuryismoredensethanwater,atmosphericpressurewillsupportacolumnofmercuryabout30incheshigh.The
exactheightvarieswithlocalairpressureandprovidesawaytomeasurechangesinairpressure.
ThePoint
Airpressureislargecomparedtothepressureexertedbytheweightofacupofwater.
139
Project37
Pressure.Sometimesthenewscanbeprettyheavy.
TheIdea
Howmuch pressure does the atmosphere exert on a sheet of newspaper? As with the previous experiments, the force
exertedbyairpressurecanbesurprisinglypowerful.
WhatYouNeed
sectionofnewspaper
table
pieceofwoodabout12to24incheslongandroughly1to2incheswide.(Thewoodshouldbethinenoughsoitcan
bereadilysnappedinhalfbysomeonewhoisnotablackbelt.Itshouldalsobestiffenoughsoitwillbreakrather
thanflexifstuck.Arulerthatyouarewillingtodedicatetothecauseofscienceusuallyworks.)
Method
1. Placethepieceofwoodonthetable,extendingapproximatelyone-halfitslength.
2. Placeafewlayersofthenewspaperoverthewood.Layitoutsoitisasflataspossible.Removeany“airpockets”
thatyoucanunderthepaperandmakesuretheedgesareflat.
3. UsingyourbestMaxwellSmartkaratechop,strikethewood.Hitithardenoughtobreakthewood.Showitnomercy
(Figure37-1).
ExpectedResults
Manypeoplewouldexpect thewoodtopushthepaperupandthrowthepaperpartwayacrosstheroom.However, if the
paperisproperlysealedoverthewood,strikingthewoodresultsinthewoodbeingpinnedtothetableandbreakingapartas
ifitwereclampedtothetable.
WhyItWorks
Let’ssayyouhavea1-inchwiderulerthatextends10inchesunderthepaper.Thismeansthat147poundsofairpressure is
pressingdownon the ruler.About thesameasamedium-sizedpersonstandingon thepaperholdingdown the ruler.Air
pressureisthatstrong.Ifthisdoesn’twork,itisn’tbecauseofinsufficientairpressure.Therulermaynotbreakif:airleaks
underthepaperfromtheedges,thewoodistooflexibletobreak,orthewoodistoothicktobreak. It isunnecessary,of
course,toactuallybreaktherulertodemonstratethestrengthofairpressureonthepaper.
140
Figure37-1Breakingaboardwithonlyairpressureholdingtheothersidedown.
OtherThingstoTry
Air pressureonpapercanalsobeobservedpressingdownon thepagesofabook.After interleaving thepagesof two
similarbooks,itwillbeverydifficult,ifnotimpossible,topullthetwobooksapart.Thisisnottheresultofthefrictionofthe
pages,butitisadirecteffectoftheairpressureholdingthepagestogether.
Thepowerofairpressurecanalsobedemonstratedusingasuctioncupsuchasthoseusedtopopoutminordentsincar
sidepanels.Todothisyouwillneedanobjectwithasmoothsurface.Onegoodexampleisalaboratorystool.
1.Attachthesuctioncuptothetopsurfaceofthestool,asshowninFigure37-2.Makesurethesuctioncupsealstothe
topsurfaceofthestool.
2.Pulluponthesuctioncup.
Thesuctioncupshouldbeabletoliftanaverage-sizedstoolupofftheground.Thereisacommonmisconceptionthata
vacuum somehow pulls or “sucks” objects to it. This is not the case. Suction cups work because of a difference in air
pressurebetweentheoutsideofthesuctioncupandthelittleairtrappedunderthesuctioncup.Thepressureonasuction
cupthatis4inchesindiameter(assumingaperfectseal)wouldbegreaterthan150pounds.
ThePoint
Airpressureexertsaforceonasurfaceinproportiontoitsarea.
141
Project38
Archimedes’sprinciple.Whatfloatsyourboat?
TheIdea
Doesironfloat?Clearlyacubeofiron,whichismuchdenserthanwater,willsink.Then,howisitpossibleforaboatmadeof
iron(orironalloy)tofloat?Inthisexperiment,youinvestigatetheforcesthatcounteracttheforceofgravitytoallowobjects
thataredenserthanwatertofloat.
WhatYouNeed
“boat”:ashallowplasticcup(suchasa¼poundcoleslawcontainer).Youcanalsouseapieceofwoodasyour
boat.
“lake”:aplastictrayorfishtankfilledwithwaterdeepenoughandwideenoughtofloatthe“boat”
“cargo”:smallweights,pennies(eachpennyhasamassof2.7g)
100mLgraduatedcylinder
Method
1. Measurethevolumeoftheboat.Youcandothisbygeometry,ifyouaresoinclined,oryoucandoitbyfillingthe
cupwithwaterandmeasuringtheamountofwatertodothis.
2. Thenumberofgramsofwaterthatoccupythevolumeoftheboatequalsthenumberofgramsofcargoitcancarry
justbeforeitsinks.
3. Testthisbyaddingtheamountofweightyoupredicted.Don’tforgettoincludetheweightoftheboatitself.Ifyou
usepennies,counteachas2.7grams(orweighthem).Asyouaddweight,becarefulnottotiptheboatoryouwill
capsizeitprematurely.
4. Compareyourpredictionwiththeamountofcargoyourboatcouldactuallycarry.SeeFigure38-1.
5. Weare takingaslight liberty here for thesakeof clarity by focusingon themass.What holds theboat up isa
buoyantforce,whichismeasuredinnewtons.Thebuoyantforceequalstheweightofthewater(alsomeasuredin
newtons)displacedbythefloatingobject.
ExpectedResults
Asaruleofthumb,forevery1mLthatanobjectisheldsubmergedbelowthesurfaceofthewater,thereisabuoyantforce
capableofsupporting1gramofmass.
Anequivalentwayofexpressingthisisanobjectwillfloatifthedensityoftheentireboat,consideringitsentirevolume,is
lessthanthedensityofthesamevolumeofwater.Thedensityofwateris1gram/cubiccentimeteror1000kilogram/cubic
meter.
Figure38-1Thebuoyantforceequalstheweightoftheboatplusitscargo.Thiscanbepredictedbydeterminingtheweight
143
ofthedisplacedwater.
WhyItWorks
Thebuoyantforceonanobjectisgivenbytheweightofthefluiditdisplaces.
Thebuoyantforceexertedonafloatingobjectequalsthevolumeofthatobjectthatissubmerged(m3)timesthedensity
ofwater(1000kg/m3)timesthegravitationalacceleration(9.8m/s2).
OtherThingstoTry
1. Take a weight of known volume. Either calculate the volume using geometry or determine how much water it
displaces. Measure the weight on a spring scale in the air. Immerse the weight in the water. How is the weight
affectedbybeingimmersedinwater?Howdoesthiscomparewiththeweightofthewaterthatwouldfillthevolume
ofthesubmergedobject?
2. Predicthowmuchweightaboatcansupportbasedontheweightofthewaterthatitcanhold.Testyourprediction.
3. Predictwhereafloatlinewillbebasedonthevolumecontainedbelowthefloatlinesetequaltotheweighttobe
addedtotheboat.
ThePoint
Abuoyantforceisexertedonanobjectthatisfloatingorsubmergedinaliquid.Anobjectwillfloatifitislessdensethanthe
liquiditisfloatingin.Thebuoyantforceexertedonanobjectfloatinginwaterequalstheweightofwaterthatwouldoccupy
thevolumeoftheobjectthatisunderwater.
144
Project39
Cartesiandiver.
TheIdea
Anobjectisbarelyfloatinginabottle.Inthisproject,youcontrolwhetheritfloatsorsinks,justbyapplyingpressureonthe
sideofthebottle.
WhatYouNeed
2-literplasticsodabottlewithareclosablecap
water
1medicinedropper
asmallobjectsuchasapapercliptofine-tunetheweightofthemedicinedropper
Method
1. Partiallyfillthemedicinedropperwithjustenoughwatertoestablishneutralbuoyancy,whichisaconditionwherethe
medicinedropperdoesnotsink,butalsodoesnotfloatinwater.Testandadjustuntiltherightamountofwaterisin
themedicinedropper.Usethepapercliptoincreasetheweightofthemedicinedropper.
2. Putthemedicinedropperinthesodabottle.
3. Fillthebottletothetopwithwater.
4. Capthebottlesecurely.
5. Observewhathappensasyouapplypressuretothesidesofthebottle.Whathappensasyourelievethepressure?
ExpectedResults
Whenthesideofthebottleissqueezed,thediverdescends.
Whenthepressureisreleased,thediverreturnstothesurface.
WhyItWorks
Pressureonthesideofthebottleistransmittedtothemedicinedropper.Thepressurereducesthevolumeofthemedicine
dropper.Thebuoyantforcedependsonthesizeofthemedicinedropper.Asmaller-volumemedicinedropperhasasmaller
buoyantforceandsinks.
145
Figure39-1Cartesiandiver.
With the pressure reduced, the volume of the medicine dropper increases, leading to greater buoyant force. Greater
buoyantforcecausesthemedicinedroppertorise.
Neutralbuoyancyoccurswhentheforceofgravityequalsthebuoyantforceresultinginequilibriumintheverticaldirection.
ThisisshownforaSCUBAdiverinFigure39-2.Adiverwouldaddweighttoabeltasyoudidabovewiththepaperclipto
fine-tunethebalanceofforces.
OtherThingstoTry
Onceyougetthehangofthis,youcanputa“treasure”intheformofasmallweightwithahookatthebottomofyourbottle.
Youcanthenhaveyourdivergodownandtrytorecoverthetreasure.
ThePoint
Buoyancydependsonthevolumeofasubmersedobject.Pressureexertedexternally reducesthevolumeofasubmersed
object,which,inturn,reducesthebuoyantforce.
Figure39-2Verticalforcesinequilibrium.PhotobyDr.MichaelDershowitz.
146
Project40
Anair-pressurefountain.
TheIdea
Thisisaniceattention-gettingdemonstrationthatproducesafountain-likesprayinaninvertedflask.Ifyouaredoingthisas
ademonstration—especiallyforyoungerchildren—bepreparedtobeaskedtodoitagain.
WhatYouNeed
ringstandwithasmall2-inchdiameterring
flask(250mlworks)
1-holerubberstoppertofittheflask
approximately12-inchsectionofglasstubingthatcanbeinsertedintothestopper
hotplate
ovenmitt
beakerofequalorlargervolumeastheflask
water(withfoodcoloringoptional)
safetyglasses
Method
1.Putonsafetyglasses.
2.Carefullyslidetheglasstubethroughthestopper,soapproximately1 inchprotrudesthroughthenarrowendofthe
stopper.Usepropertechniquesforhandlingtheglasstubing(includingwearingeyeprotection,protectingyourhands
as youpush it throughusinga towel, and lubricating theedgewithabit ofVaseline, so youdon’t have to force it
throughthehole).
3.Insertthestopperintotheflask.
4.Attachtheringontheringstandhighenoughsotheentirelengthofthetubingissupportedabout½inchabovethe
baseofthestand.
5.Fillthebeakerclosetothetopwithwater.(Foodcoloringcantemporarilystainyourfingers.)
6.Assembletheapparatus,asshowninFigure40-1.Makesureeverythingfitsandissecure.
147
Figure40-1Airpressurefountain.
7.Taketheflaskoutoftheringstandandremovethestopperwiththetubing.
8.Put(afewtablespoonsof)waterintotheflask.Setthestopperonatable.
9.Placetheflaskonthehotplate(Figure40-2).
10.Whenthewaterstartstoboilandtheflaskfillswithsteam(usingtheovenmitt),removetheflaskfromthehotplate
andattachthestopper.
11.Quickly,butcarefully(stillusingtheovenmitt),reassembletheapparatus.Oneconvenientwaytodothisistonote
thepositionofthering,removethering,andthenplacetheringoverthecollaroftheflask.Then,withthestopper
inserted,inverttheflask,and(withtheflasksupportedbytheringasitistransferred)reattachtheringonthestand.
Itwouldn’thurttochoreographthisalittlebitbeforedoingit(andhaveasecondpersonhelpyou).Theideaistodo
the transferquickly (soyoudon’t loseallofyoursteam),butsafely (becauseyouareworkingwithglassandhot
liquids).Placinganicecubeontopoftheflaskmayfurtheracceleratetheprocess.
148
Figure40-2Heatasmallamountofwaterintheflask.
12.Withtheflaskintheringstandandtheglasstubingclosetothebottomofthebeaker,observewhathappens.
ExpectedResults
Atfirst,thewaterstartstoriseupthetube.Thisbeginsslowlyatfirst.Asthewaterworksitswayupthetube,itbeginsto
pourintotheflask.Oncethewatertouchestheinterioroftheflask,itbeginstospray,formingafountainthatincreasesin
intensityuntilthewateriscompletelydrawnoutoftheflask(Figure40-3).
Ifpositionedjustright,thefountainendsinagurglingeffect.Whilemanyobserversmayexpecttheriseoftheliquidupthe
tube,thesurgeofthefountaincatchesmanypeopleoffguard.
149
Figure40-3Airpressurecausestheliquidtosprayintotheflask.
WhyItWorks
Asthesteaminsidetheflaskbeginstocool,theairpressureinsidetheflaskdrops.Thisisprimarilytheresultofthephase
changeofthesteamfromvaportoliquidwater,whichoccupiesamuchsmallervolume.Thecoolingairinsidetheflaskalso
contracts,addingtothereducedpressure.Atmosphericpressurepushesdownontheliquidintheflask,drivingupintothe
glass tube. The cooler the flask gets, the lower the pressure. This process feeds on itself in an accelerating manner,
producingthefountaineffect.
OtherThingstoTry
ThemechanismthatdrivestheliquidupintotheflaskisthebasisforwhatisknownasaTorricellibarometer.Airpressureis
measuredby howhigha columnofwater canbe supported byair pressurewitha vacuum in the flask.Mercury is used
insteadofwater because standardair pressure can support amercury column roughly 30 inches high, comparedwith a
much-highercolumnforwater.Becauseofpotentialdifficulties inworkingwithmercury inacademicsettings, it isprobably
bestjusttoreadaboutthisone.
ThePoint
Thisprojectworksbecauseofthevolumedifferencesbetweenvaporandliquid,andtheforceexertedbyairpressure.
150
Project41
Blowingupamarshmallow.Lessiss’more.Whyastronautsdonotuseshavingcreamin
space.
TheIdea
Thenexttimeyouaresittingaroundthecampfirecookingupabatchofs’mores,besuretopointouttoyourfriendsthata
marshmallowissimplyacolloidalsuspensionofairinasolid.Becausetheairinthemarshmallowisinequilibriumwiththe
atmosphere,thevolumeofthemarshmallowisstableatstandardairpressure.However,it’sadifferentstoryifwedisturbthe
equilibriumconditionsbytakingawaytheatmosphericpressure.
WhatYouNeed
marshmallow
belljar
vacuumpump
Method
1. Placeamarshmallowonthebaseofthebelljar.
2. Assemblethebelljarandapplyavacuum.
3. Observewhathappens.
ExpectedResults
Themarshmallowgrowsinvolume,asyoucanseeinFigure41-1.
WhyItWorks
Thepressureof theair trapped ineachmarshmallowcauses themarshmallow toexpandwhen thepressureoutside the
marshmallowisreduced.
151
Figure41-1Airpressure trapped inamarshmallowcausesexpansionof themarshmallow. (Thevacuum jarpicturedhere
wasadaptedfromanapparatususedtoshowthedropoffinsoundtransmissionasairpressureisreduced.)
OtherThingstoTry
Trythiswithshavingcream.Itwillincreaseinvolume.
Trythiswithhotwater,justundertheboilingpoint.Thewatershouldbegintoboilagain.
ThePoint
Commonobjectsdependonairpressureforthemtomaintaintheirphysicalshapeandappearance.
152
Project42
Relaxingonabedofnails.
TheIdea
Wouldyousitdownonabunchofnailsthatarestickingoutofawoodenboardwiththesharppointysidesupward?Thisis
yourchancetotry.Thisisnotnearlyaspainfulasitmayseembecausethelargenumberofnailsspreadstheforceovera
largerarea.
WhatYouNeed
144nails,1½to2incheslong.Whateverlengthyouuse,makesurethenailsarenearlyallthesamelength
pieceofplywood14inches×14inches×¾inchesthick(orlarger)electricdrill
drillbitwhosediameterisequaltoorjustslightlysmallerthanthediameterofthenails
inflatedballoon
Method
Assemblingthebed
1. Drawevenlyspacedlinesat1-inchintervalsrunningparallelwitheachoftheedgesoftheboard.
2. Drillaholeattheintersectionofeachoftheholes.
3. Insert the nails in the holes.They should be snugenough not to fall out. Somemay have to be driven inwith a
hammer(Figure42-1).
Testingthebed
1. Presstheballoonononeofthenailsonthecorner.
2. Press(another)ballooninthecenterofthebed(Figure42-2).
3. Placethenailsonachairandsitdownonit.
153
Figure42-1Bedofnails.
Figure42-2Theforceisspreadoutoveralargenumberofnails.
ExpectedResults
Withonenail isolated, theballoonwillburst.However,withseveralnails incontactwith theballoon, theballoondoesnot
burst,evenwithsubstantialpressureapplied.Sittingonthebedofnailsissurprisinglypainless.
WhyItWorks
Pressure is forcedividedbyarea.Foragiven forcepressingdownon theballoon, thepressure ismuchgreaterwith the
singlenailthanwiththelargegroupofnails.Whenyousitonthegroupofnails,theforceistheresultofyourweight,butthe
pressureisspreadoutoverthelargenumberofnails.
Razorbladesthatusemultiplebladesapplytheprincipleofspreadingouttheforceexertedbyanyonebladeoveralarge
surfacearea.
OtherThingstoTry
Insteadofjustaseat,whynotbuildanicecomfortablebedtosleepon?
Youcanalsoshowhowpressurecanbespreadoutoveralargerareabyusingseveralcupstosupportaperson.Setupa
boardonarowofpapercups,asshowninFigure42-3.Then,haveapersonstandontheboard.Ifyouhaveenoughcups,
youshouldbeabletostandontheboardsupportedbythepapercups.Somecupsarestronger thanothers,soyoumay
havetoexperimenttodeterminehowmanyyouneed.Placingthemevery2inchesorso,however,isagoodplacetostart.
154
Figure42-3Theperson’sweightisdistributedoverseveralcups.
ThePoint
Pressureisforcedividedbyarea.Thelargertheareaaforceisappliedover,thesmallerthepressureexperienced.
155
Project43
Blowinghangingcansapart.WhatBernoullihadtosayaboutthis.
TheIdea
Hereisasimplechallenge:hangtwoemptysodacansfromastring,separatedbyafewinches,andthenblowthemapart.
Whetheryouuseyourlungsorahairdryer,theresultwillbethesame.
WhatYouNeed
2emptysodacans
2strings
blowdryer
Method
1. Attachthestringstothecanandhangfromasupport(suchasaringstand).
2. With the blow dryer (or your own breath if you are good at blowing out birthday candles), direct a streamof air
betweenthecans.Avoidblowingsohardthatthecansstartbouncingaround,whichwillonlyservetoconfusethe
issue.
3. Observewhathappens(Figure43-1).
ExpectedResults
Insteadofblowingthecansapart,theairstreamwilldrivethemtogether.Infact,theharderyoublow,thegreatertheforce
thatmovesthecanstogether.
156
Figure43-1Greaterairvelocityresultsinlowerpressuretodrawcantogether.
WhyItWorks
WhatisgoingonherewasexplainedbyBernoulli.Akeyconsequenceoftheprinciplethatbearshisnameisthefasterair
moves,thelowertheairpressure.Thisisthemechanismforairplanelift.Thecontouroftheairplanewingdirectsairabove
thewingatahighervelocity,resultinginalowerpressureabovethewing.Aspoileronaracecardoesthesamething,but
upsidedown.AsailboattakesadvantageofBernoulli’sprinciplebydirectingtheair infrontofthesailatahighervelocity.
Thisproducesagreaterforceonthewingandenablesthesailboattomoveatagreatervelocitythanthewinddrivingit.
OtherThingstoTry
Astreamofmovingairfromablowdryerkeepsanobject,suchasaping-pongball,suspendedinmidair.SeeFigure43-2.
ThisisanotherexampleofBernoulli’sprinciple.Thefastermovingairinthecenterresultsinapressuregradientthatdraws
theballintotheairsteamabovetheblowdryer.
AnotherwaytoexploreBernoulli’sprincipleistotakeasheetofpaperandholdithorizontallyinfrontofyourmouth.The
paperwilldroopdowninfrontofyou.Blowingacrossthetopofthepaperwillreducethepressureabovethepaper,causing
ittodefygravityandstraightenouthorizontally.
Ifyouplaceadowelinthecenterofarolloftoiletpaperanddirectablowdryeracrossthetop,youcanrunouttheentire
roll! Ifanyonecomplainsabout themess, justsayyouhad todo it toproveBernoulli’sprinciple. (Then,ofcourse,please
157
cleanupthemess.)
Figure43-2PingpongballlevitatedbyBernoulli’sprinciple.
ThePoint
AccordingtoBernoulli’sprinciple,movingairresultsinlowerpressure.
158
Project44
Centerofmass.Howtobalanceabroom.
TheIdea
Experiencetellsusthatobjectsaremorestableiftheircenterofmassislowertotheground.Basedonthat,youmightthink
itwouldbeeasiertobalanceabroomwithbrushsidedown.Thisexperimentletsyouanswerwhetherthatisthecase.
WhatYouNeed
meterstick
2books(physicstextbooksarepreferred,butEnglishtextbooksworkalmostaswell)
ducttape
alternative:youcandothiswithanactualbroomoranyotherobjectthathasmuchofitsmassconcentratedatonly
oneend.Thiscanbedonewithmodelingclayattachedtotheendofabroomorpencil.
Figure44-1Whichiseasiertobalance?
Method
1. Insertthemeterstickbetweenthetwobooks,soaninchortwoofthemeterstickprotrudesbeyondthebottomofthe
book.
2. Securethebooktothemeterstick.
3. Predictwhichendofthemeterstickyoushouldsupporttomosteasilybalanceit:theheavyendorthelightend?
4. Supportthemeterstickontheheavyend.
5. Trythiswiththeheavyendupandthelightendsupportedbyyourhand.
ExpectedResults
Onemight say thatwith themassat thebottom, themeterstickwill bemorestable.The logic is, likewithadrag racer,
placingthecenterofgravityatthelowestpointpossibleresultsinthegreateststability.Theresultsoftryingthis,however,
159
revealtheoppositetobethecase.Itiseasiertobalancethemeterstickwiththeweightatthetop,notthebottom.
WhyItWorks
Thereasonforthisunexpectedbehavioristhatasmallmovementatthesupportendcreatesagreatertorquewithmostof
theweightlocatedattheoppositeend.Thisgivesthepersontryingtobalancethemeterstickgreatercontrol.Thisprinciple
isusedbytightropewalkerswhocarryapolewithaweightattheendtohelpestablishbalance.
OtherThingstoTry
Skyscrapersareoftensubjected tovibrationwhen they’reexposed towind.Sometimes,addingmass to thestructurecan
dampdowntheextentoftheswaying.Applytheresultsofthisinvestigationtodeterminewhetheritismoreadvantageousto
addmasstothetopfloorortothefirstfloorofaskyscraper.Lookupaspecificexampleofhowmasswasaddedtothe
top,ratherthanthebottom,oftheSearsTowerinChicago.
ThePoint
Addingmassawayfromthepivotpointincreasesthetorqueproducedattheotherend.Thisprovidesagreaterdegreeof
controltotheendwithouttheweight.
160
Project45
Asimplechallenge.Moveyourfingerstothecenterofameterstick.
TheIdea
OK.Hereisanothersimplechallenge:Getameterstick.Placeonefingernearthe15cmmarkandtheotherfingernearthe
65cmmark.Movebothfingerstogetheratapproximatelythesamevelocity,sotheymeettogetheratthe40cmmark. Is
thataskingtoomuch?
WhatYouNeed
meterstick
Method
1. Placethemeterstickhorizontallyandholdwithanoutstretchedfingerfromeachhand.
2. Placeyourfingersnearthe15and65metermarkingsofameterstick(Figure45-1).
3. Movebothfingersatroughlythesamevelocity,sotheymeetatthe40metermark.
ExpectedResults
Thisdoessoundsimpleenoughbutthisisjustaboutimpossibleformostpeopletodo.Youwillfindyoucanonlymovethe
fingerfurthestfromthecenter(theonestartingatthe15centimetermark)untilbothfingersarethesamedistancefromthe
center.Then,theymeetclosetothemiddle(the50cmmark).SeeFigure45-2.
WhyItWorks
Alotofphysicsisactuallyinthislittleinvestigation.Theforceisgreateronthefingerfurthestfromthecenter(becausethere
isgreatertorquetryingtorotatethemeterstickinthatdirection).Thegreatertheforce,thegreatertheforceoffriction.This
resultsinonefingerbeingabletomovemuchmoreeasilythantheother.
161
Figure45-1Thefingerthathasstartedonthe15cmmarkstartstomovewhilethefingeronthe65cmmarkhasn’tmoved
atall.
Figure45-2Bothfingerseventuallymeetatthe50cmline.Notthe40cmline.
OtherThingstoTry
162
Trythiswithdifferentstartingfingerpositions.Youmayalsoneedtoconvinceanyskepticsthatonesideofthemeterstick
doesnothavemorefrictionthantheother.
ThePoint
The furtheraweight is fromapivotpoint, thegreater the force itexerts.Greater forcebetween thesurfaces incontact
resultsingreaterfriction.
163
Project46
Centerofgravity.Howfarcanastackofbooksextendbeyondtheedgeofatable?
TheIdea
Youhavefourequalbooks.Eachis10incheslong.Youcanstackthemupanywayyoulike.Howfarfromtheedgeofthe
tablecanyouplacethefaredgeofthetopbook,soallfourbooksstillbalanceovertheedgeofthetable?Thiscanbe
donebyintuitionoranalytically.Italsomakesagoodcompetitionactivity.
WhatYouNeed
stackofobjects:bricks,blocks,books,oremptyCDcases
ruler
Method
1. Beforeyoustart,stateyourprediction.Howfarbeyondtheedgeofthetablewillthefourbooksgo,sotheybalance
withoutfalling?SeeFigure46-1.
2. Takethefourbooksandarrangethem,sothefourthobjectextendsasfarfromtheedgeofthetableaspossible.
3. Repeat with any other number of books. This makes a good friendly competition to see who can produce the
greatestoverhang.
ExpectedResults
Ifyouhavefoursimilarobjects,10incheslong,themaximumoverhangwillbejustunder9.4inches.Ingeneral,ifyouhave
fourobjectswhoselengthisL,themaximumoverhangis(justunder)0.94×L.
164
Figure46-1Howfarcanthebooksextendbeyondtheedgeofthetable?
WhyItWorks
Thebooks(orotherobjects)willbalanceonthetableifthecenterofmassforallthebooksliesoverthetable.Ifthecenter
ofmassispositionedovertheedgeofthetable,theentirestackofbookswilltopple.
Let’sstartwithonebook.Thebookbalanceswiththeoverhangnogreaterthanhalfway.Withasecondbookadded,the
equilibriumismaintainedwiththeaddedbookextendingone-quarterofitslengthbeyondthefirst.Asbooksareadded,the
addeddistancethattheentirestackcanbepushedoutisone-halfthelengthofthatofthepreviousbook,asindicatedin
Figure46-2.
165
Figure46-2Spacingforamaximumoverhang.
OtherThingstoTry
Nowthatyougotpastfourbooks,howabout100?Extendingthistoalargenumberofbooks,theoverhangisextendedby
thebooklengthdividedbyone-halfofthetotalnumberofbooks.
Figure46-3
Thetotaloverhangisthesumofalltheindividualextensions.Asanexample,for100books,eachofalength10inches,the
maximumoverhangwouldbe25.9inchesaspicturedinFigure46-3.
ThePoint
Equilibriumismaintainedwhenthecenterofmassiscenteredovertheareaofsupport.
166
Project47
Centerofmass.Theleaningtowerofpizza.
TheIdea
Howfarcananobjecttiltbeforeitfalls?LiketheLeaningTowerofPisa,thestabilityofarectangularorcylindricalobject
depends on its shape.This experiment establishes a simple condition for stability of an object and explores the ideaof
centerofmass.
WhatYouNeed
cerealbox
pizzabox
2pencils
tape
string
2nuts,largewashers,orothermatchedattachableweights
woodenboardtouseasanincline(roughly3ft×4inches×½inch,or1m×0.1m×0.01m)
Method
1. Findthecenterofeachoftherectangularfacesofthebox.
2. Start with the largest face first. Push one pencil through both sides of the box. The pencil should be roughly
perpendiculartothesurfaceitispushedthrough.
3. Tiethestring—oneendtothepencilandtheotherendtothehangableweight.
4. Attachtheotherweighttotheothersideofthepencilasacounterbalance.Youcanusestringifthatmakesthis
easier.
5. Tapetheotherpencilacrosstheincline,somewhereroughlynearthemidpoint.
6. Placetheboxontheincline,sothedownhillsideoftheboxisincontactwiththepenciltapedtotheincline.This
pencilservesasapivotpointtoforcetheboxtorotate,ratherthanslidedown,theincline.
7. Makeyourpredictions.Howfarcanyoulifttheinclinebeforetheboxtopples?
8. Trythiswiththevariousfacesofeachoftheboxes.Canyoudevelopageneralconditionforstability?
9. Youcandothisqualitativelyasdiscussedpreviouslyortakeitastepfurtherandrelatethegeometryoftheboxto
theangleitcantiltatandstillbestable.Canyoupredictthemaximumangleofstabilityforgivenboxdimensions?
ExpectedResults
Theboxwillbestableifthecenterofmass(markedbythepencil) isoverthebaseoftheboxincontactwiththeincline.
Oncetheangleincreasestothepointwhereitisoutsidethebase,theobjectwillrotate.
Objectsaremorestablewhenthecenterofmassisclosesttotheincline.
Becauseapizzaboxhasasquare-topface, itwillbestableuptoa45-degreeanglewhenproppedupwithoneofthe
longedgesplacedalongtheincline,asshowninFigure47-1.
167
Figure47-1Theleaningtowerof“pizza.”
IfA is the lengthof thesideof thebox incontactwith the inclineand ifB is theheightof thebox (for thatparticular
arrangement)abovethe incline, themaximumstableangle isgivenby: tangent (angle)=A/B. (Theanglecanbefoundby
takingtheinversetangentorarctan,whichcanbefoundonmostscientificcalculators.)
For instance, a 17-ounce box of Honey Nut Cherrios has dimensions 12 inches× 7¾ inches× 2¾ inches. The sixpossibleplacementsforthisboxaresummarizedinTable47-1.
AfewoftheseareillustratedinthefollowingFigures47-2,47-3,and47-4.
WhyItWorks
Massiveobjectstendtoactasifalltheirmasswasconcentratedinasinglepointcalledthecenterofmass.Gravitypulling
onthatpointcausestheboxtorotateaboutthepivotpointestablishedbythepencil.Ifthecenterofmassisabovethebase
ofsupport,theobjecttendstorotateinsuchawayastoremainstableontheincline.However,asthecenterofmassmoves
outfromabovethebase,atorqueisapplied,whichtendstorotatetheobject,soitrollsdowntheincline.
OtherThingstoTry
Thisapproachcanbeeasilyextendedtoothershapes.Youcancutacardboardtubeatananglenearthebottomedgeto
forma replicaof theLeaningTowerofPisa (notnecessarily toscale).Try tocut it insuchaway that the tube remains
standingattheminimumpossibleanglewithrespecttotheground.Thiswouldmakeafunchallengeforagroup.Thiscanbe
doneeitherby trial-and-errororbycalculationsbasedonanapproximately rectangularcross-section.By theway, thereal
LeaningTowerofPisaiscurrentlytiltedat5.6degreesandwouldtoppleifthatangleincreased1.4degrees,accordingtoa
tilt angle of 7 degrees (Rossella Lorenzi, Discovery Channel Online News www.discovery.com, September 1998,
http://www.endex.com/gf/buildings/ltpisa/ltpnews/ltpdisc092298.htm).Themassdistributionof the LeaningTowerofPisa is
notstrictlythatofacylinderandcurrentlybenefitsfromvarioustechniquesofshoringitup.
Table47-1
168
Figure47-3
Figure47-4
Bythesametoken,youcancutcardboardmailingtubesin3″,6″,9″,and12″lengths.Then,placethemonaboardwithastoptokeepthemfromsliding.Asyoutilttheboard,eachofthetubeswilltoppleinsequence,startingwiththetallest.
170
Section5
Energy/Momentum
Project48
Thependulumandyourphysicsteacher’sMingdynastyvase.
TheIdea
Energy is neither created nor destroyed; or asphysicists say, energy is always conserved.This project is a test in one’s
confidenceinthistime-honoredprinciple.Thisexperimentcanbedonewithanysizependulum.However,alargependulum
withaheavymassraisesthestakesandincreasesthesuspense.
WhatYouNeed
pendulum
–mass:consistingofanymassthatcanbesecurelysupported(suchasahookedmassorabowlingball)
–stringorcablestrongenoughtosupportthemass
–secureoverheadsupportsuchasaceilingbeamthatcansafelyhandlethemovingmass
fragile object you do not want destroyed by the pendulum. You may want to start with a plastic bottle before
attemptingthisonyourmoreexpensivepottery.
Method
1. Setupthependulum,soitswingsfreely.
2. Setanobjectinthepathofthependulum.
3. Positionthependulummass,soitisbetweentheobjectandtheequilibriumpoint,andjusttouchingthevase.
4. Release,butdon’tpushthependulummassfromitspointofcontactwiththeobject.
5. Letthependulumgothroughafullexcursionfromwhereitwasreleased,andthenback.
ExpectedResults
Ifthemasswasreleasedandnotpushed,itwillnevergohigherthanthepointfromwhichitwasreleased.Thependulumwill
returnto,butneverexceed,thereleasepoint.
For people who are still in the process of developing a sense of confidence in the law of conservation of energy, a
momentofsuspensemayexistasthependulumreturnstoitsoriginalheight.Inanyrealpendulum,thereisacertainamount
offrictioninthepointofcontactandfromairresistance.Becauseofthis,thependulumreturnstoapointslightlylowerthan
thepointfromwhichitwasreleasedfrom.
172
Figure48-1Whatgoesdown,mustcomeup(toalmostthesameheightthatitwasreleasedfrom).
WhyItWorks
Thepotentialenergyofanobjectisequaltoitsweighttimestheheightitisraisedto.Forobjectsreleasedfromrest,asis
thecasehere,thereisnostartingkineticenergy.So,theamountofpotentialenergyyoustartwithequals(orisslightlylower
than) the final kinetic energy. The pendulumwill never quite return to the level that it was released frombecause some
energyis“lostto”frictionasthemechanicalenergyistransformedintothermalenergy.
OtherThingstoTry
Avariationonthisinvolvestherelatedideaofconservationofangularmomentum.Ifyoureleaseapenduluminsuchaway
thatitdoesnothitthevase,nomatterhowmanytimesitswingsbackandforth,itwillnothitthevase.
ThePoint
Theamountofenergycontainedinamovingobject,suchasaswingingpendulum,canneitherbecreatednordestroyed.
173
Project49
Twoslopes.Differentangle,sameheight.
TheIdea
Thisexperimentcompareshowmuchenergyanobjecthasafter followingseveraldifferentpaths.Wecandeterminehow
muchenergyaballhasafterrollingdownaninclinebymeasuringhowfaritrollsoffatable.
WhatYouNeed
2inclinessupportedbyaringstandorastackofbooks(oneinclinethatworkswellwithgolfballsisavinylbullnose
sectionofmoldingavailableathomesupplystores)
2golfballsorothermatchedobjectstorolldowntheincline,suchasmarbles,coffeecans,toycars,oraairtrack
glider
meterstickortapemeasure
optional:motionsensor
Method
1.Setuptheinclinesattwodifferentslopes,asshowninFigure49-1.Allowenoughspaceatthebottomoftheincline
sothatthegolfballsrolloffthetablehorizontally.
2.Avoidananglethatissosevereastocausethegolfballstobounceontheedgeofthetable.
3.Aligntheinclinessotheyarepointinginthesamedirection.
4.Holdthetwogolfballsatequalheightabovethetable.Thismaybeeasierwithtwopeople.
174
Figure49-1
5.Predictwhatyouthinkwillhappenwitheachoftheballs.Whichwillcomedownwiththegreatestvelocity?Thevelocity
canbedeterminedeitherbyusingamotionsensororbycomparingthepointthatithitsthefloorafterrollingoffthe
table.
6.Releasebothgolfballsandcomparetheresultswithyourprediction.
ExpectedResults
Bothballsshouldmovewiththesamevelocity,astheyrollhorizontallyacrossthetable.Theballsthenhittheflooratthe
samedistancefromtheedgeofthetable.
WhyItWorks
Inthis,asinallotherprojects,energyisconserved.Theenergyeachofthetwogolfballsstartsoffwithisthesamebecause
they are released from the same height. This is equal to the object’s weight times gravitational acceleration. All of this
energyisconvertedtokineticenergy(neglectingfrictionallosses)whentheballsgettothebottomoftheincline.Withequal
kineticenergy,theobjectswillmoveatthesamevelocity.
OtherThingstoTry
Pickoneoftheslopesandholdagolfballontheinclineateachofthreedifferentplaces(forexampleat6-inchintervals
startingfromthetopoftheincline).Predicttheoutcome.Releasetheballfromeachofthethreepositionsandcomparethe
resultswithyourpredictions.Here,theballstartswiththreedifferentamountsofpotentialenergy.Itcomesofftheinclinewith
threedifferentvelocities,asshowninFigure49-2.Accordingtothe lawofconservationofenergy(neglectingfriction), the
potentialenergy(mgh)isconvertedtokineticenergy(½mv2).Thedistancethatahorizontalprojectiletravelsisproportional
toitshorizontalvelocity.Asaresult,therangeordistancealongthefloorwillgoasthesquarerootoftheheightabovethe
table.
ThePoint
Total mechanical energy (consisting of kinetic and potential energy) is conserved unless some energy is consumed in
overcomingfriction.Objectsreleasedfromthesameheighthaveequalpotentialenergy.Whenthisenergy isconvertedto
kineticenergy,thepaththeobjectsmovetowardthebottomisnotimportant.
175
Project50
Racingballs.Thehighroadversusthelowroad.Whichwins?
TheIdea
Whichpathwilltaketheleastamountoftimeforarollingball?
apaththatisstraightandhorizontal,or
alongerpaththatstartshorizontally,dipsinacurvedpathwithoutexcessivefriction,andthenreturnstothesame
horizontallevelitstartedfrom.
Onepath isshorter.Soyoumight think itwill take the leastamountof time.Becausebothobjects return to thesame
height, theywindupwith thesameamountofenergy.Howdoes thataffect theoverall time for the journey?Figure50-1
showsthetwopaths.
WhatYouNeed
2golfballs
materialstobuildatrack:
–flexibleflatwoodenmolding—onesection8feetlongandonesection6feetlong
–asideboardabout6feetlong
–acoupleof2″×4″×6″piecestoserveasabase–smallflat-headwoodscrews
–smallwoodenormetalright-anglebraces—1inchcornermoldingwillwork
–optional—abasketorplasticcup
Thistypeofapparatusisalsocommerciallyavailable,asshowninthelaterFigures50-6and50-7.
Method
Buildingthetrack
1.Draworsketchtheshapeofthecurvedsection.Thiscanbetraced,copied,oreyeballed.Amoreexactingapproach
wouldbetogenerateageometriccycloidandformthecurveintothatshape.
2.Attach theflexible track to thesideboardwithastraightsection,adownwardcurve returning toasecondstraight
section. Attach the braces to the side board and secure the flexible track to the braces. (Keep the profile of the
screwsaslowaspossible,soitdoesnotinterferewiththemotionofthegolfball.Itmaybenecessarytocountersink
thescrewhole,sothescrewheadisbelowthelevelofthetrack.)
177
Figure50-1Bothballstartatthesameheight.CourtesyDanSilver.
3.Attachthestraightsectiontothesideboard,afewinchesabovethesectionwiththedetour.
4.Attachthebaseinsuchawaythatthepaththeballwillfollowisslightlytiltedtowardthesideboard.Thisminimizes
thefrictiontheballencounters,butitwillallowtheballtorollwithoutfallingoffthetrack.
5.Youmaywanttoaddsomewaytocatchtheballsaftereachracetoavoidhavingtochasethemeverytime.
6.Arampofequalslopeandequallengthisplacedatthestartofeachpathtogiveobjectsracingdownthetwopaths
thesamestartingvelocity.Besuretokeepanyseamsinthetrackaslowprofileaspossible.
Racing
1. Beforedoingthis,observerscanmaketheirprediction.Whichtrackisfastest:a)theflattrackb)thetrackwiththe
detourc)boththesame?
2. Release both balls from the sameheight (above the initial flat section of track) at the same time. Observe the
progressoftheballs.Repeatafewtimestomakesuretheresultsareconsistent.
Comparingenergy
Attheendofthetrack,regardlessofwhichballfinishesbeforetheother,measurethevelocityonthefinalflatsection.You
candothisinseveralways:
1. Useamotionsensortomeasurethespeedoftheballsoneachoftheflatsections.Ifyouhavetwomotionsensors,
youcanmeasurethematthesametime.Ifyouhaveone,youcandothemoneaftertheother.Ineithercase,the
mostdefinitiveconclusionwillresultfromagoodstatisticalsample.
2. Anotherwaytomeasurevelocityistotakeadvantageofthefactthattherangeofahorizontalprojectile(asyou
sawinProject6)dependsonlyon itsheightabovethegroundandthevelocitywithwhich it leavesthehorizontal
surface.IntheapparatusshowninFig50-1itisclearthatthestartingandstoppinglevelforeachofthetracksisat
adifferentheightabovetheground.Thisdoesnotaffecttheirmovementrelativetoeachother.However, itdoes
givethetrackontopanadvantagewhereitwilllandunlesstheheightdifferenceiscompensatedforbyraisingthe
landing level. If this is done, balls thatmove the samedistancealong thegroundhave the same velocity. Some
designssuchasatrackusedatMichiganStateUniversity(http://demo.pa.msu.edu/PicList.asp?DID=DID18)arebuilt
withthetwotracksside-by-side,sothisvelocitycomparisoncanbemademoreeasily.Plansforasimilarracing-ball
track are available from the University of Maryland Physics Department at
http://www.physics.umd.edu/deptinfo/facilities/lecdem/services/demos/demosc2/c2-11dwg.jpg.
ExpectedResults
Theballontheflattrackwillmovewithconstantvelocity(Figure50-2).
Theballfollowingthedetourwillincreaseitsspeed,soitisgoingfastenoughtomakeupfortheextradistance(Figure
50-3).
Oncereturningtotheoriginalheight,theballthatwentthroughthedetourwillreturntoitsoriginalspeed.However,nowit
willbeaheadoftheballontheflattrack.Theballonthedetourwillreachtheendofthetrackfirst(Figure50-4).
178
Figure50-2Bothballsbeginwiththesamevelocity.CourtesyDanSilver.
Figure50-3Theballonthe lowertrackpicksupenoughspeedtomoveaheadofthetopballdespitetheextradistance.
CourtesyDanSilver.
Figure50-4Bothballcompletetheirtripatthesamefinalvelocitybutwiththe lowerballclearly inthe lead.CourtesyDan
Silver.
WhyItWorks
Thestraightpath iseasy.Theball travelswiththesameconstantvelocity it isgivenatthestart. Itdoesnotgainor lose
energy,exceptforthe(relatively)smalllossduetofriction.
Onthestraightsectionofthecurvedpath,thesecondballtravelswiththesamevelocityasthefirst.Asitgoesdownhill,it
picksupspeed.Iftheshapeisright,theincreaseinspeedwillbemorethanenoughtocompensateforthelongerdistance.
OtherThingstoTry
In1696,JohannBernoullichallengedthemostbrilliantmindsofhisdaytosolvewhatisnowknownasthebrachistochrone
problem—basedontheGreek“brichistos”(shortest)and“chronos”(time).Basically,theproblemisthis:findthepathbetween
twopointsatdifferentlevelsthatanobjectactedononlybygravitywilltravelintheleastamountoftime.Thisissimilarto
theracingballconfigurationpreviouslydefined,except,inthiscase,theballsstartfromrestwithoutanyinitialvelocity.
Galileopreviouslyhadattemptedasolutiontothisproblem.ThepathGalileodefinedwasthecirculararcconnectingthe
twopoints.This,althoughagoodapproximation,wasnotthecorrectsolution.
The correct solution was found by five mathematicians who responded to Bernoulli’s challenge. This included, among
others,asolutionbySirIsaacNewton,whichwassubmittedinjustoneday.Thepathtakingtheshortesttimewasfoundto
beamathematicalcurveknownasacycloid.
Acycloidisdefinedbytheequationsx=r(t−sint)andy=r(1−cost),wherercanbethoughtofastheradiusofthecirclethatsweepsoutthecycloidandtistime.
An(inverted)cycloidgenerated(withr=1,tvaryingfrom0to3,andwithxvaluesasnegative) isshowninFigure50-5.
ThisisactuallysimilartoashapegeneratedbyapencilattheedgeofcircleinaSpirograph.
Althoughintheracing-ballscenario,wedohaveaslightheadstartintheformofaninitialvelocity,thecycloidcurveisa
goodapproximateminimaltimepathfrompointAtopointB.
Anextensiontothisprojectwouldbetobuildatrackthatcomparesagolfball followingacycloidcurvewithastraight
pathdown.
179
Figure50-5Curveshapegeneratedbyaninvertedcycloid.
Althoughthelargetrackismorefuntowatch,aminiversionofeitherofthesetrackscanbeassembledfromfoamboard
withatrackshapecutoutbasedontheshapeinFigure50-5andgluedtothebaseboard.Aclearplasticmodelcanalso
workandofferstheaddedadvantageofworkingwithanoverheadprojector.
A track system that can be used to study various aspects of conservation of energy can also be purchased. Two
examplesareshowninFigures50-6and50-7.
Figure50-6Horizontalracingballtrack.CourtesyPASCO.
180
Figure50-7Brachistochronetrackandstraightincline.CourtesyPASCO.
ThePoint
Thepaththattakesadvantageofincreasingthevelocityduringpartofthetriptakeslesstimethanoneofconstantvelocity.
Thisprojectdemonstratesthat(asidefromfrictionallosses)energyisconserved.Asthepotentialenergyisreduced,itis
transformedintokineticenergy.Becausebothballshavereturnedtotheiroriginalheightandfinishedwiththesamevelocity,
weconfirmthatkineticenergyisconserved,regardlessofthepathtraveled.
181
Project51
Linearmomentum.Wherecanyoufindaperfect90-degreeangleinnature?
TheIdea
Canyouthinkofanythingthatformsaperfectrightangleinnature?Oneexampleofarightangleisthefractureplaneof
body-centeredcubiccrystal,suchascalcite.Thisexperimentexploresanotherexampleofanaturalrightanglethatresults
fromanelasticcollisionbetweentwoobjectsofequalmass.
WhatYouNeed
2low-frictionobjectsofequalmass.HoverPucksareexcellentforthis.Penniesonasmoothtablecanalsowork.
flat,levelsurface
protractor
2lengthsofstring
Method
1. Markthestartingpointof thefirst (stationary)puck. (Findareasonableflatplaceonthefloor toprevent thefirst
puckfromdriftingawayprematurely.)
2. Placethesecondpuckashortdistancefromthefirstone.(Dowhatworksforyou,but18inchesmaybeagood
startingpoint.Ifyouaredoingthiswithpennies,youprobablywanttoshortenthistoafewinches.)
3. Pushthesecondpuck(theshooter) towardthestationarypuck.Aimsothecollision isataglancingangle, rather
thanheadon,hittingthestationarypuckoff-centerasshowninFigure51-1.
4. Markoneormorepointsalongthepathofeachofthepucksafterthecollision.Youmayfindafewextrasetsof
handsarehelpfulhere.
5. Takeapieceofstringandplaceoneendat thecenterof thestationarypuck.Place theotheralong thepath it
traveled.
6. Placetheotherpieceofstringwithoneendalsoatthecenterofthestationarypuckandtheotheralongthepathof
thepuck.
7. Measuretheanglebetweenthetwostrings.
182
Figure51-1Apuck(movingtowardyou)abouttohitastationarypuck.
8.Getabetterstatisticalsamplebyrepeatingthisafewtimesandtakingtheaverage.Ifyourcollisionistoodirect,your
anglewillbezeroorclosetoitandshouldn’tbeincludedinyouraverage.
ExpectedResults
Theanglethetwopathsmakeshouldformarighttriangle,aspictureinFigure51-2.Oneexceptionisifthemovingpuckhits
alongthecenterlineofthestationarypuck,itmaystopandsendthestationarypuckmovingalongthesamepath.
WhyItWorks
Whentwoobjectscollide,momentum(givenbymasstimesvolume)isconserved.However,forelasticcollisions,suchasare
beingexplored here, kinetic energy is also conserved. The only way kinetic energy can be conserved is for the colliding
objectstoformaperfectrighttriangle.
Kineticenergyisgivenbyone-halfthemasstimesthevelocitysquared(or½mv2).Ifvcisthevelocityoftheshooterbefore
thecollision,andvbisthevelocityoftheshooterafterthecollision,thenvaisthevelocityofthestationaryobjectafterthe
collision.(Thereis,ofcourse,novelocityforthestationaryobjectbeforethecollisionbecauseitisstationary.)Conservation
ofenergygivesus:
Becausethemassisthesameforeachobject,thisreducesto:
ThisistheformatofthefamiliarPythagoreanformula(c2=a2+b2),whichappliesonlytorighttriangles.Figure51-3may
helpvisualize this.Because thevelocitiesmustbeconsistentwith thiscondition, theangle the twoHoverPucksmoveat
mustbearightangle.
OtherThingstoTry
Thisexperimentcanalsobedoneonapooltable.However,Ihaveyettoknowofanyoneactuallyimprovingtheirgameby
applying the laws of physics. The felt of a pool tablemay introduce enough friction to prevent the collisions from being
183
completelyelastic.Asheetoffoamboard,asshowninFigures51-4and51-5,canhelpthecollisionbesufficientlyelasticto
beat(nearly)a90-degreeangle.
Figure51-2Afterthe(nearlyelastic)collisionbothpucksmoveoffat90degrees.
Figure51-3ConservationofenergyrequiresthattheHoverPucksmoveoffatrightangles.
184
Figure51-4Thesolidballishittingthestrippedball.
Figure51-5Elasticcollisionfromobjectsofequalmass.
Whenresearchingthecollisionsofsubatomicparticles,sometimestheincomingparticlestrikesastationaryparticleofthe
samemass.Acollisionbetweenamovingprotonandastationaryprotonmeetsthesecriteria.Becausesubatomicparticles
followthelawofconservationofmomentum,thetrajectoryofthetwoequalmassparticles(absentanymagneticfields)as
theymoveoffisatacharacteristic90-degreeangle.
ThePoint
Conservationofkineticenergyforelasticcollisionsrequirestheangleformedbythecollidingobjectstobearightangle.
185
Project52
Elasticcollisions.
TheIdea
Whenoneobjectstrikesanother insuchaway that theobjectsbounceoffeachother, thecollision issaid tobeelastic.
When this happens,whatevermomentum you start offwith, you have at the end. In the case of an elastic collision, the
objectsalsomoveoffwiththesameoverallkineticenergytheystartedwith.Inthisproject,weexplorewhathappenswhen
collisionsareelastic.
WhatYouNeed
4poolballs(orhardballsorgolfballs)
trackfortheballstorollinonedimension(Thiscaneasilybesetupbytaping2metersstickstoasmoothboard)
largeball,suchasabasketball
smallerball,suchasaping-pongball
optional—aNewton’scradle,asshowninFigure52-1
Method
Oneballhittingthree
1. Placethreeballsofequalmassinthetrack.
2. Placethefourthballafewinchesawayinthetrack.
3. Rolltheball,soitcollideswiththeotherthree.(Thereareseveralotherwaystodothis,includingaNewton’scradle
orfourequalmassslidersinanairtrack.)
Bigball/smallball
1. Placethesmallballontopofthelargeball.
2. Dropbothballstogether.(Caution:dothisinaplacewhere,ifthesmallballgoesflyingoff,itwon’tbreakanything
andwon’thurtanyone. If theballs youareusingaresmallenough, youmaybeable todo this inaclearplastic
verticalguideorinalargegraduatedcylinder.)
186
Figure52-1Conservationofmomentumandkineticenergyrequiresthattwoballshittingthegroupalwayscausestwoballs
toslideout.
ExpectedResults
Oneballhittingfour
The incomingballcomestoadeadstop,asshown inFigures52-2and52-3.Theoutermoststationaryballmoves in the
samedirectionandatthesamevelocityastheincomingball.Theotherthreestationaryballsdonotmove.
Bigball/smallball
Theballsbouncetogether.Afterstrikingtheground,thesmallerballfliesoffwithmuchgreatervelocitythanthelargeball.
WhyItWorks
Withthestackofballs,itisnothardtounderstandhowthemomentumoftheincomingballistransferredtotheballthatgets
knockedoutofthestack.Thisisaclearillustrationofconservationoflinearmomentum.
Butwhyisonlyoneballknockedoutofthestack?Why,forinstance,doweneverhavetwoballsknockedoutwitheach
takingonehalfofthemomentumoftheincomingball?Thatwouldalsobeperfectlyconsistentwiththelawofconservation
ofmomentum. The problem is these collisions are elastic collisions, whichmeans not only ismomentum conserved, but
kineticenergyisalsoconserved.Theonlywaythiscanhappenisforasingleballtoemergefromthestackwiththesame
momentumastheincomingball.
Withthelargeandsmallballs,thelargeballhavingalargermassconservesmomentumbycausingthesmallerballwitha
lowermasstoflyoffwithalargervelocity.
OtherThingstoTry
ANewton’scradle,asshowninthepreviousFigure52-1,isanothergoodwaytostudyelasticcollisions.InaNewton’scradle,
twoballsneverreboundwhenstruckbyasingleballandthreeballsneverreboundwhenstruckbytwoballs.Thisistheresult
ofbothconservationoflinearmomentumandconservationofenergy.
187
Figure52-2Oneballhittingthegroup—beforecollision.CourtesyDanSilver.
Figure52-3Aftercollision—resultsinonlyoneballknockedout.CourtesyDanSilver.
ThePoint
Inanelasticcollision,bothlinearmomentumandkineticenergyareconserved.
Whenmomentumistransferredfromoneobjecttoanother,alargervelocitycompensatesforasmallermass.Inthecase
ofanelasticcollisionbetweenobjectsofequalmass,thisconditioncanbemetonlywhenthesamenumberofballsmove
afterthecollisionasweremovingbefore.
188
Project53
Inelasticcollision.Stickingtogether.
TheIdea
Whenobjectscollide,theyeitherbounceoffeachotherortheysticktogether.
WhatYouNeed
2low-frictioncarts
Velcroorducttape
low-frictiontrack(optional)
motionsensor
indexcard
tape
Method
1. Measurethemassofeachofthetwocarts.
2. AttachVelcrototheendofeachofthecarts,sowhentheymeet,theysticktogether.Youcouldalsouseducttape
formedintoaloopandattachedsticky-sideouttoeachofthecarts.
3. Setupthemotionsensoratoneendofthetable.
4. Placethefirstcartnearthemotionsensor.TheVelcrosideshouldbeinfront,awayfromthemotionsensor.Ifyou
havealow-frictiontrack,placethecartonthetrackinalinepointingawayfromthemotionsensor.
5. PlacethesecondcartnearthemidpointofthetablewiththeVelcrointherear.
6. Itmaybehelpfultoattachanindexcardtothebackofthefirstcarttomakeiteasierforthemotionsensortopick
itup.Ifyoucangetawaywithoutdoingthis,youcanavoidairresistancethatcouldslightlyaffectyourresult.
7. Setupthemotionsensortoreaddistanceandvelocityversustime.
8. Startthemotionsensor.Itshouldbeonthecartsettingandfocusedonthecardofthefirstcart.
9. Givethefirstcartapushinthedirectionofthesecondcart.Itshouldbeslowenoughtogetagoodreadingfromthe
motionsensor,butfastenoughtorear-endthesecondcartandpushitalongforatleastafewsecondsormore.
Thefirstcartcollideswiththesecondtotallyinelastically,whichmeanstheysticktogetherafterthecollision.
10. Whenbothcartsstopmoving,stopcollectingdatafromthemotionsensor.
11. Fromthemotion-sensorgraphs,findthevelocityofthefirstcartbeforethecollisionandthevelocityofbothcarts
joinedtogetherafterthecollision.Thegraphofvelocityversustimemaybealittleerraticrightafterthecollision,
reflectingtheimpact.Pickapointwherethevelocityhassettleddown.
12. Momentumisdefinedasmasstimesvelocity.Comparethemomentumbeforeandafterthecollision.
13. Kineticenergyisdefinedas½timesthemasstimesthevelocitysquared.Comparethekineticenergybeforeand
thekineticenergyafterthecollision.
Figure53-1Inelasticcollisionwithoneorbothcartsinitiallymoving.CourtesyPASCO.
189
The experimental setup is shown in Figure 53-1. (This actually shows a motion sensor at both ends. The previous
procedureusesonlyonemotionsensor,butthiscaneasilyextendedtoincludebothcarts inmotion.Forsimplicity,wewill
startoutwithoneofthecartsstationary.)
ExpectedResults
Themomentumofbothcartsbeforethecollisionshouldequalthemomentumofbothcartsafterthecollision.
Beforethecollision,oneofthecartsisstationary,whichmeansithasnomomentum,sothemovingcartistheonlyone
withmomentumbeforethecollision.
After thecollision,bothcartsstick togetherandmoveoffwith thesamevelocity.Thecombinedmassof the twocarts
togethertimestheircombinedvelocityisthemomentumafterthecollision.
Figure53-2showsthepositionversusthetimegraphbeforeandafterthecollisionobtainedbyamotionsensor.Notice
howtheslopeofthelineabruptlydrops,indicatingthecollision.
Figure53-3 shows the velocity versus time graph before and after the collision. The velocity before and after can be
determineddirectly from thegraph. You can noticea slight downward slope indicating someslowingof the carts due to
friction.Thisisnotashowstopperfortheexperiment,butitshowstheextenttowhichanairtrackcanimprovetheoverall
results.
Themostreliablevelocitymeasurementisimmediatelybeforethecollision.Thecollisionshowssomebouncingaroundand
variabilityinthevelocityforashortperioduntilthetwocartssticktogetherandmoveasone.Thisprovidessomeinsightinto
the nature of inelastic collisions, which result in the loss of kinetic energy (but not linearmomentum). Themost reliable
postcollisionvelocitytouseisthepointwhereanewhorizontallinebegins.Theresultsshouldbefairlyaccurate,butsome
lossesduetofrictionmaybeencounteredwithoutanairtrack.Also,excessivemasscanloaddownthewheelbearingand
increasethelossestofriction.
Figure53-2Motion sensor measurement of distance versus time for an inelastic collision between a moving car and a
stationarycart.
Figure 53-3 Motion sensor measurement of velocity versus time for an inelastic collision between a moving car and a
190
stationarycart.
WhyItWorks
Thetotalmomentumbeforeaninelasticcollisionequalsthetotalmomentumafter.
However,unlikeanelasticcollision,thekineticenergyforaninelasticcollisionislessafterthecollision.
OtherThingstoTry
1. Ifyouhavetwomotionsensors,youcanrepeatthiswithbothcarts initially inmotion.Youcangetthevelocityof
eachcartrightbeforethecartscollideandthevelocityofbothcartstogetherafterthecollision.Bothsensorswill
readapositivevelocitybeforethecollisionasthedistancefromthesensorincreases.Afterthecollision,onesensor
readsapositivevelocity,whiletheotherreadsanegativevelocity.ResultsareshowninFigure53-4.
2. Compare elastic and inelastic collisions using so-called “happy/sad” balls. The balls appear to be completely
identical.However,oneiselasticandbouncesbackfromthefloor,whiletheotherisinelasticanddoesn’tbounceat
all.
3. Hangelasticandinelasticballstoformapendulum.Standupawoodenblockinfrontofthependulum.Swingthe
inelasticballfirst,soitdoesn’tquiteknocktheblockover.Comparethattowhathappenswiththeelasticballswung
underthesameconditions.Elasticcollisionsresultindoublethechangeinmomentumasaninelasticcollisionunder
thesameconditions.Thisisbecauseintheelasticcollision,themomentumnotonlystops(asitdoesinthecaseof
aninelasticcollision),butitalsoreversesitselfintheotherdirection.
ThePoint
In an elastic collision, the objects bounce off each other in such as way that linear momentum and kinetic energy are
conserved.Thisistruetotheextentthatnoexternalforceoccursduringthecollision.
Inaninelasticcollision,theobjectsinteractinsuchawaythatlinearmomentumisconserved(aslongasnoforcesaffect
thecollision).However,kineticenergyisnotconservedinaninelasticcollision. Inaperfectly inelasticcollision,theobjects
sticktogetherandmoveafterthecollisionasiftheywereasingleobject.
Figure53-4 Motion sensor measurement of velocity versus time for an inelastic collision between a moving cart and a
secondmovingcart.
191
Project54
Impulseandmomentum.Eggstremephysics.
TheIdea
Whatdoyouthinkwillhappenifyouthrowaraweggashardasyoucanatablanketheldvertically?Thereisreallyonlyone
waytofindout.Thisexperimentgivesyouanopportunitytoexploretherelationshipbetweenmomentumandimpulse.
WhatYouNeed
1rawegg
blanket
3people
mopandpapertowelsforcleanup(veryoptional)
Method
1. Hold the blanket vertically, with the bottom edge curled out to form an overhang, as shown in Figure 54-1. This
requiresatleasttwopeople.
Figure54-1Throwingaraweggatablanket.
2.Thethirdpersonthrowstheeggattheblanket.Don’tholdback.Giveitagoodshot.Youcanthrowashardasyoucan
withouthavingtheeggbreakinyourhandsasyouthrow.
ExpectedResults
Youknowwhatwillhappenifyouthrowaraweggagainstacinder-blockwall.However,iftheeggisstoppedbytheblanket,
thedecelerationoccursoverasufficientlylongtime,whichpreventstheeggfrombreaking.
WhyItWorks
Momentumischangedbyaforceexertedovertime.Theabilitytochangeanobject’smomentumiscalledimpulse,whichis
definedastheforceexertedmultipliedbythetime.Anytimeanobjectisbroughttorest,thechangeinmomentumequalsthe
momentumtheobjecthadtostart,appliedintheoppositedirection.Theimpulsetobringthatobjecttorestcancomefrom
anycombinationofforceandtime,whichwhenmultiplied,equalthemomentumchange.
Iftheobject’smomentumchangesinashorttime,whichwouldoccurifaneggisthrownatacinderblockwall,theforceis
192
greater.However,iftheeggisthrownatablanketthatbringstheeggtoastopoveramuchlongerperiodoftime,theforce
ismuchsmaller.Thisiswhytheeggdoesnotbreakwhenit’sthrow,atablanket.
OtherThingstoTry
CheckouttheESPNvideoRelaxingwithMomentumthatshowswhathappensifyoudropawatermelonfromadivingboard
ontoconcrete,comparedwithdroppingawatermelonintothewater.
ThePoint
Themomentum to stopanegg thrownagainstawall andablanket is the same. However, the force in the case of the
blanketisspreadoveragreatertimeandismuchsmaller.
193
Project55
Usinggravitytomoveacar.
TheIdea
Energycanneitherbecreatednordestroyed.Oneformofenergy,however,canbechangedintoanotherformofenergy.For
instance,thecombustionthatoccursinacarengineproducesheatenergy,which,inturn,isconvertedtomechanicalmotion
bythemotor.Inthisproject,youconvertgravitationalpotentialenergyintomechanicalenergy.
WhatYouNeed
wheels:oldCDsorDVDs
posttoholdtheweight:adowel1minlengthand½to1inchindiameter
1kgweight
string
axles(dowelsworkwell)
materialstobuildthebodyofthecar
plumbingfittingorablockofwoodtoattachtheposttothecarbody
tapemeasure
stopwatch
Method
1.Assemblethecar.UseFigure55-1asaguide,butfeelfreetodevelopandbuildyourownconcept.
2.Thebasicdesigncriteriaforthecarincludes:
–TheCD(orequivalent)usedforwheelsshouldturnfreely.
–Thedescendingmassshouldfreelyturnanaxletoproduceforwardmotionofthecar.
–Thecarshouldbebalancedwiththemassinbothelevatedandfallingpositions.(Remember,a1kgmassraised1
meterabovethegroundcanexertalotoftorquethatcouldtopplethecar.)
–Themassshouldfallontothecarafteritdescends(ratherthandraggingalongtheground,whichcanlimithowfarit
goes).
–Thereshouldbeenoughsymmetrybetweenleftandright,sothecarmovesforward,ratherthanturning.
194
Figure55-1Kilogramcar.
3.Wrapthestringaroundoneoftheaxlesandattachtheotherendtotheweight.Decideifyouwantfront-wheelorrear-
wheeldriveandwrapaccordingly.
4.“Arm”thecarbyraisingthemassandleavingsomeofstringstillwrappedaroundtheaxleitwillturn.
5.Orientthecaronadesignatedcourse,andthenreleasethemass.
6.Measurehowfaritgoes.
7.Ifseveralindividualsorgroupsareinvolved,itmaybefuntodothisasaracetoseewhichcargoesthefarthestor
whichcarcrossesthefinishlinefirst.
ExpectedResults
Itmighttakeafewhourstobuildthecar(s),dependingonwhatmaterialsareavailable.Ifbuiltcorrectly,thecarshouldmove
asthemassdescends.Oncethemassfallsandcomestorest(somewhereonthecar),thecarhasenoughmomentumto
keepmoving.
WhyItWorks
Amassataheightcontributesanamountofenergyequaltoitsmasstimestheheightabovethegroundtimesgravitational
acceleration. Inthiscase,1kgdroppingadistanceof1meterwillcontribute9.8 joulesofenergy. (One joule isaboutthe
amountofenergyneededtoliftanapple1meter.)
OtherThingstoTry
Avariationof this is touseamousetraptosupply theenergy.Themousetrap isstarted in theopenposition.Aswiththe
previouskilogramcar,thepotentialenergystoredinthespringofthemousetrapistransferredtotheforwardmotionofthe
car.
ThePoint
Energyisconserved.Thepotentialenergyyoustartwithequalsthekineticenergygiventothecar(plusanyenergylostto
friction).
195
Project56
HowcanCSImeasuremuzzlevelocity?Theballisticpendulum.
TheIdea
Youcantellhowfastanobject,suchasabullet,ismovingbyhowitaffectsthemomentumofanotherobject.
WhatYouNeed
projectileandlauncher:
–golfballandaramp
–precisionprojectilelauncher
–hand-thrownhardballorgolfball
balancetomeasuremass
box
tape
string
ringstandorimprovisedsupport
protractor
meterstick
Method
1.Build(orbuy)areceiverboxthatmeetsthefollowingconditions:
–Themovingprojectileshouldbecaughtandretainedinthebox.Liningtheinteriorwithdouble-sidedducttapeorfoam
rubbercanservetocapturetheprojectile.
–Theboxissuspendedfromtheringstand.
2.Suspendtheboxfromtheringstandusingthestring.
Determinethemassoftheprojectile.
Determinethemassofthecatcherboxandincludeanyofitscontents.
Directtheprojectiletowardthecatcherboxandallowtheboxwiththeprojectilecaughtinsidetoswingupward.
Measure the maximum height above the initial starting position that the catcher box and the projectile reach.
(Alternatively,theangleandradiusofthependulumformedbythesupportedcatcherboxcanberecorded.)
ThebasicdesignoftheapparatusisshowninFigure56-1.
Thevelocityoftheprojectilecanbedeterminedfromthefollowingequation:
wheremisthemassoftheprojectile,Misthemassofthe“catcherbox,”gisthegravitationalconstant=9.8m/s2,andhis
theheightthatthecatcherboxisliftedbythemomentumoftheprojectile.
196
Figure56-1Ballisticpendulum.
ExpectedResults
Themoremomentum theprojectilehas, thegreater theangle thependulumswings through.Foragivenmass,agreater
velocitycausesagreaterprojectile.
WhyItWorks
Themomentumoftheprojectile(“bullet”)istransferredtothebox.Thegreaterthemomentumoftheprojectile,thehigherthe
boxisdriven.
OtherThingstoTry
Asemiqualitativeversionofthisconsistsofplacingacardboardboxfilledwithtissuepaperonthefloorandcomparingthe
distanceitmoveswithballsrolledorthrownintoitatdifferentspeeds.Thiscanberefinedbymeasuringthecoefficientof
kineticfrictionbetweentheboxandthefloorandthedistancetheboxslidesalongthefloor.Useoftheequationsofmotion
canbesolvedtodeterminetheinitialvelocityofthebox.
Variousballisticpendulumdesignsarealsoavailablefromsciencesupplycompanies.
ThePoint
Thevelocityofamovingobjectcanbedeterminedbymeasuringitseffectaftercollidingwithanotherobjectofknownmass.
Theballisticpendulumisbasedonconservationofmomentumappliedtoapendulum.Thelargerthevelocityoftheincoming
object,thehigherthependulumswings.
197
Project57
Angularmomentum.Ridingabike.
TheIdea
Abicycleisunstablewhenitisstationary.Ifyoutrytobalanceabikethatisnotmoving,itwillfall.Thisexperimentexplores
howitispossibletodefygravityandrideabike.
WhatYouNeed
rope—aboutameter(aboutayard)inlength
bicycletire
dowelorsectionofbroomhandletofitsnugglyintotheaxleofthetire
Method
1. Attachtheropetotheaxleofthebicycletire.Thetireshouldbeabletoturnfreelyaroundtheattachmentpoint.If
thereisnoaxle,insertacylindricalpieceofmetaloradowelforthetiretorotatearound.
2. Suspendthetirefromtherope,soittanglesfreely.Eitherholdtheotherendoftheropeinyourhandorattachitto
somethingoverhead.
3. Holdingthetireverticallybytheaxle,spinthetire.
4. Withthetirespinning,releasethetire,soitissupportedbytherope.
5. Trythiswiththetirespinningrapidlyandslowly,asshowninFigure57-1.
ExpectedResults
Thefirstthingtonoticeisthetirewillremaininclosetotheverticalposition.Also,itdoesn’ttakemuchofaspintokeepthe
tire stable. You should also be able to observe that if left alonewith the tire near the vertical position, the spinning tire
rotatesaboutthepivotpointestablishedbytherope.Thisiscalledprecession.
198
Figure57-1Itiseasyforaspinningbicyclewheeltoremainvertical.CourtesyPASCO.
WhyItWorks
Afullexplanationofthissimplesituationcangetcomplicatedinahurry.Thebasicideaisthataspinningtirehasangular
momentum.Gravity tries to rotate the tire from the vertical position that it is spinning in to the horizontal position that a
nonrotatingtirewouldbein.Theforceexertedbygravityproducesatorquethatisatrightanglestoboththeforceexerted
bygravityandthedirectionoftheangularmomentum,whichisalongthelineoftheaxle.Thisnotonlykeepsthewheelfrom
falling,butitalsocausesittoprecessinacircle.Thisformsthebasisforgyroscopicmovement.
OtherThingstoTry
Likeabicycle,atoygyroscopebecomesstableonlywhenithassufficientangularmomentumtocounterbalancethepullof
gravity.Asanextension,studyagyroscope.Observewhathappenswhenitsturningaxisisdisplacedfromastableposition.
Whataffectstherateofprecession?
ThePoint
Abicycletireisstablewhenitisrotatingbecausethetirehasangularmomentum.ThegravitationalattractionoftheEarth
exertsaforcethatwouldpullthetiretoahorizontalpositionwereitnotfortheangularmomentumofthespinningtire.The
interactionofthetorquecausedbygravityandtheangularmomentumofthespinningtireresultsintheprecessionofthetire
aboutthepivotpoint.
199
Project58
Momentofinertia.Iceskatersanddumbbells.
TheIdea
How do ice skaters get spinning so rapidly?Where do they suddenly get the energy? Are they violating conservation of
energy?Thisprojectexploreshowthisworks.Theterm“dumbbells”shouldinnowaybeconstruedtorefertotheskatersor
theexperimenters(orthewriterofthisbookforthatmatter).Theyrefertoactualdumbbells.
WhatYouNeed
(low-friction)rotatingstool
2masses,suchasapairofdumbbells(5kgorgreater)
1person
bicycletiremountedonanaxle
Method
1. Sitonthestoolwhileholdingthetwomasses.
2. Whilesittingandbalancingonthestool,rotatebypushingoffwithyourfeetorbybeingpushedbysomeoneelse.
3. Liftbothfeetfromthefloor.
4. Startwithbothmassesextendedoutatarm’slength.Then,bringtheminclosetoyourbody,asshowninFigure58-
1.
ExpectedResults
Extendingyourarmsslowsyoudown;bringingthemclosertoyourbodyletsyouspeedup.Therotationalspeed(orangular
velocity)isgreaterwhenthemassesareclosesttothecenterofrotation.Thisworksbestifthestoolrotatesveryfreelywith
aminimumof friction. The stool can be picked upat a yard sale or purchased commercially. There is also usually less
frictionforalower-massperson.
200
Figure58-1Pullinginyourarmscausesyoutospinfaster.CourtesyPASCO.
WhyItWorks
Thisprojectisanillustrationoftheprincipleofconservationofangularmomentum.Angularmomentumforarotatingmass
increaseseitheriftheobjectrotatesfasterorifthereismoremassatagreaterdistancefromthecenterofrotation.Ifthe
mass is moved further from the center of rotation, the angular velocity must increase to keep the angular momentum
constant.
OtherThingstoTry
Spinningabucketonarope
1. Sitonthestoolwithbothfeetoffthefloor.
2. Swingthebucketinacircularpathparalleltothefloor.
3. Observetheeffectofswingingfasterandslower.
4. Observetheeffectofusinglongerorshorterlengthsofrope.
Themainthingyounoticeisyourotateintheoppositedirectionthatthebucketisswung.Thefasterthebucketrotatesina
clockwisedirection,thefasteryourotateinthecounterclockwisedirection.Alongersectionofropeturnsyoufasterthana
shortersection.
ThePoint
201
Aspinningobject,suchasaskater,mustconserveangularmomentum.Amovementofmassclosertothecenterofrotation
iscompensatedbyanincreaseinhowfasttheskaterrotates.
202
Project59
WhatcausedVoyagertopointinthewrongdirection?
TheIdea
TheVoyager programproduced someof themost remarkable spacecraft ever built, providing an unprecedented viewof
nearlyeveryplanet in the solar system.AsVoyager II approached theplanetUranus, thespacecraft precisely trained its
instrumentson thatplanet’ssurface to takeadvantageof theshortwindowofopportunity togethigh-resolution,close-up
pictures.Justasthereel-to-reeltaperecorderonthespacecraftturnedontocapturethishistoricmoment,theorientationof
thespacecraftwasthrownoutofwhackandthenavigationalsystemhadtocompensatewithlast-minutecorrections.This
projecthelpsyouinvestigatewhythiscouldhavehappened.
WhatYouNeed
freelyrotatingstool
bicycletirewithhandles(themoremassivethebetter)
2people
Method:
1. Sitontherotatingstoolasbefore.
2. Havesomeonehandyouthebicycletirethathadpreviouslybeensetintomotion.SeeFigure59-1.
3. Startwiththetireinahorizontalposition.
4. Withthetirerotating,turnthetireupsidedown(soitisnowspinningintheoppositedirection).
5. Waitafewseconds.Then,turnthetireupsidedownagain.
ExpectedResults
Youwillrotateonthestoolintheoppositedirectionfromwhichthetireisrotating.Whilechangingthepositionofthetire,you
willfeelasurprisinglystrongforce,asifyouwerepushingagainstasolidwall(Figure59-2).
WhyItWorks
Startingfromrest,boththepersonandthestoolhavezeroangularmomentum.Forangularmomentumtobeconserved,itis
necessary that the person on the stool rotate in the opposite direction as the rotation of the tire to preserve angular
momentum.Whenthereel-to-reeltaperecorderonVoyagerIIturnedontorecordthespectacularimagesofUranusforthe
first time in history, it began turning with a new angular momentum. See Figure59-3. Just like the person on the stool,
Voyagerbegantoturnintheoppositedirectionasthetaperecordertoconserveangularmomentum.
203
Figure59-1Arotatingwheelhasangularmomentum.CourtesyPASCO.
Figure59-2Angularmomentumisconserved.CourtesyPASCO.
OtherThingstoTry
Thisprincipleisdemonstratedbyatoytrainrunningonacirculartrack.Thetrackismountedonaplatformattachedtoa
freelyrotatingsupport.Asthetrainmovesinonedirection,theplatformrotatesintheoppositedirectiontoconserveangular
momentum.
Figure59-3Conservationof angularmomentum requiredapositioning correctionaboardVoyager II to compensate for a
rotatingreel-to-reeltaperecorder.SourceNASA.
204
ThePoint
Angularmomentumisconserved.Thisappliestothecasewhereasystemstartswithzeroangularmomentum.
205
Project60
Momentofinertia.Thegreatsoupcanraceorthat’showIroll.
TheIdea
Iftwoidenticalcansarereleasedfromresttorolldownaninclineatthesametime,willthetopcancatchupwiththebottom
can?Doesitmatterwhatthecontentsofthecansare?Thisprojectdealswithhowthingsroll.
WhatYouNeed
2cansofthicksoup(suchasmushroomsoup)
1canofthinsoup(suchaschickenbroth)
incline
Method
Part1
1. Verifythattheexternalshapeofeachofthethreecansisthesame.
2. Setupaninclineabout1meterinlength.Theheightshouldbeabout30cm.
3. Hold the twocansofmushroomsoupon the inclinewithadistanceofabout10cmbetween them,asshown in
Figure60-1.CallthetopcanAandthebottomcanB.
4. Predictwhatwillhappenwhen thecansare released:a) thedistancebetween themwill increaseb) thedistance
betweenthemwilldecreasec)thedistancebetweenthemwillremainthesame.
Part2
1. Placeoneofthemushroomsoupcans(A)andthecanofbroth(C)ontheinclinewithA10cmhigherthanC.
2. Predictwhatwillhappenwhenthecansarereleased:sameoptionsasnumber4.
3. TrythisagainwithcanCastheuppercanthistime.
ExpectedResults
The twocanswith thesamecontentswill accelerateat thesame rate.Becausebothcansstart from rest, thedistance
between them remains constant. However, themushroom soup has a greater density than the broth and it will rollmore
slowly.
206
Figure60-1Howwillthedistance,d,changeasthecanrolldowntheslope?
WhyItWorks
Whenanobjectrolls,someofitsenergyisassociatedwithmovingfromonepointtoanother(calledtranslation).Themore
mass theobjecthasand the faster itgoes, themoreenergy ithas. Inaddition,someof theenergyofa rollingobject is
relatedtothefactthatitisrolling.Theamountofthisrotationalenergyisrelatedtothewaythemassisdistributedaround
thecenterofrotation.Agreaterdensitycenter(mushroomsoup)requiresmoreenergytorollatthesamerateasalower
densitycenter(broth).
Physicsalert:Apropertycalledmomentofinertiameasureshowmassisdistributedaroundacenterofrotation.Acanof
densesouphasagreatermomentofinertiathanacanofthinsoupand,asaresult,tiesupmoreenergyasitrolls.
OtherThingstoTry
Aninterestingfollow-upwouldbetodropbothtypesofsoupcansfromadistanceandreestablishtheprinciplethattheyboth
accelerateatthesamerateinfree-fall.Translation(falling)isdifferentthanrolling.Theeffectofrollingmakesthedifference
hereandgivestheless-densesouptheadvantage.
ThePoint
Aforceappliedtoacylindricalobjectcancauseiteithertotranslateorrotateorsomecombinationofboth.
207
Project61
Makingwaves.IthoughtInodethis.
TheIdea
Many of the things physics dealswith arewaves. This includes sound, light, and vibrations inmatter. It is helpful to use
vibratingobjects,suchaswedointhisproject,tohelpvisualizemoreabstractwaves,suchaselectromagneticwaves,which
includelight.
WhatYouNeed
slinky
coiledspring“snakey”
string
stopwatch
tapemeasure
short,thin,metalpoleorwoodendowel(10cminlengthand2mmindiametershouldworkwell)
Method
Forthefollowing,becarefulwhenworkingwithstretchedsprings.Becarefulnottoletthespringgoaccidentally,whichcould
causethespringtowhiparoundandpossiblyhitsomeone.
Longitudinalwavewithaslinky
1. Stretchtheslinkytoaboutdoubleortripleitsoriginallength.Thisrequirestwopeople.
2. Measurethedistancebetweenthetwoendsoftheslinky.
3. Fromoneoftheends,pullbackontheslinkyinthedirectionthattheslinkyisstretchedbyafewinchesandrelease.
4. Observe the pulsemoving from one end of the slinky to the other. Time how long it takes to go themeasured
distancefromoneendtotheother.
5. Calculate thevelocityof thepulsebydividing thedistance thewave travelsby the time it takes. (Useconsistent
units,meaningifyoumeasurethedistanceinmeters,thevelocitywillbeinmeterspersecond.Ifyoumeasurethe
distanceininches,thevelocitywillbeininchespersecond.)
6. Increasethetensionandcalculatethevelocity.
7. Decreasethetensionandcalculatethevelocity.
Transversewavewithacoiledspring
1. Stretchthesnakey(coilspring)toaboutdoubleortripleitsoriginallength.
2. Measurethedistancebetweenthetwoendsofthespring.
3. Fromoneoftheends,displacethecoilalongthefloorperpendiculartoitslengthbyafewinchesandrelease.
4. Measurethevelocityofthepulsewithincreasedanddecreasedtensionasintheprevioussection.
Reflectionfromfixedandunconstrainedends
208
1. Workingwiththecoiledspring,releaseatransversepulsedownthespring.
2. Bothendsofthespringshouldbeheldtight.
3. Observewhathappenstothepulsewhenitreachestheendheldtightlyinplace.
4. Now,insertthedowelorametalrodthroughoneoftheendsofthecoil.Thedowelshouldpassthroughoneora
fewcoilsinsuchawaythatthecoilisabletoslidefreelyonthedowel.
5. Againreleaseatransversepulsedownthespringandobservewhathappenswhenthepulsereachestheend.
Wavescrossingintodifferentmedia
1. Connecttheslinkyandthecoiledspringtogetherwithastring.
2. Observewhathappenstoapulsesentfromtheslinkyside.
3. Nowseewhathappenstoapulsesentfromthecoiledspringside.
4. Inwhichsection(slinkyorcoiledspring)doesthepulsemovefastest?Ifyourspringsarelongenough,timeitand
calculate the velocity. With everything else equal, a less-tense spring gives you a little more time to make the
measurement.
Superposition—constructiveanddestructiveinterference
1. Placeacoilonthefloor.Holdthecoilfrombothendsusingtwopeople—oneoneitherside.Stretchitfairlytight.
2. Eachpersonholdingthecoilsimultaneouslyshouldreleaseapulsethesamesizefromthesamesideofthecoil.
Observewhathappens.
3. Peopleholdingthecoilshouldnowreleaseapulsethesamesizefromtheoppositesidesofthecoil.Howdoesthis
comparewiththepulsereleasedfromthesameside?
Standingwavesandnodes
1. Placeacoilonthefloor.Holdthecoilfrombothendsusingtwopeople—oneoneitherside.Applymoderatetension.
2. Onepersonshouldholdtheendofthecoilstationary.
3. Theotherpersonshouldbeginshakingthecoil,slowlyatfirst.
4. Observewhathappens,foragiventension,asyouincreasethefrequencyofthevibrations.Anodeisapointonthe
wavethatdoesnotmovewhilethewavevibrates.SeeFigure61-1.
5. Quantifythisbycountingthenumberofnodesasafunctionofthefrequencyofthevibration.Thefrequencycanbe
determinedbythenumberofsecondsittakesfortenvibrations(backandforth)dividedbyten.
6. Observewhathappensasyouincreasethetensioninthecoil.
ExpectedResults
Longitudinalwave
Thevelocityofalongitudinalwaveincreasesasthetensionincreases,butisnotdependentontheamplitude.
209
Figure61-1Transversewave.
Transversewave
Similarly,thevelocityofatravelingwaveincreasesastensionincreases.
Reflection
Whenawavecomestotheendofthespringthatisrigidlyheld,thewavereflectsbyflippingovertotheoppositeside.Ifthe
springisfreetomove,thewavereflects,butbeginsitsreturnonthesamesideitcamefrom.
Differentmedia
Whenawavegoesfromonespringtoanother,thewaveispartiallyreflectedandpartiallytransmittedintothesecondspring.
Superposition
Pulses coming from the same sideof the coil add together to forma larger combined pulse.This is called constructive
interference.
Pulsescomingfromtheoppositesideofthecoilnegateeachother,resultinginasmallerpulseatthepointorevenno
pulse.Thisiscalleddestructiveinterference.
Aftercombining,theoriginalpulsescontinuemovingthroughthespring.
Standingwaves
Thegreaterthetensionandthemorerapidlythespringisshaken,thegreaterthenumberofnodesformed.
WhyItWorks
Wavesexhibit characteristic properties that include: travelingwaves, standingwaves, reflection,movingbetweendifferent
210
media,superposition,andinterference.
OtherThingstoTry
1. Standingwavescanalsobeshownby vibrating (or rotating)a string held under tensionby two vertical supports.
Wavescanbegeneratedbyamotororaspeaker,aspictureinFigure61-2.
2. Afunwaytodosomeoftheseinvestigationsistouseglow-in-the-darkropeavailablefromPASCO.
3. A significant, but often overlooked, point is the connection between the frequency of the traveling waves and
standingwaves inacoil.Theyshouldbe thesame,and thepreviously techniquesdevelopedareagoodway to
verifythis.Astandingwaveisreallyamixtureofmanystandingwavestravelingbackandforthalongthecoil.The
overall standingwavepattern isgeneratedby the travelingwaves interferingconstructivelyanddestructively.The
relationship between standing waves and traveling waves is used when measuring the speed of sound by
determiningthewavelengthofaresonantstandingwave.Thisworksbecausethespeedofbothisthesame.
ThePoint
Thepropertiesofwaves,includingmovementinamediumandreflection,canbeobservedinsprings.
Figure61-2Generatingastandingwave.CourtesyPASCO.
211
Project62
Rollinguphill.
TheIdea
Mostpeoplewillnotseetheresultsofthislittledemonstrationcoming,especiallyifit’sdoneasanimmediatefollow-upto
thepreviousproject.YoucanmakeacanactuallyrolluphillforashortdistancewithoutviolatinganyofNewton’slaws.
WhatYouNeed
coffeecan
weight—anoldbatteryshouldworkwell
strongglue—suchasGorillaglueorepoxy
incline
Method
1. Gluetheweighttotheinsideofthecoffeecan.
2. Concealtheinteriorwiththeplasticcoverofthecoffeecan.
3. Placethecanontheinclinewiththemassontheuphillsideofthecan’scenterline.SeeFigure62-1.
4. Asksomeoneobservingthiswhattheythinkwillhappen.Youcanaddtotheeffectbycreatingtheillusionthatyou
areinvestigatingoneofthesituationsofthepreviousdiscoverybyusingtwocoffeecanswithweights.
212
Figure62-1Gravitycreatesatorqueonthecancausingittorolluphill.
ExpectedResults
Oncereleased,thecanrollsuphillafewinches.
WhyItWorks
Gravity pulls on theweight, which exerts a torque on the can. If theweight is positioned on the uphill side of the can’s
centerline,thecanwillrolluphill(untiltheweightisbroughtdirectlyunderthecan’scenterofgravity).
OtherThingstoTry
Anothersimilarideaistoattacharubberbandwithaweightinthemiddletotheinsideofthecan.Asthecanrolls,therubber
bandiswoundup.Whenthecanrolls,itreachesaturningpoint,andthenreturnsbackinthedirectionfromwhichitcameas
therubberbandwiththeweightunwinds.
ThePoint
213
Iftheforceexertedbygravityonanobject’scenter-of-massproducesatorqueontheobject,theobjectcanbrieflyrolluphill.
214
Project63
Gettingaroundtheloop.Fromhowfarabovethegrounddoestherollercoasterneedto
start?
TheIdea
Energyisconserved.Anobjecthaspotentialenergybecauseit isacertaindistanceabovetheground.Asitrollsdownan
incline,someofitsenergychangesintokineticenergy
WhatYouNeed
aluminumtrackusedtosecureshelvinginbookcases.Thisisthetypehungverticallyonthesidesofthebookshelf
andholdsclipsthatsupporttheshelves.Thistrackshouldbeflexibleenoughsoyoucanbendittoformacircular
shape.(Youdon’twanttheheavy-dutyshelvingtracksyouwouldusetosetupabookshelftoholdallyourphysics
textbooks.)
1marbleorsteelballthatsmoothlyrollsinthetrack
circularobjecttouseaguide,suchasasmallbucketoraonegallonpaintcan
Figure63-1Wheremusttheballbepositionedtomakeitaroundtheloopwithoutfalling?
frametomounttheframeon
–incline(2feetlong×3incheswide×¾inchthickwilldofine)–bottom3feet×3inches×¾inches–verticalbrace1foot×3inches×¾inch–smallright-anglebrackettosupporttheverticalbrace
youmaywanttoaddsomekindofnettocatchthemarbleattheend,soyoudon’thavetochaseiteverytime
smallflat-headwoodscrews—thesmallerthebetter,butjustlargerthanthescrewholesinthetrack
ameterstick
Thisapparatusisalsocommerciallyavailable,asshowninFigure63-2.
Method
Buildingthetrack
215
1.Assembletheframebyattachingthepiecesofwood,asshown.
2.Formacircularloopbycarefullybendingthetrackaroundtheform.Note,thechannelshouldbetowardtheinsideof
thecirclewhenyoudothis.
3.Predrillholesforthewoodscrewsinthewoodusingadrillbitasizeortwosmallerthanyourscrews.
4.Securethelooptotheframeusingthewoodscrews.Itisimportantthatthe(flat)headsofthewoodsscrewsdonot
interferewiththemotionoftheball.Ifyoufindyourwoodscrewprotrudesintothepathofthemarble,youcanwork
around this by enlarging the holes or by countersinking the holes in the track, so the screw head is flushwith the
bottomofthetrack.
Figure63-2CourtesyPASCO.
5.AlignthetrackasshowninFigure63-1.Theloopshouldbeassymmetricalaspossiblewiththeoverallpathmakinga
verticalloop.Also,makeenoughseparationbetweenthepartofthetrackgoingintoandoutoftheloop,sothereis
enoughclearancebetweenthemarbleandthetrack.
6.Youcan(optionally)attachsomekindofcatcher(anetorcup)toavoidchasingmarbles.
Testingit
1.Takeaguessastowherethemarblemustbeplacedtonegotiatetheloop.Herearesomechoices:a)equaltothe
radius,b)equaltothediameter,c)greaterthanthediameter,ord)twicethediameter.(Takeintoaccounttherewillbe
somefriction.)
2.Pickyourstartingpointandobservewhathappens.Findtheminimumpointtoconsistentlynegotiateoneloop.What
happenstothemarbleifyoureleaseitatapointthatishigherorlowerthanthisminimumpoint?SeeFigure63-1.
Figure63-3CourtesyPASCO.
ExpectedResults
Withalow-frictionslidingobjectcar,suchasacartwithwheelsorarollercoastercar,theheightmustbeatleast2.5times
theradiusoftheloop.Actualloopsrequireslightlygreaterheighttoovercomefriction.
Forrollingobjects,suchasasteelballormarble,someofthepotentialenergyistiedupinrolling,sotheheightmustbeat
least2.7timestheradiusoftheloop(again,withoutaccountingforfrictionallosses).
216
WhyItWorks
Thepotentialenergyyoustartwith(byraisingittocertainheightonthetrack)ischangedintokineticenergy.Thehigheryour
releasepoint, thefaster itgoes. If theobject isrollingratherthansliding,someofthepotentialenergy isusedtogetthe
objectrolling.Ifthereisfrictionalongtheway,someadditionalpotentialenergyisconsumed.
Tonegotiatetheloop,thecentripetalforce(providedbythetracktomaintainacircularpath)mustjustequaltheforceof
gravity.With lessvelocity, itwill fallbeforecompletingthe loop.Withextravelocity, itwillgetthroughwithsomeenergyto
spare.
OtherThingstoTry
Nowthatyouhaveoneloopdown,youcantryasimilartrackwithmorethanoneloop.Youstillonlyneedoneramptogive
themarbleaninitialvelocity.
ThePoint
Totalmechanicalenergyisconserved.Potentialenergyisconvertedtokineticenergyandviceversa.
217
Section6
SoundandWaves
Project64
Whatdoessoundlooklike?Oscilloscopewaveforms.
TheIdea
Whatdoesyourvoiceprintlooklike?Youcannotseesound.Butyoucanchangethesoundwavesintoelectricalsignalsthat
canbedisplayedonascreen.Justasyoufoundwaystovisualizemotionandtorepresentmotionusingvariousgraphs,in
thissectionyoudeveloptechniquestovisuallyrepresentwaves.Thiscanenableyoutostudybasicwavepropertiesandto
observehowwavescombinetoformnewpatterns.
Youcangoaboutthisintwoways.Onewayistouseanoscilloscope,whichisaninstrumentthattakesanelectricalsignal
anddisplaysitingraphicalform.Recently,amuchlowercostalternativehasbecomeavailablethatmakesitpossibletoturn
acomputerintoanoscilloscope.
Thisprojectfocusesonhoweithertypeofoscilloscopecanbeusedtostudythewavepropertiesofsound.
WhatYouNeed
oscilloscopes,whichrangeincostfromjustunder$600tothousandsofdollars
soundcardoscilloscope.Youcanturnyourcomputerintoaoscilloscopeinseveralways:
– PC sound card distributed for private and noncommercial use in educational institutions at
www.zeinitz.de/Christian/Scope_en.html. (Oscilloscope images shown in this and other sections are based on this
soundcardoscilloscopeandappearcourtesyofC.Zeinitz.)
–Zelscopeisavailableforasmallchargeatwww.zelscope.com(thisusedtobecalledWinscope).
tuningfork
adapters
–Toconnectmicrophonetocomputer.Microphonesareeitherhigh-or low-impedanceconnectionsandthecomputer
inputistypicallyamini.
–Microphoneoutputtooscilloscopeinput(typicallyBNCconnector).
–Dependingspecificallyonwhatconnectionsyouneedtomake,youcanmostlikelyfindconnectorsatRadioShackor
buildtheconnectoryouneed.
–Caution:Soundcardoscilloscopescanhandleonlylow-voltageinputs,suchasfrommicrophones.Attemptingtousea
soundcardoscilloscopeforlargerelectricalsignalmaydamageyoursoundcard.Areferenceforhowtoassemblea
high-impedancecircuitthatcanenableusingasoundcardoscilloscopeforhighervoltagesisgiveninProject115.
wavegenerator
–stand-alonedevicedesignedforthispurpose
–keyboardwithappropriateconnectors
–waveformgeneratoravailablewithsomecomputeroscilloscopes
Method
218
Settinguptheoscilloscope
1. Connectthemicrophonetotheoscilloscopeinput.
2. Collectatestsignal,suchasyourvoiceoramusicalsound.
3. Adjusttheverticalscale,sotheentirewaveisdisplayed.
4. Adjustthehorizontal(time)scale,sothewaveisdisplayed.
5. Ifnecessary,adjustthetriggertoenablethewavetobeproperlydisplayed.(Chosecontinuousratherthansingle-
eventsettingsforthetrigger.)
Displayingwaves
1. Generateapitchaudiblywithatuningfork,akeyboardsynthesizer,orbyawaveformgenerator.(Dependingonyour
setup,youcanusethewaveformgeneratortoproduceanaudiblesignalthroughaloudspeakerorsenditdirectly
intotheinputoftheoscilloscope.)
2. Increasethepitch(frequency)andcomparetothepreviousshape.
3. Decreasethepitchandcomparetothepreviousmeasurements.
4. Increasethevolume(amplitude)ofthesoundandobservehowthewavechanges.
5. Tryyourvoiceusingthemicrophone.Howdoesthatcomparetoapuretone,suchasproducedbythetuningfork?
6. Observedifferentwaveformshapes,suchassinusoidal,triangular,squarewave,andsawtooth.Howdotheysound?
Whatmusicalinstrumentsdoeachofthepreviouswaveformsmostcloselyresemble?
7. Playvariousmusicalinstrumentsandidentifyfundamentalwaveformsthatappeartobepresentintheinstruments’
waveforms.
8. Just for fun:Observe varioussamplesofmusic.Can youdistinguish variousmusical styles justby lookingat the
waveform?
9. Canyourecognizethe“voicesignature”ofdifferentpeopleascrimelabsdoallthetimeonTV?
Addingwaves
1. Generateatoneorfrequency.Let’ssaywestartwith440hertz(Hz),aconcertA.DisplaythisonChannel1.
2. Generateasecondtoneorfrequency.Let’ssayweuse100Hz.DisplaythisonChannel2.
3. Manyoscilloscopesletyoudisplaytwosignalsononedisplay.Ifyouroscilloscopehasthecapabilitytodisplaytwo
inputsononedisplay,showthecombinedsignalsfrom1and2.Howdoesthecombinedsignalcomparetothetwo
individualsignals?
4. Youcanalsoaccomplish thisbygenerating twoaudible tonesat thesametime,suchasplaying twonotesona
keyboardsynthesizeratthesametime.Soundingtwotuningforksatthesametimewillalsowork.
ExpectedResults
Increasedpitchshowsupontheoscilloscopeasincreasedfrequency.
Increasedvolumeisdisplayedasincreasedamplitude.
A tuning forkorawavegeneratorproducesapuresinewave.Figure64-1shows the relativelypure sinewavepattern
producedbytheflutesettingofanelectronicsynthesizerplayinga440Hztone.
Sawtoothandtriangularwavessoundmore“reedy,”likeaclarinetorsaxophone.
Othersoundsarecomplexmixturesofsimplerforms.Forinstance,asynthesizedrockorganconsistsofawiderrangeof
overtones combined with the fundamental tone. Figure 64-2 shows several higher frequencies combined with a 440 Hz
fundamental.
219
Figure64-3100Hztone.
Addingtwowaveformsresultsinacombinedsound.Figure64-3showsa100HztoneandFigure64-4showsa400Hz
tone.
Figure64-5showsbothofthesetonescombined.Theoverallpatternshowshowbothofthesetonesaddtoproducea
combinedwavepattern.
Musical sounds are complex mixes of many individual frequencies with a large variety of overtones. Figure 64-6 is a
samplefromTheBeatlesandFigure64-7isanAllisonKrausefiddlesolo.
Anoscilloscopecanalsoshowthemixoffrequenciesinaparticularsound.Forinstance,asynthesizerviolinsoundwhen
playinga440Hztonealsohassomeovertonesat880Hzand1360Hz,asshowninFigure64-8.
222
Figure64-6“EleanorRigby”byTheBeatles.
Themixofovertonescontributestoestablishingthemusicalidentitiesofvariousinstruments.Forinstance,arecorderhas
a very pure tone with very few overtones. Other sounds, such as a rock organ or a distorted bass, have amuchmore
complexmixofovertones.
WhyItWorks
Anoscilloscopeprocessesanelectricalsignalanddisplaysit invariousways.Theoriginoftheelectricalsignalmaybea
microphonethatconvertsasoundpatternintoanelectricalpattern,whichtheoscilloscopecanworkwith.Themostbasic
formofdisplayisasinglesignalversustime.Thescalesareadjustabletopermitawiderangeofsignalstobedisplayed.
Oscilloscopesalsodisplaytwosignalsbothindividuallyonthesamescreenoradded.Aplotofonesignalagainsttheother
andadistributionoffrequenciesarealsocommonoptions.
225
Figure64-8Frequencydistributionofa440Hzviolintoneshowingovertones.
OtherThingstoTry
Hereisalow-techwayofpicturingsound:Coverasoupcan(clean,empty,andwiththetopremoved)withLatexorother
rubberymaterial.Put iton tight, likeadrum.Attach itwithawire tie, hoseclamp,orgoodstring.Glueasmall (roughly1
centimeteronaside)pieceofmirrortothetopoftheLatex.Touseit,holdthecaninonehandandshinealaseronthe
mirror,so thebeamprojectsonto theceiling (orawall). If youdon’thavea laser,directsunworksaswell.With the light
reflectingoffthemirror,createsoundsthatwillcausetheLatextovibrate.Becauseoftheopticalgeometry,themovement
ofthereflectedlaserislarger(amplified)thanthesmallermovementofthemirror.Becausethe“drum”willbevibratingintwo
dimensions,itisnothardtogeneratetheLissajouspatternswherethereflectedlightretracesacurvedpath.
ThePoint
Soundisawavethat,ifconvertedintoanelectricalsignal,canbedisplayedinagraphicalform.
227
Project65
Rippletank.
TheIdea
Waterwavesareprobably themost tangible typeofwave. For this reason,waterwavescanbe useful in studyingwave
propertiesingeneral.Arippletankprovidesasimple,convenientwaytoproduceandstudywavesandthevarioustypesof
obstaclestheycanencounter.
WhatYouNeed
shallowtrayortankwithatransparentbottomorcommerciallyavailablerippletank
water
brightlightthatcanbeheldormountedabovethetank
oneorseveralplainsheetsofwhiteposterboardtoserveasascreenonwhichtoviewtheimagesproducedbythe
rippletank
variouspropsincludingastraightwall,acurvedwall,athickglassplateaboutone-halfthethicknessofthewaterin
thetank,acup,apencil,andamanualormechanicalsourceofripples
optional:awaytoprojecttheshadowsgenerated,suchasanoverheadprojectoravideomonitor
Method
Basicwavegeneration
1. Setupthetankwiththelightoverhead.Theshadowpatternshouldbevisibleonthefloor.
2. Adjusttheheightofthelightabovethetankandthescreenbelowthetanktogivethebestfocusoftheshadows
fromtheripplesonthefloor.
3. Usingthetipofaruler,tapthesurfaceofthewatertoproduceripples.Ifyouhaveavibratingripplegenerator,using
thatmightgivemoreconsistentresultsandyouwon’tgettiredasquicklyfrommakingripples.
4. Youshouldseetheripplesspreadoutinacircularpattern.Thetankshouldbelargeenough,sothisoutwardmoving
circularpattern isnotobscuredbythereflectionof theripplesfromthesideof thetank.Sometimes,aborderof
foamcushioningisusedtominimizesidereflections.
5. Estimatethewavelength(averagedistancebetweenripples)andfrequency(numberofripplespersecond).Estimate
the velocity of the ripples. Compare this with the velocity predicted by the wave equation (which applies to all
waves):velocity=wavelength×frequency(incyclespersecond,whichisthesameashertz). Ifyoumeasurethewavelengthincentimeters,thevelocitywillbeincentimeterspersecond.
Reflection
1. Insertastraightbarrier—awall—inthetank.
2. Generateripplesmovingtowardthebarrieratvariousangles.
3. Observetheanglethereflectedwavesmakecomparedwiththeincomingwaves.
228
Figure65-1Rippletankshowingshadowsofwavepatternsonwhiteboard.
Concaveandconvexcurvedreflector
1. Inserttheconcavereflector.Thisiswherethesidescurvetowardthesourceoftheripples.Observehowthewaves
arereflected.Dothewavesconvergeordiverge?
2. Generateripplesthatoriginateatthatfocalpoint.Howdotheripplesmove?
3. Insert(orreshape)thereflector,soitisconvex.Thisiswherethesidescurveawayfromthesourceoftheripples.
Dothewavesconvergeordiverge?
Refraction
1. Placeathickplateinthetank.
2. Whathappens to thespeedof thewavesas thewavescrossover theplate?Whathappens to thewavelength?
Doesthismakesensegiventhatthefrequencydoesn’tchange?
3. Directwavestotheplateatanangle.Whathappenswhenthewavescrossfromthedeepwatertotheshallower
water?
Diffraction
1. Generateripplesandobservewhathappenswhentheyencounterapencilheldverticallyintheirpath.
2. Whathappenswhenalargerbarrier,suchasaglassorbeaker,isheldinthepathoftheripples?
Interference
1. Generate ripples from twodifferent locations.The ripplesshouldbesynchronized insuchaway thateach ripple
makergoesupatthesametimeanddownatthesametime.(Thismeansthesourcesofthewavesareinphase.)
2. Observewhathappenstothepatternasthewavesfromthetwosourcesoverlapandinteractwitheachother.
ExpectedResults
Straightbarrier:theincomingangleequalstheoutgoingangle.
Concavebarrier:thereflectedwavesconvergeatafocalpoint.
229
Concavebarrier:ripplesgeneratedatthefocusregroupandemergeasasinglewave.
Convexbarrier:wavesdivergefromanylocation.
Plate:thewavesslowastheycrossovertheplate;thewavelengthincreases.
Plate:thewavescomingtowardtheplateatananglearebenttoaless-severeangle.
Figure65-2Ripplepatternscrossovertheconvexshapedbarrier,resultingintheconvergenceofthewavepattern.Courtesy
PASCO.
Figure65-3Thisrippletank(withverticaldisplay)showsthediffractionpatternproducedbytwoseparatesourcesofwave
generation.CourtesyPASCO.
Diffraction:thewavefrontsregrouparoundasmallbarrier,butnotalargerone.
Interference:tworipplelocationsresultinafixedpatternofhighandlowwaves.
WhyItWorks
Waterwavesexhibitbasicwaveproperties,including:
Reflectionfromstraightsurface:Angleofincidenceequalsangleofreflection(withallanglesdefinedwithrespectto
theperpendicularornormallinethatcanbedrawntothereflectingsurface).
230
Reflectionfromaconcavesurface:Wavesarereflectedfromacurvedsurfacewiththelawofreflectionapplyingto
thetangentlineofthecurveatthatpoint.Forapproximatelyparabolicreflectorsthatincludesemicircularreflectors,
this results inwavespassing througha focal point. If thewavesaregeneratedat that focal point, they become
focusedandpropagateinasingledirection.
Reflection from a convex surface: Waves diverge and propagate over a wider range of angles than when they
started.Thereisnofocalpointwhenwavesreflectfromaconvexsurface.
Refraction:Wavesbend toward theperpendicular line (called thenormal line)when theyentera regionwhere the
lightwavesmovemoreslowly.
Diffraction:Waves bend around a barrier in their path if the diameter of that barrier is small comparedwith the
wavelength.
Interference:Crestsandtroughsofwavescombinetoformanoverallpatternbasedonconstructiveanddestructive
interference.
OtherThingstoTry
Alargestationarybodyofwatercanserveasalargerippletank.Inthiscase,travelingwavescanbeobservedwithoutthe
complicationofreflectionsfromthesideoftherippletank.PicturedinFigure65-4isaninterferencepatternformedbytwo
rocksthrownintoalake.
ThePoint
Wavesexhibitcertaincharacteristicbehavior, includingreflection, refraction,diffraction,and interference.Theseproperties
arecommontoalltypesofwaves.
Figure65-4Tworocksformaninterferencepatternastheripplestheyproducespreadacrossthesurfaceofalake.
231
Project66
Simpleharmonicmotion.Theswingingpendulum.
TheIdea
Apendulumundergoesatypeofmotionthatispredictable.Theconsistencyofpendulummotionhasallowedittobeusedto
drivethetimingmechanismofclocks.Inthisexperiment,youinvestigatewhatcausesapendulumtoswingfasterorslower.
AtleastforapendulumonthesurfaceoftheEarth,onlyonevariabledeterminesthetimeittakesforapendulumtoswing
backandforthonetime.
WhatYouNeed
severalmassesthatcanbeattachedtoastring(suchas20g,50g,100g,200g)
severalstringsofvaryinglengthsfrom0.1to1.0m(strongenoughtosupportthemasses)
supportforeachpendulum
stopwatch
meterstick
Method
1. Setupabasicpendulumwithameasuredlengthandmassfreetoswing.
2. Pullthependulumbacktothesidethroughasmall(lessthan15degrees)angleandgetthestopwatchready.
3. Releasethependulumandstartthestopwatchasthependulumisreleased.
4. Counttencyclesbackandforth.Cyclenumberoneiswhenthependulumreturnstoitsoriginalposition.Becareful
nottocount“one”whenthependulumisreleased.
5. Thelengthofthependulumisthedistancefromthepointwherethestringissupportedtothecenterofthemass.
6. Recordthetime(inseconds)forthependulumtocompletetencompletecycles.
7. Dividethetimefortencyclesbytentogetthetimeforonecycleortheperiodofthependulumfortheconditions
youaretesting.
8. Youcanproceed inseveralwaysat thispoint,withmanyopportunitiestodevelopyourownplan.Hereareafew
suggestions:
– What variable matters: Mass? Length? Angle? Test the selected variable while holding the others constant. For
instance,testlight,medium,andheavymass,andthendeterminewhethertheperiodofthependulumisdependenton
mass.Thiscanbedonebymeasuringtheperiodofapendulumconstructedwitheachofthethreemasses.Itcanalso
bedonequalitativelybysettingupthreependulaandobservinghowfasttheyswingcomparedtoeachother.
–Onceyoudeterminewhichvariable(s)affectshowfastthependulumswings,youcansetupanexperimenttomeasure
howtheperiodchangesoverarangeofthevariablesyouselected.Theothervariablesshouldbekeptconstant.
232
Figure66-1Simpleswingingpendulum.
ExpectedResults
Theonlyvariablethataffectstheperiodofapendulumislength.Themassdoesnotmatteratall.Foranglessmallerthan
15degrees,angleisinsignificant.Insignificantmeanslessthan1percent.
Thelongerthestring,thelongertheperiod(periodisthetimetogobackandforthonetime).
Thedependenceofperiodonlengthisnotlinear.
233
Figure66-2Periodversuslengthforapendulum.
AgraphofperiodversuslengthisshowninFigure66-2.Themodelforthegraphshowstheperiod isdependentonthe
squarerootofthelength.
WhyItWorks
Theperiodofapendulumisthetimeittakesforthependulumtomovefromonepositionandreturntothesameposition.
Theperiodofapendulum(inseconds)isgivenby:
whereListhelengthofthestring(inmeters)andgisthegravitationalacceleration(9.8m/s2).
Thisshowsthedependenceonthesquarerootofthestringlength.Becausethereisnomassintheequation,theperiod
does not depend onmass. The period also depends on the gravitational acceleration of the Earth, which under normal
circumstancesisnotavariable.
OtherThingstoTry
Trythiswithapendulum,consistingofabowlingballattachedtoarope.Makesurethepointofattachmentandtheropecan
securelyhandletheweightoftheswingingpendulum.
Trythiswithaplaygroundswing.Isthenaturalfrequencyofoscillationwhatyoupredictbasedonthepreviousequation?
Whathappensifyoupushwitharhythmconsistentwiththatnaturalfrequency?Whathappensifyoupushwitharhythmvery
differentfromthenaturalfrequency?
ThePoint
Theperiodofapendulumdependsononlyonevariable,whichisitslength.
234
Project67
Simpleharmonicmotion.Thespringpendulum.
TheIdea
Amasshangingfromaspringisanotherexampleofasystemthatmovesinarepeatableandconsistentway.Thisiscalled
simpleharmonicmotion.Thisexperimentisaboutfindingwhatcausesaspringpendulumtovibratefasterorslower.
WhatYouNeed
severalmassesthatcanbeattachedtoastring(suchas20g,50g,100g,200g)
several springs of varying stiffness—it should be possible to partially stretch the spring by hanging each of the
masses to thebottomof thespring. If themassescan’tstretch thespringor if thespring is fullyextendedwhile
supportingthemass,chooseeitherothermassesorothersprings
supportforeachpendulum
stopwatch
meterstick
springbalance(fortheextension)
Method
1. Setupaspringpendulumconsistingofaspringwithoneendsupportingamassandtheotherattachedtoasupport
abovethespring.
2. Allowtheweightofthemasstostretchthespringandcometorest.
3. Pullthependulumstraightdownthroughasmalldisplacement.(Increasingtheelongationofthespringbyabout10
percentisagoodstartingpoint.)
4. Releasethependulumandstartthestopwatchasthependulumisreleased.Trytoreleasethespring,soitgoesup
and down in a vertical direction. Bear in mind that, after a few cycles, a spring may have a tendency to start
swinging,whichcomplicatesthetypeofmotionweareinvestigatinghere.
5. Counttencyclesupanddown.Cyclenumberoneiswhenthependulumreturnstoitsoriginalposition.Becarefulnot
tocount“one”whenthependulumisreleased.
6. Recordthetime(inseconds)forthependulumtocompletetencompletecycles.
7. Divide the time for ten cycles by ten to get the time for one cycle. This is the period of the pendulum for the
conditionsyouaretesting.
8. Aswiththepreviousstudy,youcanapproachthisinvestigationinseveralways.Youareencouragedtodevelopyour
ownapproachtothis.Hereareafewsuggestions:
–Whatvariablematters:Mass?Springstiffness?Amountofdisplacement?Testtheselectedvariable,whileholdingthe
others constant. For instance, you can test squooshy, medium, and stiff springs, all using the same mass and
displacement.(Wedefine“squooshy”inquantitativetermsinaminute.)Similarly,youcantestlight,medium,andheavy
masstodeterminewhethertheperiodofthependulumisdependentonmass.
235
Figure67-1Springpendulum.
–Onceyoudeterminewhichvariable(s)affectshowfastthependulumswings,youcansetupanexperimenttomeasure
howtheperiodchangesoverarangeofthevariableyouselected.Theothervariablesshouldbekeptconstant.
ExpectedResults
Thebehaviorofthespringpendulumisquitedifferentthantheswinging(simple)pendulumstudiedinthepreviousproject.
Twovariablesareimportantforaspringpendulum:massandspringstiffness.
Theheavierthemass,thelongertheperiod.Also,thestifferthespring,theshortertheperiod.The“springiness”ofaspring
iscalledthespringconstant,whichgivesanumericmeasureofhowstiffaspringis.
Within a fairly broad range, it should not matter whether you pull the spring through a small displacement or a larger
displacement.
Thedependenceofperiodonmassandspringconstantisnotlinear.
WhyItWorks
Theequationfortheperiodofaspringpendulum(inseconds)isgivenby:
236
wheremisthemass(inkilograms)andkisthespringconstant(inN/m).Noticetheperiodvariesasthesquarerootofthe
massandtheinversesquarerootofthespringconstant.
OtherThingstoTry
Predictandmeasuretheperiodofthespringpendulum.Youcandothisbyfirstfindingthespringconstantusingthemethod
ofProject30.Youfindthespringconstant,k,bymeasuringthedisplacement,x,ofaspring(inm)resultingfromagivenforce,
F(inN),accordingtotheequation:
k=–F/x
Thenegativesignreflectsthefactthatforceanddisplacementarealwaysintheoppositedirectionresultinginapositive
valuefork.
Onceyouhavedeterminedthespringconstant,predicttheperiodofthespringpendulumusing:
(Theperiodwillbegiveninsecondsiftheforceisenteredinnewtonsandthedisplacementinmeterstogetk.Themass
must be in kg. Remember 1000g= 1kg.)Once you’ve called your shots, set your pendulum inmotion and compare your
predictionwithyourmeasuredresult.
ThePoint
The period of a spring pendulum increasesas the square root of themass.Theperiod of a spring pendulum increases
inverselywiththesquarerootofthespringconstant.
237
Project68
Generatingsinewaves.
TheIdea
Thesimplicityofthespringpendulumprovidesanexcellentopportunitytoobserveitsmotionindetail.Themovement, like
othervibrationsinnature,followsasinewave.Wecanalsoidentifyparticularpointsinthespring’smovement,suchaswhere
thevelocityisatamaximumandaminimumduringitscycle.Wecanalsomonitorhowtheforcevariesandhowitrelatesto
the acceleration. These relationships form the basis for amore complete understanding of how the various aspects of
motionareinterrelated.
WhatYouNeed
springpendulum—setupasinpreviousexperiments
Method
1.Setthependuluminmotionandfirstobservewhenthefollowingoccursinthecycle:
–Zerovelocity
–Maximumvelocity
–Zeroforce
–Maximumforce
–Zeroacceleration
–Maximumacceleration
2. Place amotion sensor to view themotion of the spring pendulum from underneath. If themass presents a small
target,youcantapeanindexcardtothebottomofthemasstomakeiteasierforthemotionsensortofind.(Toavoid
airresistance,keepitsmall.)
3.AdjustthesettingsintheDataStudioprogramtogivethemaximumnumberofreadingspersecond.
4.Openfilestoreadsimultaneously:distance,velocity,andacceleration.
5.Displacethespringandbereadytoreleaseit.
6.PressStartontheDataStudioscreentobeginloggingdata.
7.Releasethespring.
8.Recordafewcycles.
9.Adjust thescales, if necessary, tobestdisplay thecharts.Use thesmoothing tools, if needed, togiveasmoother
curveiftheaccelerationdataappearsslightlychoppy.
ExpectedResults
Theequilibriumpositionisthepointwherethestationarymasshangswithoutmoving.Attheequilibriumposition,thevelocity
ismaximum,buttheforce(and,therefore,theacceleration)iszero.
Atthemaximumdisplacementposition(thepointfromwherethespringwasreleased),thevelocityiszeroandtheforce
(and, therefore, theacceleration) ismaximum.Graphsgeneratedbyamotionsensormeasuringapendulumareshown in
Figure68-1.
238
Figure68-1DataStudiographsofmotionsensordatashowingdistance,velocity,andaccelerationversustime(setupbyT.
DragoiuandJ.Silver).
Thedistanceversustimegraphisasinewave.
Thevelocityversustimegraphisacosinewave.Thevelocityiszerowhenthedistanceisatamaximum.Thetwowaves
haveasimilarshape,butthevelocitycurveisdelayedbyone-quarterofaperiodcomparedtothedistancecurve.
Theaccelerationcurveisalsoasinewave.Itisataminimumwhenthedistanceismaximum.Theaccelerationcurveis
zerowhenthedistancecurveiszero.Thedistanceandaccelerationcurveshaveasimilarshape,excepttheacceleration
curveisdelayedbyone-halfofawavelength.
WhyItWorks
Apendulumworksbecausethefurtherthemassmovesfromequilibrium,thegreatertheforcethatreturnsittoequilibrium.
Thisisthebasisofanyuniformlyvibratingobject(knownasasimpleharmonicoscillator).Theresponseofarestoringforce,
suchasexertedbyaspring,istoproducemotionthatfollowsasinewave.Theaccelerationmovesintheoppositedirection
asthedistancebecausetheforceexertedbyaspringisoppositeitsdisplacementfromequilibrium.Thisalsocausesthe
velocityandaccelerationcurvestobeoutofphasewithrespecttothedistance.
OtherThingstoTry
Avariationonthisistoattachaforcegaugetothespringtotracktheforcealongwiththemotionofthependulum.
Physicsalert:Thoseofyoufamiliarwithcalculuswillrecognizethatvelocityisthefirstderivativeofdistance.Acceleration
isthefirstderivativeofvelocityandthesecondderivativeofthedistancewithrespecttotime.Ifthedistancefollowsasine
curve,thevelocity(thefirstderivative)isacosinecurveandtheaccelerationisasinecurve.
ThePoint
Aspring is a simple harmonic oscillator whose distance follows a sine wave pattern. Velocity and acceleration follow a
similarshape,butaredelayedwithrespecttothedistancecurve.Thevelocityisatamaximumatthepointofthegreatest
displacement.Accelerationisatamaximumatthepointofgreatestextension.
239
Project69
Naturalfrequency.
TheIdea
Whenyoupushsomeoneonaswing,timingisimportant.Ifyoupushjustastheswinghascometoitshighestpointandis
readytobeginitsreturn,youwillkeeptheswinggoingandincreaseitsamplitude.However,ifyoupushrandomly,yourefforts
willbefar lesseffectiveand,attimes,youwill tendtoslowthemotionoftheswing.Thereasonforthis isaswinghasa
naturalfrequency.Ifyourpushingisatthenaturalfrequencyoftheswing,theswingwillresonate.Thisexperimentexplores
theideaofresonance.
WhatYouNeed
2ringstands
1⅜inchdiameterwoodendowel,12incheslong2clamps(toholdthedowel)
stringofvariouslengths,fromabout3inchesto10inches
setof several smallmasses thatcanbeattached to thestring (largestainlesssteel nutsworkwell hereorany
attachablemassesintheoverallrangefrom10–50g)
Method
1.Tieloopsatoneendofeachofthestringsandtietheotherendtoamass.Atleasttwoofthestringsshouldbethe
same length. The other should be random—some larger and some smaller than thematched pair. Avoid, however,
havingalltheotherstringshalfordoublethesizeofthematchedpair.
2.Slidethe loopsontothedowelandspreadthestringsoutevenlyacrossthe lengthofthedowel.Thetwomatched
stringsshouldnotbenexttoeachother.
3.Attachthedoweltothetwouprightpostsoftheringstandsusingtheclamps.Leaveenoughspace,soallthemasses
arefreetoswingwithouthittingthetable,whichtheringstandsareplacedon.Thedowelshouldbeslightlyflexible,but
constrainedbytheringstands,soitwillnotswayorswivelwhenthemassesareswinging.SeeFigure69-1.
4.Steadyallthemasseshangingonthestrings.
5.Takeonlyoneofthemassesonthematchedstringsanddisplaceit,soitisswingingperpendiculartothedirectionof
thedowel.
ExpectedResults
Whatwewanttoseehereisforthestationarystring,whichisthesamelengthastheonethatwassetinmotion,toalso
startmovingbackandforth.Theothermassesmightjostlearoundabit,buttheyshouldnotbesetintoasignificantswinging
motion.
WhyItWorks
Theresonantfrequencyofapendulumisdeterminedexclusivelybythelengthofthestringthatsupportsit.Thestationary
pendulumisstimulatedbytheswingingpendulumthathasthesamelengthand,therefore,thesamenaturalfrequency.
241
Figure69-1Resonantfrequencydependsonlyonstringlength.
OtherThingstoTry
Otherquestionsthatcanbeaddressedare:
1.Wouldapendulumwiththesamestringlength,butdifferentmass,havethesameresonantfrequencyastheswinging
pendulum?
2.Whatifwethrowinafewharmonics?Whatistheresponseofapendulumthatisone-halfthelengthoftheswinging
pendulum?Whatistheresponseofapendulumthatisdoublethelengthoftheswingingpendulum?
ThePoint
Asimpleharmonicoscillator, suchasaswinging (simple)pendulum,hasanatural frequency. If stimulatedat that natural
frequency,theamplitudeofthatpendulumwillbegreatest.
242
Project70
Bunsenburnerpipeorgan.Resonantfrequency.
TheIdea
If youblowacross the topofasodabottle, youproduceasound.Themoresodayoudrink, thedeeper thepitchof the
sound.This isbecausetheresonantfrequencyofthebottle increasesastheheightoftheairabovethe liquid increases.
Thisprojectdoesthesamething,exceptonamuchbiggerscale.Youuse longertubesthatproducedeepersounds.You
may just want to give the person who is responsible for the building you are in (such as the building principal) advance
warningthatthesoundtheywillbehearingisnotanearthquake,notawaterbuffaloinlabor,andnotthepropulsionsystem
foraspacealienspacecraft.
WhatYouNeed
largeBunsenburner
cylindricaltubesroughly0.8–2metersinlength—goodcandidatesforthisarecardboardtubesusedforcarpetrolls
orhollowmetalsectionsofolddrivewaybasketballbackboardsupports
fireextinguisherand/orbucketofwater(youshouldnotneedthis,butjustincase)
Method
1. PlacetheBunsenburneronthefloor.
2. Routeahoselongenoughnottogettangledandconnectittoanaturalgasoutlet(which,atthispoint,isnotturned
on).
3. Positionacylindricaltubeonthefloor,soitcaneasilybeplacedovertheburner.
4. Lighttheburnerandadjustit,sotheflowismaximum,withthegreatestflame.
5. Make sure nothing flammable is near the burner, including possible objects on the ceilingand loosepapers that
mightinadvertentlybedrawnintotheflamebyconvections.
6. Liftthecylinderwithbothhandsandpositionitabovetheburner.Holditafewinchesabovethetopoftheburner,
butnotsolowthatitconstrictstheairgoingintotheburner.SeeFigure70-1.
7. Be somewhat careful toavoid charring theedgeof the tube.Donot hold theedgeof the tubedirectly over the
flame.Ifheldcorrectly,thetubewillnotburn.Alsoexercisesimilarcaretoavoidexcessivelyheatingametaltube,
whichcouldpossiblyresultinaburninghazard.
8. ItmaytakeasmuchasaminuteorsountilasufficientstreamofexhaustfromtheBunsenburnerflowsthroughthe
tubetoproduceanacousticresonance.
9. Measure (or, if you prefer, observe) the pitch (or frequency) of the sound produced using the pitch gauge or
oscilloscope.Youcanalsocomparethepitchwithaknownfrequency,suchasproducedbyhittingatuningforkor
soundingamusicalinstrument.
10. Removethecylinderanddon’tforgettoturnofftheburnerwhenyouarefinished.
243
Figure70-1Resonatingtube.
ExpectedResults
Withasufficientflowofheatedair,thetubeshouldresonate.Thetallertubesproduceamuchlowerpitchthantheshorter
tubes.Thediameterofthetubedoesnotaffectthepitch,butitmayaffectthevolumebyimpactinghowmuchaircanflow.
Foragivenlength,thefrequencyofthetubeisgivenby:
The shorter columns produce tones consistent with the sounds of common concert instruments. The longer columns
produceverydeep,resonantpitches.
WhyItWorks
Theflowingair,justlikeawindinstrument,createsaresonantstandingwaveinthetube.Thelongerthetube,thelongerthe
wavelength,buttheshorterthefrequency.
Thefrequencyforanopentubeisgivenbyf=v/2L.Foragiventubelength,thisfrequencyistwiceashighasitwouldbe
foraclosedtube.Refiningthistotakeintoaccounttheslightoffsetofthenodefromtheendsofthetube,theequationis:
f=v/2(L+0.8d)
wheredisthediameterofthetube(inm),Listhelengthofthetube(inm),andvisthespeedofsound(inm/s).
244
OtherThingstoTry
Ifyouhavemorethanonetubewhosediametersaresimilar,youcannestseveraltubestogether,oneinsidetheother,as
showninFigure70-2.Thiscan letyoucontinuouslyvary thepitchof the tube, likea trombone.Youmaywant topractice
beforeauditioningforthespringmusical.
ThePoint
Theresonantfrequencyinanopenpipeislowerforagreaterlength.
Figure70-2Changingthenotelikeatrombone.
245
Project71
Springsandelectromagnets.Resonance.
TheIdea
Ononesideoftheroom,youhaveabarmagnetsuspendedfromaspring.Themagnetissurroundedbyanelectricalcoil,
whichisattachedtoanothercoilontheothersideoftheroom.Anidenticalmagnetisplacedinsidethesecondcoil.Asthe
first coil startsmoving, an electrical current is produced, which also causes the secondmagnet to startmoving. This is
impressive to seeanddemonstratesseveral principlesofphysics, including resonance,magnetic induction,andmagnetic
force.
WhatYouNeed
2barmagnets
2equalsprings
2wirecoilswithan interioropening just largeenoughfor themagnets (thesecanbemadeorareavailablefrom
scientificequipmentsupplycompanies)
2ringstandswithclampstosupportahorizontalconnectingbar;2pendulumclampswouldbeperfect
string
table
connectingwire
optional:4LEDs
Method
Overall,youaregoingtosetuptwoidenticalpartsoftheapparatus,showninFigure71-1,connectedtogetherelectrically.
Todothis,followthesesteps:
1. Suspendeachofthetwospringstothesupports.
2. Attachthetwobarmagnetstothebottomofthespringsusingstringorwire.
3. Positionthebarmagnets,sowhenthespringisdisplaceddownward,themagnetextendsintothecoil,butitdoes
nottouchthetablethecoilsaresittingon.
4. Startwithbothspringshanging.
5. Displaceonespringtosetitoscillating,butleavetheotherspringhangingundisturbed.Observetheresult.
ExpectedResults
Initially,thefirstmagnet,afterbeingsetinmotion,goesupanddownbyitself.Themotionofthefirstmagnetgeneratesan
electricalcurrentthatcausesthesecondmagnet/springcombinationtostarttooscillate.
WhyItWorks
The firstmagnetmoving through thecoil generatesacurrent.This current is transmitted to the secondcoil.Thecurrent
flowinginthesecondcoilexertsaforceonthesecondmagnet,whichsetsitinmotion.Becausebothspringsareamatched
setwithnearly identicalspringconstants,thefrequencyoftheelectricalsignaldrivingthesecondspring isat itsresonant
frequency.Asmalldrivingforceattheresonantfrequencyhasamuchgreaterimpactthanaforceatanyotherfrequency.
246
Figure71-1Themovementofonespringcausestheotheronetoresonate.
OtherThingstoTry
Ifyouwanttopushyourluck,youcanputanLEDintheelectricalcircuit.LEDsconductcurrentinonlyonedirection.Apairof
LEDs,eachorientedintheoppositedirectionandconnectedinparallel,wouldbeneededtopreventblockingthecurrentflow.
Youcanalsoputagalvanometeroracurrentsensorinserieswithoneofthewiresandmeasurethecurrentflowdirectly.
Anothersimplewaytoshowoscillationbetweenmagnetsistosuspendtwomagnetshorizontallyfromsprings.Startwith
thenorthpoleofonemagnetfacingthesouthpoleoftheothermagnet.Then,turneachofthemagnetsfromthatequilibrium
line.Theycanbeturnedthroughanangle inthesameoropposingdirections.Themagnetswillmovetobringthemselves
backtothatequilibriumposition.Buttheywillovershootandkeepgoinguntil theirenergyis losttofriction.Untilthen,they
formasimpleharmonicoscillator.Trythiswithdifferentstartingangles.
ThePoint
Amagnetmovinginacoilofwiregeneratesanelectricalcurrent.
Anelectricalcurrentmovinginawireexertsaforceonamagnet.
Asimpleharmonicoscillator(inthiscase,thespring)resonatesifdrivenatitsresonantfrequency.
247
Project72
Speedofsound.Timinganechooldschool.WhyGalileocouldn’tdothiswithlight.
TheIdea
Thespeedofsound,likeanyothersound,canbefoundbymeasuringthetimeittakestogoacertaindistance.Thissimple
andstraightforwardmeasurementcangiveareasonableballparkestimate,butnothighlyaccurateresults.Wewill,however,
belimitedbythelargedistancesweneedtoworkwithandthesmalltimesweneedtoaccuratelymeasure.Wemeasurethe
speedofsoundusingamoreaccuratemethodinthefollowingprojects.
WhatYouNeed
long tapemeasure (or someotherway toestimatea longdistance, suchascountingcinder blocksofa known
lengthonabuildingorclockingthedistanceofseveralblocksusingtheodometerofacar)
meansofgeneratinga loudsound(suchasanairhorn,garbage-can lid,orbaseballbat,orsomeonewitha loud
voice)
stopwatch
partner(whichmaynotbeneededifyoucansetupanecho)
Method
1. Measureorestimateacourseofknownorestimateddistancewithoutvisualobstruction.Afootballfieldorpossibly
multiple lengthscanwork.Youcanalsouseabuildingornaturalgeographicfeature,suchasacliff toreflectan
echo.Thiseffectivelydoublesthedistancethesoundtravels.
2. Generatethesoundandnotethedifferenceintimebetweenwhenthesoundwasgeneratedandwhenitisheardat
adistantlocation.(Thiscanbeaccomplishedbyobservingwhenthegarbage-canlidwasstruckorobservingata
distancewhentheairhornissounded.)
3. Togetthespeedofsound,dividethedistancebythetime.SeeFigure72-1.
ExpectedResults
Thespeedofsoundisabout343meterspersecondorabout1096feetpersecondat20°C.Itisunlikelythistechniquewillgiveanaccuratevalueforthespeedofsound,butitshouldprovideaballparkestimate.
248
Figure72-1Measuringthevelocityofsounddirectly.
WhyItWorks
Velocityisdistancedividedbytime.Becausethespeedoflightissomuchgreaterthanthespeedofsound,thetimeittakes
lighttotravelthedistancecanbeconsideredessentiallyzeroandisinsignificantcomparedtothespeedofsound.
NotethatGalileotriedtomeasurethespeedoflightusingasimilarmethod.Lightmovessoquickly,however,itrequires
extremelylargedistancestomeasurethetimeittakestotravelusingastopwatch.RatherthansayingthatGalileofailedin
hisattempt,weliketosayhesucceededinprovingthatlightwasmuchfasterthanhecouldmeasure.
OtherThingstoTry
Thedistance toa lightningstrikecanbedeterminedbycounting thenumberofsecondsbetweenseeing the lightingand
hearingthethunder.Usingaknownvalueforthespeedofsoundmultipliedbytimecanprovideanestimateofthedistance
tothelightningstrike.Similarly,thespeedofsoundcanbedeterminedifthedistancetothelightningstrikeisknown(orcan
bemeasured, suchasbydriving towhere the lightningwasobserved tohit) anddividedby the timebetweenseeing the
lightningandhearingthethunder.
ThePoint
Speedisdistancedividedbytime.However,theaccuracyofanyexperimentislimitedbytheresolutionoftheleastcertain
measurement.Evenifdistancecanbemeasuredaccurately,thetimemeasurementsarelimitedbythereactiontimeofthe
observer.
249
Project73
Speedofsound.Resonanceinacylinder.
TheIdea
Inthisexperiment,wemeasurethespeedofsoundbasedontheresonancethatatuningforkproducesoveracolumnof
water inacylinder.Unlike theverydirectapproachof theprevioussection,we takeadvantageof thewavepropertiesof
soundtomakeamuchmoreaccuratemeasurement.
WhatYouNeed
tuningforkofknownfrequency
rubbermallet
closedwatertightcylinder(about15–20cmtall)—a1–2Lgraduatedcylinderwillwork
ruler
200mLbeaker(orothercontainerwithaspouttopourwaterintothegraduatedcylinder)
water
quietroom
Method
1. Strike the tuning fork with the rubber mallet. Hitting the tuning fork on a hard surface may result in altering its
frequency.
2.Holdtheringingtuningforkoverthetopofthegraduatedcylinder,asindicatedinFigure73-1.
3.Placeyourearnearthetopofthegraduatedcylinderandlistentothesoundofthetuningfork.
250
Figure73-1Findingthecolumnlengththatresultsinresonanceataparticularfrequency.
4.Slowlyaddwater to thecylinderandcontinue to listen.This canbea several-personoperation.Becareful not to
causethewatertosplash,whichcandistractthelistenerfromhearingthesoundofthetuningfork.
5.Atacertainheight,asthewaterlevelisraised,thesoundofthetuningforkbecomesmarkedlylouder.Youmayneed
tolistencarefullytohearit.
6.Onceyouthinkyoufoundtheresonance,pouroutsomeofthewaterandconfirmthatthesoundlevelforthetuning
forkbecomeslower,andthengetslouderagainasthewaterlevelisbroughtbackup.Itshouldalsogetlowerasthe
water level is raisedabove the resonance level. (If youmiss the first resonance,continueaddingwaterandyouwill
hearthesecondresonance.Usingthewavelengthforthesecondresonancewillresultinaspeedofsoundthatishalf
thecorrectvalue.)
7.Determinethefrequencyofthetuningfork,eitherbynoticingthemarkingonthetuningforkorbymeasuringit.You
canuseaninstrumenttunertomeasureorverifythefrequencyofthetuningfork.
8.Calculatethespeedofsoundusingthisequation:
v=4Lf
whereListhelengthoftheaircolumnabovethewaterandfisthefrequencymarkedonthetuningfork.
9.Amoreexactexpressionwhichaccountsforthenodeofthesoundwavenotbeingexactlyattheopeningofthetube
ofdiameter,d,is:
251
v=4f(L+0.4d)
ExpectedResults
Theacceptedvalueforthespeedofsoundat20°Cis343m/s.Thewarmertheair,thefasterthespeedofsound,accordingtotheequationv=331m/s+0.6TwhereTisthetemperatureindegreescentigrade.
Togetan ideaof theappropriate height needed in the resonantair column for variouscommon tuning forks, youcan
check the following table. These values do not include the correction factor used in the experiment to account for the
diameterofthecylinder.Itispossiblethatsomeonedoingthisexperimentmaynotnoticetheresonanceofthefundamental
frequencyandwillcontinuefillingthegraduatedcylinderuntilarrivingattheresonanceforthesecondharmonic.Table73-1
servesasaguidetofindthecolumnheightthatproducesaresonantfrequency.
WhyItWorks
Theresonanceoccurswhenthelengthofthecolumnproducesanaturalresonancethatisthesameasthetuningfork.
Table73-1
Onewaytothinkaboutthisisthat,atthespeedofsound,thesoundgoestothebottomofthecolumnandbackinthe
sametimeasthetuningforkgoesthroughonevibration.
Anotherwaytosaythisisthefrequencyofthestandingwavethatresonatesequalsthefrequencyofthetuningfork.The
waveequationstatesthatthevelocityofawaveequalsitswavelengthtimesitsfrequency.Theequationis
v=λfwherevisthevelocity(inm/s),λisthewavelength(inm),andfisthefrequency(incyclespersecondorHz).
OtherThingstoTry
Comparethismethodtotheothermethodsofmeasuringthespeedofsoundfoundinthisbook.
ThePoint
The speed of sound can be determined bymeasuring the length of an air column at which a tuning fork establishes a
resonance.One-quarterwavelengthfitsintheaircolumn.Measuringtheaircolumncanthendeterminethewavelengthofthe
sound.Thiscombinedwiththefrequencydeterminesthespeedofsound.
252
Project74
Racingagainstsound.Dopplereffect.
TheIdea
WeatherforecastersusetheDopplereffecttodetectwindshear.Astronomersuseittodeterminethatdistantgalaxiesare
movingawayfromeachotherinanapparentexpansionoftheuniverse.Thisexperimentdemonstrateshowthefrequencyof
asoundmovingtowardorawayfromalistenerisaffectedbytheDopplereffect.
WhatYouNeed
1meterlengthofstring
1electricbuzzerorothersourceofasustainednote(thebuzzermusthaveapointofattachmentforapieceof
stringandmustnotrequiresomeonetocontinuouslyactivateaswitchtomakeitsound)
2people
optional:microphone,oscilloscope,orsoundcardoscilloscope
Method
1. Securelyattachthebuzzertothestring.
2. Turnonthebuzzer.
3. Onepersonspinsthebuzzerinacircle,movingtowardandawayfromthesecondperson,asshowninFigure74-1.
4. The observer should listen to the sound the buzzer makes as it comes toward and away from where they are
located.
ExpectedResults
Thepitchofthesoundincreasesanddecreasesatarateestablishedbytheperiodoftherotatingbuzzer.Thevolumeofthe
buzzersoundmayalsoincreaseanddecrease,butthatisnottheDopplereffect.Thefasterthebuzzerspins,thegreater
thedifferenceinpitch.
Thepitchishigherasthesoundmovestowardyouandlowerasitmovesawayfromyou.
WhyItWorks
Whensoundiscomingtowardyou,thepeaksandtroughsofthewavesareclosertogether,asindicatedinFigure74-2.This
resultsinahigherfrequencyofthesoundwave.Fromtheperspectiveofthelistener,thesoundwavesseemtocomemore
frequentlyandareperceivedtohaveahigherpitch.
OtherThingstoTry
Attachthemicrophonetoeitheraphysicaloscilloscopeorasoundcardoscilloscope.Displaythesoundandcomparethe
frequencyproducedbythebuzzercomingandgoing.
253
Figure74-1Soundvariesinpitchasitmoveswithrespecttothelistener.
Figure74-2Asthebuzzermovestowardthelistener,theperceivedpitchofthesoundishigher.Asitgoesaroundthecircle
andmovesawayfromthelistener,thepitchbecomeslower.
Attachabuzzertoanyobjectthatcanmoveinamoreorlesshorizontaldirection(suchasanairtrackglider,africtionless
cart,orevenanoldskateboard).Astheobjectmoves,listentothesound.Ifyoucan,alsotrydisplayingthewaveformonan
oscilloscope.
ThePoint
TheDopplereffectoccurswhenthesourceofthesoundiseithermovingtowardyouorawayfromyou.Whenthesourceof
soundismovingtowardyou,thepitchorfrequencyofthesoundishigher;whenthesourceofsoundismovingawayfrom
you,thepitchislower.
254
Project75
Addingsounds.Beatfrequency.
TheIdea
Whenwavesmeetupatthesamepointinspace,thewavesaddtogethertoformanewwave.Thiscombiningofwavesis
calledsuperposition.Thewavesaddtogetherinaprocesscalledinterference.Ifthecrestsformatthesameplace,wehave
constructiveinterferenceandthecombinedwaveissmaller.Ifacrestmeetsatrough,wehavedestructiveinterferenceand
asmallerwave.
Sometimeswhenwavescombine,thepatterntheyproduceisitselfawave.Wecanhearthebeatfrequencyofasound
wavemosteasilywhentwosoundwavesareseparatedbyasmallfrequencydifference.
WhatYouNeed
sourceoftwotonesthatdifferbyafewHz.Someoptionsforthisinclude:
–adjustabletuningforkpairwithresonantcavities
–2matchedtuningforks,oneofwhichcanbedetunedbyapplyingasmallmasstothetinesofoneofthetuningforks
–(Polyphonic)keyboardsynthesizer
waveformgeneratorwithtwochannelsortwowaveformgenerators
optional:agoodpairofears
optional:anoscilloscope—eitheraphysicalinstrumentorasoundcardoscilloscope
Method
1. PlaytwotonesatthesametimethataredifferentbyonlyafewHz.Forinstance,youcanuse440and445Hz.Or,
youcanplaytwonotesonakeyboardseparatedbyasteportwo.
2. Listencarefully.Seeifyoucandistinguishthefirsttoneandthesecondtoneindividually.Then,listenforafadingin
andoutoftheoverallsound.Thatthrobbingofthebasictoneiscalledthebeatfrequency.Thepulsationitselfhasa
frequencyequaltothedifferencebetweeneachofthetwoindividualfrequencies.
3. UsingthetechniquedevelopedinProject64,displaythecombinedwavesforeachofthetonesontheoscilloscope.
4. Measure the frequency of the overall pulsating wave pattern that envelops both waves. Compare that to the
differenceinfrequencyforeachofthetwoindividualwaves.
ExpectedResults
Youshouldhearapulsatingthrobbingtonethatcausesthecombinedtonestoperiodicallygrowlouderandsofter.
Asanexample,bycombininga440Hzwavewitha445Hzwave,yougetacombinedtonethatgetslouderandsofter
everyfiveseconds,asshowninFigure75-1.Thebeatfrequencyisthedifferencebetweenthetwooriginalwaves.
255
Figure75-1Additionoftwofrequenciesproducesabeatfrequency.
WhyItWorks
Whentwowavesareproducedatthesamelocation,thebeatfrequencyequalsthedifferencebetweenthefrequenciesof
thetwowaves.
OtherThingstoTry
Wecanalsolookattheproductofthetwowavesthatexaggeratestheoverallpatternofthebeatfrequency,asshownin
Figure75-2.Manyoscilloscopesdisplaytheproductofthetwoinputwaveforms.
256
Figure75-2Multiplyingtheamplitudesoftwosoundwavesshowsthebeatfrequencymoreprominently.
ThePoint
Thebeatfrequencyisthedifferencebetweenthefrequenciesofthetwoindividualwaves.
257
Project76
Pendulumwaves.
TheIdea
Thisdemonstrationusesanapparatusbuilt fromseveraldifferentmasseshanging fromstrings.Eachpendulum isslightly
shorterthanitsneighbor.Becausetheperiodofapendulumislongerforlongerstring,eachpendulumwillgobackandforth
inslightlylesstimethanitsneighbor.Thisdifferenceresultsinanoverallchangingpatternofstandingwavesandtraveling
waves.
WhatYouNeed
8–12smalluniformmasses(nuts,hookedmasses)
stringorfishingline
frame,asshowninFigures76-1and76-2,whichallowsthestringforeachsuccessivemasspendulumtobecome
progressivelylarger
ThisapparatusisalsocommerciallyavailablefromEdmundsScientific(itemnumber3123752).
The followingequation (fromPendulumWaves:ThePhysicsofaSetofTunedPendulums, BradDeGregorio, found at
member.cox.net/brad.degregorio/PendulumWave.pdf)givestheoptimallengthsforeachpendulumstring:
Lengthofnthpendulumstring:
where,Tmaxistheperiodofthelongestpendulum,kisthenumberofcyclestheapparatusgoesthroughbeforerepeatingits
pattern,andnisthenumberofthependulum(n=1isthefirstpendulum,n=2isthesecond,andsoon).
Figure76-1Invertedstaircaseframeforpendulumwave.
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Figure76-2Simpleframeforpendulumwave.
Table76-1
Table76-1givesthelengthofasetofstringsforapendulumwavetorepeatevery30secondswith25oscillationsforthe
longeststringduringthattime.
Noticethattheoptimalstringlengthisnotlinear.Somependulumwaveframesareactuallycurvedtoaccommodatethe
shapegivenbythepreviousequation.
Method
1. Attachthestringstothemasses.
2. Adjustthestringlengthsbetweenthemassesandtheframe,soallthemassesarethesamelength.
3. Attachtheotherendofeachstringtotheframe,soeachofthemassesisatthesameheightfromtheground.The
massesshouldbelowenoughsotheycanbeobservedfromabove.
4. Securetheframetoatableorothersupports,soeachofthemassesisfree-swingingabovethefloor.
5. Holdallthemassesandpushofftoonesideusingameterstickorflatboard.Themassesarenotpushedtoward
eachother.
6. Release themasses and observe from above. Placing a board underneath themassesmay help in viewing the
patterntheyformastheymove.
ExpectedResults
Themassesdefineacontinuouslychangingpattern.Withthefirstswing,themassesallswingprettymuchtogether,resulting
inthepatternsshowninFigures76-3,76-4,and76-5.
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Figure76-3Linearalignment.
Figure76-4Quarterwave.
Figure76-5Fullwave.
WhyItWorks
Theperiodofapendulum,orthetime,T(inseconds),ittakestoswingbackandforthonetimeincreaseswiththelengthof
thependulum,accordingtotheformula:
T=2π(L/g)½
whereListhestringlength(inmeters)andgisthegravitationalaccelerationconstant(inm/s2).
Becauseeachsuccessivemasshasaslightlylongerstring,itsperiodislongerthanthemassbeforeit.Themorecycles
themassesgothrough,themoredifficultitisforthemassesonthelongerstringstokeepup.Thedelaythatoccursinthe
slowermassesbeginstodevelopintothepatternsdepictedinthepreviousfigures.
OtherThingstoTry
A follow-up to thisexercise is topredict theperiodduringwhichasequenceofpatterns repeats.Thiscanbeverifiedby
measuringhowoftenaparticularpatterntakestorecurcomparedwiththestepsizeforeachsuccessivependulum.
ThePoint
This project illustrates the variability of the period of a pendulum with string length. It also shows how changes in the
frequencyofawavecanhaveaneffectonwhetheritisinphaseoroutofphasewithothermassesinthesystem.
260
Project77
Usingwavestomeasurethespeedofsound.
TheIdea
Inthisexperimentyouwilldeterminethespeedofsoundbymeasuringhowlongittakessoundtogetfromonemicrophone
toanotherseparatedbyaknowndistance.ThisisalmostthesamethingyoudidinProject72.Theonlydifferenceisthat
hereweuseanoscilloscopetomeasurethedifferenceintimeinsteadofastopwatch.
Youcantakeadvantageofthewavepropertiesofsoundtofindthedistancebetweenthepositionswherethesoundis
loudest.Thisoccurswherethesoundconstructivelyinterferes.Thisletsyoufindthewavelengthofthesound.Knowingthe
wavelengthandfrequencyofsoundletsyoudetermineitsvelocity.
Thisexperimentprovidesanopportunitytoexplorebasicpropertiesofwavesingeneral.Theoveralltechniquesusedhere
can,withsignificantrefinements,alsobeusedtomeasurethespeedoflight.
WhatYouNeed
2speakers
2approximately6-footlengthsofhookupwire
tonegeneratororasingletonewavfileplayedthroughacomputerordigitalaudioplayer
2microphonesconnectedtoanoscilloscope(orasensitivesoundmeter)
tapemeasure,meterstick
quietroom
Method
Twospeakers/onemicrophone
1. Connectthetonegeneratortothetwospeakersusingthehookupwire.Connectthepositiveterminalofthetone
generatortothepositiveterminalofeachofthespeakers.Thenegativeterminalofthetonegeneratorisconnected
tothenegativeterminalsofeachofthespeakers.
2. Positionbothspeakersside-by-sidedirectedtowardthemicrophone.Atthispointandthroughoutthismeasurement,
eachspeakershouldhaveanunobstructedline-of-sightviewtothemicrophone,asshowninFigure77-1.
3. Turnon the tonegenerator.Verify thatbothspeakersarefunctionalandat roughly thesamevolume.Youshould
hearasteady,continuoustone.Anymidrangerangefrequencyshouldwork,suchas440Hz,althoughthismethod
workswellforallaudiblefrequencies.
4. Connect themicrophone toyouroscilloscope. (Alternatively, youcanuseasoundmeteror just listencarefully to
determinethepositionsofmaximumandminimumsoundintensity.)
5. Display thewaveformpickedupby themicrophoneson theoscilloscope.Adjust theamplitude, timescale,and, if
needed,thetriggersetting.
6. Slowly move one of the speakers (either forward or back) along the line between it and the microphone. Each
speakershould,atalltimes,continuetofacethemicrophone.
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Figure77-1Findingthedistancebetweenpositionsofmaximumintensitytodeterminethespeedofsound.
7. Monitortheamplitudeofthesignaldisplayedontheoscilloscope(ortheintensityonthesoundsensor;youcanalso
heartherelativeintensityofthesoundwithreasonableaccuracy).Becarefultoavoidanyobjectsthatcouldblockor
reflectthesoundwavesstrikingthemicrophone.
8. Notethefrequencyofthesoundwaves(fromthesettingonthetonegeneratororthewavfileyouused).However,if
youdon’tknowthefrequency,orjustwanttoconfirmit,determinehowmanysecondsittakesonthetimescalefor
onefulloscillationtooccur.Thetimeittakesforonewavelengthtooccuriscalledtheperiodofthesoundwave.
Thereciprocaloftheperiodisthefrequency,f(inHzorcyclespersecond).
9. As you adjust the distance between the speakers, you should see the amplitude of the combined sound waves
decrease,reachaminimum,andthenreturnbacktoitsmaximumlevelasthespeakersaremoved.
10. Thedistance between the speakerswhen the sound is at amaximum is a fullwavelength. This is the result of
constructivereinforcementofthesignals.Thedistancebetweenthespeakerswhenthesoundisataminimumisa
halfwavelength,resultingindestructiveinterference.(ThecomponentsforthisexperimentareshowninFigure77-2.)
Figure77-2Componentstomeasurethespeedofsound.
11. Measure the distance between the two speakerswhen the sound is atmaximum level. This distance is one full
wavelength,λ,ofthesoundwave.Ifyoumeasurethisinmeters,yourcalculationforthespeedofsoundwillbeinmeters per second. (You can get additional data points by measuring different locations, finding the one-half
wavelengthfromthepositionswhenthesoundisataminimum,andthenrepeatingthisatvariousfrequencies.)
12. Oncewehavethewavelength,λ,andthefrequency,f,youcanmultiplythemtogethertogetthevelocityusingthewaveequation:
v=λf
ExpectedResults
262
Asbefore,thespeedofsoundat20degreescentigradeis343meterspersecond.
Thespeedofsound(inmeterspersecond)asafunctionoftemperature(indegreescentigrade)isv=331+0.6T.
Usinga440Hz tone, thedistanceseparating themicrophones togeta343meterper second value for thespeedof
soundis0.78meters(78centimeters).
A1000Hztonewouldrequirea0.343meterseparationtoresultintheexpectedvalueforthespeedofsound.
WhyItWorks
Twowavestravelinginthesamedirectionaddtogethertoformanewwave.Ifthecrestsofthetwowavesriseatthesame
time and place, the waves are said to be in phase and reinforce each other to produce a louder sound. This is called
constructiveinterference.Thisoccurswhenthetwosourcesofthesoundareseparatedbyexactlyonefullwavelength.(One
wavegetsaone-wavelengthheadstart,butbothareinphaseatthedetector.)Ifweknowthewavelengthandthefrequency
ofthesound,wecaneasilydetermineitsvelocityaccordingtotherelationshipv=λf.
Figure 77-3 Sound waves (amplitude versus time) shifted by one-half a wavelength as a result of traveling through the
distancebetweenthetwospeakers.
Destructiveinterferenceoccurswhenonewavecrestswhilethetroughofasecondwaveispassing.Thishappenswhen
thesourceofthetwowavesisseparatedbyhalfawavelength.
OtherThingstoTry
Twomicrophones/onespeaker
If you can set up two microphones to your oscilloscope, there is another way to do this that shows the process of
263
interferencemoreclearly. Inthiscase,youfollowbasicallythesameprocedureasthepreviousone,exceptyouhaveone
speakerandtwomicrophones.Youmovethemicrophonesuntilyouobservedestructiveinterference.Thisoccurswhenthe
crestofonewaveisatthesameplaceasthetroughoftheotherwave,asshowninFigure77-3.Thismethoddoesnotwork
usingasoundintensitymeterorbylisteningcarefully,asdidthepreviousmethod.
Followingthismethod,youcanusethecapabilitythatmanyoscilloscopeshavetodetectthepointatwhichthewavesare
separatedbyone-halfawavelength.Thisinvolvesplottingonesignalversustheotheronthedisplay.Whenthisxversusy
plot isastraight linewithaslopeequal toanegativeone,asshown inFigure77-4,yoursignalsare180degreesoutof
phaseandseparatedbyone-halfwavelength.
Figure77-4x–yplotoftwosoundwavesshowingtheseparationofone-halfwavelength.
Interferencealongaline/doubleslitanalogy
AnotherconfigurationthatcanbeusedtofindpositionsofaconstructiveanddestructiveinterferenceisshowninFigure77-
5.ThismethodisanalogoustothedoubleslittechniqueusedbyThomasYoungwithlightandisexploredinProject83.The
wavelengthisgivenby:
λ=dsinθwhered is theseparationbetween thespeakersandθ is theanglebetween themidpointbetween thespeakersand thepointwhereconstructiveinterferenceisidentified.
Speedoflight
Usingasimilarprinciple, thespeedof lightcanalsobemeasured in the lab.Anapparatus iscommerciallyavailable that
determines the wavelength of a known frequency of light by measuring the distance between positions of constructive
interference. Themeasurement is much trickier than the one in this experiment because the speed of light is somuch
greaterthanthespeedofsound.Thesamebasicapproach,however,canbeappliedtoeithersoundorlight.
264
ThePoint
Thespeedofsoundcanbedeterminedifthewavelengthandfrequencyofthewaveareknown.Thewavelengthforagiven
frequencycanbedeterminedbyfindingthedistanceatwhichconstructiveinterferenceoccurs.
Figure77-5Findingthelocationsofmaximumandminimumsoundintensitytodeterminethespeedofsound.
265
Section7
Light
Project78
Rayoptics.Tracingthepathoflightusingalaser.
TheIdea
Thisisaperfectwaytoseeforyourselfhowlightmoveswhenitencountersmirrorsandlenses.
WhatYouNeed
laserpointer
setoflenses,includingconvex,concave,rectangular,andsemicircularlens;rectangularprismand60andright-angle
prisms(90°,45°,45°)and(90°,30°,and60°)2smallflatmirrors
sheetofpaper(plainorgridded)
ruler
protractor
darkroom
Method
1. Caution—Youshouldusealow-powerlaserpointerandbecarefulnottoshinethelaserwhereitcouldhitanyone’s
eyes.Remember,youareworkingwithopticaldevicesthatchangethepathofthelight,sobecarefultoavoidstray
lightraysthatcouldaffectanyone’seyes.
2. Placeyourobjectlens(ormirror)onaflattable.
3. Placeasheetofpaperunderneaththelens.
4. Tracetheoutlineofthelensonyourpaper.Leaveenoughroomtodrawincomingandoutgoinglines.
5. Darkentheroom.
6. Shinethelaserataslightangle,soitsstraightlinepathcanbeseenonthepaper.
7. Foreachofthelenses,putthreeormoredotsalongthepathtodefinetheincidentpath.
8. Observeitspaththroughthelens(orreflectedfromthemirrors).Youmayneedtoslightlyadjusttheangle(tothe
planeofthetable)tomakethetransmittedrayvisible.Dependingonyourlenses,youmaynotbeabletoseethe
laserlightgoingthroughthelens.Also,becarefulnottomistakelightthatmaysneakunderneaththelensasaray
that follows the intended optical path through the lens. Also (again depending on your lenses), youmay need a
slightlydifferentangletomaketheincidentlaserlinevisibleasyouwouldneedfortherefractedline.Ifthisisthe
case,makesureyoucomeintothelensalongthesameincidentlinethatyoudrew.
9. Makethreeormoredotstodefinetherefracted(orreflected)paths.
10. Makeadotwherethelightentersthelensandwhereitleavesthelens.
11. Connectthedotswithstraightlinesshowingtheincident(incoming)line,thestraightlinethroughthelens(whichis
therefractedline),andthetransmittedorreflectedlines.
12. Exploreasmanyofthefollowingopticalobjectsasyouhaveavailable.Thefollowinglistsseveralspecificthingsto
focuson.
266
(Note:Allthiscanbedone,ifyouprefer,onamagneticchalkboardusinglenseswithmagneticbacks.Youcaneitherglue
strongmagnets toyour lensorsimplyhold the lens to thechalkboard.Makesure that themagneticchalkboard isstrong
enough to hold the lens securely and that themagnet does not block the path of the light. Laser levelsmay be useful
becausetheyhavebuilt-inanglestomakethelinevisiblealongasurface.However,theymaybealittletrickiertofocusall
thewaythroughthelens.)
Singlemirror
Drawaperpendicular linetothesurfaceofthemirror.Shinethe laseratthepointwheretheperpendicular linemeetsthe
mirror.Placedotsalongtheincidentlineandthereflectedline,andthenconnectthedots.Comparetheincidentanglewith
thereflectedangle.Trythisforseveralsetsofangles(Figure78-1).
Mirrorsatarightangle
Shine the laserononeof themirrorsand trace itspath (byplacingdotsalong thepathandconnecting them).Thepath
shouldhitthesecondmirror,andthenreflectoffthesecondmirror.Trythisforseveralanglesofincidenceonthefirstmirror.
(Ifyoulikegeometry,setthemirrorsatanacuteangle.Then,predictandtesttheangleoftheoutgoingrayforagivenangle
ofincidence.)
Figure78-1Reflectionfromaplanemirror.
Convexlens
267
Aconvexlensistheonethatisthickeratthemiddlethanattheends.Drawacenterlineperpendiculartotheaxisofthelens.
Tracethefollowingpaths:a)astraightlinealongthecenterlinethroughthecenterofthelens,b)alineabovethecenterline
runningparalleltothecenterline,c)alinebelowthecenterlinerunningparalleltoit.Traceallthelines.Noticewherethethree
linescross.Measurethatdistanceandputadotonthecenterlineontheincidentsideofthelensthatsamedistancefrom
thelens.Directthelaseratanyanglethroughthatdotandtraceitspaththroughthelens.Trythisforseveralangles.
Figure78-2Mirrorsatarightangle.
Figure78-3Convexlens.
Concavelens
Aconcavelensistheonethatisthinneratthemiddlethanattheends.Drawacenterlineperpendiculartotheaxisofthe
lens. Trace the following paths: a) straight line along the center line through the center of the lens, b) a line above the
centerlinerunningparalleltothecenterline,c)alinerunningbelowthecenterlinerunningandrunningparalleltoit.Traceall
thelines.Howdotheseresultscomparewiththosefromtheconvexlens?
Semicircularlens
Thesemicircularlenshasonecircularsideandoneflatside.Placethecircularsidetowardyou.Tracethelensanddrawa
268
centerlineon the flat side.Shine the laserat a30-degreeangle to that centerline, but hit thepointwhere thecenterline
meets the flat side of the lens. This particular arrangement avoids refraction in the glass because the light comes in
perpendiculartothetangentatthecircularedge.Inthiscase,theonlyrefractionthatoccursisattheglass-to-airinterface.
Observewhathappensfordifferentangles.Takeittotheextremesofhighandlowanglesofincidence.
Figure78-4Concavelens.
Figure78-5Semicircularlens.
269
Figure78-6Rectangularprism.
Rectangularprism
Drawaperpendicularlinetooneoftheedgesoftheprism.(Makesuretheedgesyouareusingareclearandnotfrosted.)
Directthebeamtowardthepointwheretheperpendicularmeetstheedgeandtracethepathofthelaserthroughtheprism
atvariousangles.
Right-angleprisms
Therearetwomaintypesofright-angleprisms:90°,45°,45°and90°,30°,60°.Hereisachallenge.Tryiteitherbyworkingoutthelightraysfirstorbyjustplayingwiththeprismsandfiguringitoutbytrial
anderror:
a)Howcanyoudirectalightraythroughtheprismandhavearayemergeat90degreestotheincomingray(basedonly
ontotalinternalreflection)?
b)Howcanyoudirectalightraythroughtheprismandhavearayemergeat180degreestotheincomingrayheading
backinthedirectionthatitcamefrom(alsobasedonlyontotalinternalreflection)?
ExpectedResults
Singlemirror
Themeasurementsshouldvalidatetheideathattheangleofincidenceequalstheangleofreflection.
270
Figure78-745-degreeprism.
Mirrorsatarightangle
Regardlessoftheangleatwhichthelaserraystrikesthemirror,therayreflectedfromthesecondmirrorwillbeparallelto
theincomingray,butheadingintheoppositedirection.
Convexlens
Raysstriking the lens travelingalong thecenterlinewill gostraight through the lenswithoutbeingdiverted.Rays traveling
paralleltothecenterlinebendtowardthecenterlineandcrossatapoint(calledthefocalpoint)ontheoppositesideofthe
lens.
Figure78-860–30right-angleprism.
271
Rayspassingthroughafocalpointonthesamesideofthelensasthelaser(samedistanceasthefocalpointmeasured
previously)emergefromthelensparalleltothecenterline.
Concavelens
Nomatterwheretherayshitthelens,theraysdonotcross.Abovethecenterline,theraysbendup.Belowthecenterline,the
raysbenddown.
Semicircularlens
Rayshittingthesemicircularsideanddirectedtowardthecenterofthecirclebend(orrefract)onlywhenemergingfromthe
glasstotheair.
Rectangularprism
Raysemergingfromthelensareparalleltotheincidentray,butoffsetinthedirectionthatraysmovethroughthelens.As
withalltheseobservations,thepaththeraytakesintheprismisastraightline.
Right-angleprism
Raysstrikingoneofthetwoshorteredgesofthe(90°,45°,45°)prismmakea90-degreeturn,andthenreflectback.Raysstrikingthelonger(hypotenuse)edgeofthe(90°,30°,60°)prismmakea180-degreeturn,andthenreflectback.
60-degreeprism
Theseproducearangeoftransmittedanglesandconditionsfortotalinternalreflection.
WhyItWorks
Lenses are optical devices that refract light passing from onemedium (air) through another (glass or plastic), and then
typicallybacktotheair.Ateachinterface,thelightisbentaccordingtoSnell’slaw.
Mirrors,whetherinvolvingoneormanysurfaces,reflectlightinsuchawaythattheangleofincidenceequalstheangleof
refraction.
OtherThingstoTry
Thelensesandmirrorspreviouslydescribedcanalsobestudiedusingthefollowingadditionalmethods:
Ray tracing with split beam. You can make or buy an apparatus that projects several parallel beams of light.
Basically,theapparatusconsistsofabulbcoveredbyanenclosurethatshinesthroughparallelopeningsintheside
of theenclosure.Thebeamsof light,whendirectedat thevarious lensesandmirrors,showthepropertiesof the
devicesinagraphicandintuitiveway.Thisapproachisbettersuitedtosmallerlensesandmirrors.
Ray tracing by locating images. Amore traditional approach is to view a vertical object such as a pin or a nail
through the lens.This isaccomplishedby:a) tracing theoutlineof the lens,b) locating thepositionof the image
seenthroughthelens,andc)drawingalinetoshowtheincident,refracted,andtransmittedpathsoflight.
ThePoint
Lensesandmirrorsdivert light inpredicableways.Lensesarebasedon refraction,whilemirrorsemploy reflection.Some
lensesareconverginganddirect raysof lightpassing through themthrougha focalpoint.Other lensesaredivergingand
directtheraysoflightinsuchawaythattheynevercross.Thereflectionatthesurfaceofanyplanemirroroccursinsucha
waythattheangleofincidenceequalstheangleofreflection.
272
Project79
Twocandles,oneflame.
TheIdea
No, this is not the title of a bad country western song. This is a great optical illusion that is best shown to a group of
observerswhohavenothadthebenefitofseeinghowitwassetupbeforehand.
WhatYouNeed
2nearlyidenticalcandles
matchorlighter
table
paneofglass(orPlexiglas)
waytoholdtheglassperpendiculartothetablesafelyandsecurely.Thisworkswithsomeonesimplyholding the
paneofglassonthetable.Aringstandwithabeakerclamp(ortwo)alsoworkswell.
Method
Setup
1. Securetheglassperpendiculartothetable.
2. Placeonecandleonthetableintheuprightpositionononesideoftheglass.
3. Placetheothercandleuprightonthetableontheothersideoftheglassalongthesamelineandthesamedistance
asthefirstcandle.
4. Pickonesideoftheglasstoview.
5. Lightthecandleontheviewingside.
Figure79-1PhotobyS.Grabowski.
Viewing
1. Allobserversshouldbeonthesideofthepanewiththelitcandle.
274
2. Observetheappearanceofbothcandles.
ExpectedResults
Youcanseethe imageof theflamefrombehindtheglass,superimposedonthewickof the (unlit)candle in frontof the
glass.
Figure79-2PhotobyS.Grabowski.
WhyItWorks
Whenlightstrikesatransparentsurface,suchasapieceofglass,someofthelightisreflected,whilesomeofthelightis
refractedandtransmittedthroughtheglass.Theimageoftheburningcandleinfrontoftheglassisreflected.Theimageof
thecandlewithoutaflamefrombehindtheglassistransmitted.Boththereflectedandtransmittedlightraysformimages
thatfallontopofeachother.Thiscreatestheillusionthatasingleimageexistsandthecandlebehindtheglassisburning.
Figure79-3PhotobyS.Grabowski.
OtherThingstoTry
Anotherwaytodothisistoreplacetheunlitcandlewithabeakerofwater.Thewaterlevelshouldbeabovethelevelofthe
candle.Thereflectedimageofthelitcandlecombinedwiththetransmittedimageofthebeakerofwatercreatestheillusion
thecandleisburningunderwater.
Asimilarillusioncanbecreatedbymultiplereflectionscreatingavirtualimagefloatingintheair.InFigure79-4,theimage
ofthespaceshuttleappearstobehoveringoverthedome.
275
Figure79-4Illusionoftheshuttleappearstobefloatingintheair.
However,whenviewedfromaslightlydifferentangle,therealtoyshuttlecanbeseenatthebottomofthedome,producing
thevirtualimagealsopicturedinFigure79-5.
Thislookssoreal,itiscommonforobserverstoreachinandtrytotouchthevirtualimagetoconvincethemselvesitisnot
real.
ThePoint
Atransparentobject,suchasglass,canbothtransmitandreflectlightthatisincidentonit.Reflectedlightfollowsthelawof
reflection,wheretheangleofincidenceequalstheangleofreflection.
Figure79-5Therealtoyshuttleseenatthebottomofthedomeisthesourcesoftheillusion.
276
Project80
Laserobstaclecourse.
TheIdea
Thisisasimpleandfunwayofexploringthelawofreflectionthatprovidesaninitialinsightintowhatisneededtoachieve
opticalalignment.Thisproject(whichIfirstheardfromTomMisniak)makesagoodteam-buildingactivityandcanbeused
asthebasisforafriendlycompetition.
WhatYouNeed
low-powerlaser(alaserpointerisfine)
apparatus(suchasatripod)tomountthe laserpointandhold it illuminatedandstationaryforasustainedperiod
(youmayneedtotapethelaserpointtokeepitonwithoutholdingit)
severalplanemirrors
smallwhiteboards
waytomountthemirrors,suchasringstandsandclampsormodelingclay
darkroom
timer
Method
Competition1(Roundrobin)
1.Caution:Becarefulnottoshinethelaserbeamatanyone’seyes.Althoughthepowerofthelasershouldbelow,itisa
goodideatotakecarenottoexposeanyone’seyes.
2.Distributeamirrorandassociatedmountinghardwaretoeachparticipant.
3.Drawatargetandmountitinalocationwhereeveryonehasaclearline-of-sighttoit.
4.Setupthelaserpointerinacentrallocation.
5.Placetheparticipantsatdifferentlocationsaroundtheroom.
6.Defineasequenceforthebeamtoreflectfromonepersontothenextand,finally,tothetarget.
7.Optional:darkentheroom.
8.Directthebeamtothefirstmirror.Usethewhiteboard,ifnecessary,to“capture”thebeam.
9.Optional:startthetimer.
10.Next,alignthepointerandthefirstmirrortomakethebeamreflecttothesecondmirror.
11.Continuefromonemirrortothenextuntilthelastmirrordirectsthebeamtothetarget,asshowninFigure80-1.
277
Figure80-1Laserobstaclecourse.
12.Optional:incasethisgetstooeasy,requirethefinalbeamtopassthroughacardboardtubemountedinfrontofthe
target.
13.Compasses(forCompetition2).
Competition2:Backtothetarget
1. Takesimilarprecautions,distributemirrors,andestablishatarget,asinCompetition1.
2. Placetheparticipantsatdifferentlocationsaroundtheroom.
3. This time, however, have each participant work out their angles and alignment based on applying the law of
reflectionandmeasuringangles.
4. Giveeachparticipantasettime.
5. Whenthetime isup,allparticipantsmustno longer touchthemirrors. In fact,youcanhavethem leavethearea
altogether.
6. Thencomesthemomentoftruth,whereyouseehowcloseeachoftheparticipantsisabletodirectthelasertothe
target.
ExpectedResults
Itisnotunreasonabletohavesixreflectionsinabouttenminutes.Thisrequiresinteractionandcoordinationbetweengroups.
Onelessonpeopledoingthislearnisthatsmallchangesatthebeginningofthecourseresultinlargeerrorsattheend.Even
vibrationsinthefirstmirrorinthesequencecanthrowoffthealignmentdownstream.Adjustmentsmayneedtobemadeat
eachstep.Anothervaluablelessonistherecomesatimewhenitisbesttoleavethemirroraloneandstopmakingchanges.
Oneotherthingthatmaynotimmediatelybeobviousisthisisathree-dimensionalalignmentproblem.Younotonlyneedto
adjustleftandright,butalsoupanddown.
WhyItWorks
Thisisanapplicationofthelawofreflection.Becausethereflectionanglefromonemirrorbecomestheincidentangleof
thenextmirror,errorsinincidencedoublewitheachreflection.
OtherThingstoTry
278
Forthetrulydedicated:workouttheanglesformultiplereflectionsandbacktothetargetonpaperfirst.
ThePoint
The angle of incidence equals the angle of reflection. Small alignment errors can be quickly compoundedwhenmultiple
reflectionsoccur.
279
Project81
Lightintensity.Puttingdistancebetweenyourselfandasourceoflight.
TheIdea
Weallknowthatstarsareintensesourcesoflight,buttheyappearasfaintobjectsintheskybecausetheyaresofaraway.
Howdoesthatwork?Ifyouincreasethedistancebetweenyourselfandalightsource,doesthelightbecomeone-halfofits
originalbrightnessordoesitdropoffsomeotherway?Checkitoutandseeforyourself.
WhatYouNeed
Alight-sensingcircuitassembledfrom
–solarcell
–insulatedwire(youneedtwo15-inchlengthswiththeinsulationremoved)
–wirestripper(apenknifeorapairofscissorswilldo)
–ammeter(ifyouhaveamultimeter,configureitasanammeter)
–solderingironwith(resincorePb/Sn)solder
–athirdhand(orasecondpersontohelpsolder)
oracommerciallyavailablelightmeter,suchasshowninFigure81-1
Figure81-1Lightsensor.CourtesyPASCO.
lightbulb(notafocusedsource,suchasalaserorflashlight)
tapemeasure
darkroom
Method
Attachingwirestoasolarcelltouseasasensor
1. Pluginthesolderingiron.Makesurethetipisinasafeplace.Itgetsveryhotinafewminutesandshouldnotbein
contactwithanybodyoranythingthatisflammable.
2. Placethesolarcellwiththebluesideupandlocateapadneartheedgeintendedforwireattachment.
3. Asthesolderingirongetshot,“wet”thetipbymeltingsomeofthesolderonthesolderingirontip.
4. Stripabout¼inchoftheinsulationfromtheendofeachoftwo15-inchlengthsofwire.
5. Positionthewireononeofthecontactpadsontheedgeofthesolarcell.
6. Positiontheendofsolderfromthecoilonthepadandnearthewire.
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7. Touchthesolderingirontothewiretogetitashotaspossible.Thismayhappenabitfasterifitisatfirstraised
abovethesolarcelltoavoidheatbeingconductedbythesolarcell.Youalsowanttoavoidoverheatingthesolar
cell,whichcouldcauseittoshortoutiftheheatisexcessive.And,youshouldavoidhavinganyelectricalcontact—
whetheritisthewiretouchingorsolder—betweenthefrontpadandthebackofthesolarcell.Thiscanshortoutthe
solarcellandpreventitfromgeneratinganelectricaloutput.
8. Touchthesoldertotheheatedwireand,asitmelts,havesomeofthemoltensolderformabridgetothesolder
pad.
9. Removethesolderingironanddon’tmoveuntilthesoldersolidifies.Ifdoneproperly,thesoldershouldsticktoboth
thesolarcellpadandthewireformingamechanicalbond.
10. Similarlyattachawireanywheretothebackofthesolarcell.
11. Attach thewire coming from the back of the solar cell to the positive terminal of the ammeter. Attach thewire
comingfromthefrontofthesolarcelltothenegativeterminaloftheammeter.
12. Atthispoint,youcan(carefully)holdthesolarcellormountitbygluingortapingittoaboard.Remember,solarcells
are extremely fragile and will break if the slightest pressure is put on them. The solar cell may still function if
fractured,butreasonablecautioncanavoidthat.
Makingthemeasurement
1.Positionthelightbulb,soafewmetersareinfrontofitwithoutobstruction.
2.Turnofftheroomlights.
3.Pickalocationsuchasabout25cmfromthelightbulbandtakeareadingonthelightmeter.(Thisstartingdistance
isarbitraryanddependsonthesensitivityofthemeteryouareusing.)
4.Recordthedistance(anychoiceofunit,inches,ormeterscanwork,butbeconsistentthroughoutyourinvestigation).
Recordthelightintensity,asshowninFigure81-2,intheunitsinwhichthelightmeteriscalibrated(suchaslumem/m2
lm/m2).
Figure81-2CourtesyPASCO.
5.Ifyouareusingthesolarcell,orientitsoitisperpendiculartothelinebetweenyouandthesourceoflight;theunitof
measurement will be in amps. Be careful not to block the front of the solar cell with your fingers, which can
compromisetheaccuracyofyourreading.
ExpectedResults
Thefartherawayyouget,thelessintensethelightbecomes.
Therateofdrop-offisnotlinear.Thefartherawayyouget,thefasterthelightintensityfallsoff.
Morespecifically,thelightintensitydropsoffastheinverse-squareofthedistance.ThisisshowngraphicallyinFigure81-
3.
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Figure81-3CourtesyPASCO.
WhyItWorks
Lightintensityisrelatedtothedistancefromitssourceaccordingtotheequation:
I=Io/r2
whereIrepresentslightintensityatdistance,r,betweenthelightsourceandthepointofmeasurementforaninitialintensity,
Io.
OtherThingstoTry
Asimilarinversesquarelawrelationshipcanbefoundwithasourceofsoundandasoundintensitymeter.
ThePoint
Lightintensitydropsoffastheinversesquareofthedistancefromthesourceoflight.
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Project82
Howdoweknowthatlightisawave?ThomasYoung’sdoubleslitexperimentwitha
diffractiongrating.
TheIdea
SirIsaacNewtonwasdefinitelynoslouchwhenitcametophysics.And,ifyouaskedNewtonwhetherlightwasawaveora
particle,hewouldsayitwasaparticle.Newtonwasactuallycorrectforreasonsthatwouldnotbecomeclearuntilseveral
centurieslater.ThomasYoungprovedtheoppositewastrue—thatlightwas(also)awave.Today,werecognizethatlighthas
bothparticleandwave-likebehavior.Were-createYoung’sexperiment in thisproject toexplore light’swave-likebehavior.
Youngobservedtheeffectoflightemergingfromtwosmallslitsinanopaqueplate.Insteadoftwoslits,youcreateasimilar
effectusingadiffractiongratingwhichletsyouexploretheeffectofdozensofopenings.
WhatYouNeed
diffractiongratingavailablefromscientificsupplycompanies,including
–Edmunds300130713,500lines/inchhttp://scientificsonline.com
–PASCOOS9127600lines/mm(15,000lines/inch)http://store.pasco.com
–FreyScientific155909972115,000lines/inchhttp://www.freyscientific.com
laserpointer
meterstick
rulerwithmetricdivisions(centimeters)
indexcard
darkroom
holderstosupportrulers
holdersforcard,diffractiongrating,andgrating
Method
Settingup
1. Mountthediffractiongratingwiththelinesorientedupanddown.
2. Mounttheindexcard,soitisparalleltothediffractiongrating.
3. Arrange themeterstick, so you canmonitor the distance between the diffraction grating and the screen as you
adjust this distance. (If it is convenient to set up, one possible approach is to attach the diffraction grating and
screen directly to the meterstick, and then determine the distance between them from the difference in the
readings.)Agoodstartingdistanceisseveralcentimeters.
4. Hold(orsecure)thelaserpointer,sothelaserbeamisdirectedperpendiculartothediffractiongrating.SeeFigure
82-1.
5. Darkentheroomandturnonthelaser.(Caution:Aswithanyprojectinvolvingalaser,usealow-powerlaser,suchas
alaserpointer,andbecarefultoavoidcontactwithanyone’seyes.)
6. You should see the path of the laser through the diffraction grating. The brightest spot is called the central
maximum.Drawaverticallinethroughthecentralmaximum.
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7. Oneithersideofthecentralmaximum,youshouldalsofindamuchdimmerspot.Thisiscalledthefirstorderline. (It
ismore likeaspot thana line inourcasebecauseweareusing light froma laser, rather than theverticalslits
originallyusedbyYoung.)
Figure82-1Apparatususedforthisproject.
ExpectedResults
Apatternofspotsisproducedtotherightandleftofthecenterline.Thesearetheresultoftheconstructiveinterferenceof
waves.Thisprovesthatlightisawave.Or,moreaccurately,inadditiontohavingparticle-likeproperties,lightisalsoawave.
Ifthedistancetothescreenisincreased,thedistancebetweenthebrightspotsalsoincreases.Thedistancebetweenthe
laserandthediffractiongratingshouldnotmatter,however,becausethelightstrikesthediffractiongratinginaperpendicular
direction,regardlessofhowfaritiscomingfrom.
WhyItWorks
Whenwavesmeet, if thecrestsoccurat thesame time, thewavesadd.This iscalledconstructive interference. If when
wavesmeetacrestandtroughcometogether,thewavescancel.Thisiscalleddestructiveinterference.
Interferenceisabasiccharacteristicofwaves.Thelight-anddark-spotpatternistheresultofinterferenceofthewaves
emergingfromtwoadjacentopeningsinthediffractiongrating.
OtherThingstoTry
Onceyoulocatethefirstorderbrightspots,youcantrytolocatethesecond,third,andpossiblyhigherorderlines.Thismay
requireaverydarkroom.
ThePoint
This project recreates one of the most significant experiments of the twentieth century in which Thomas Young
demonstrated that light is a wave. Interference patterns are a unique characteristic of waves. Because light in this
experimentexhibitsaninterferencepattern,itprovesconclusivelythatlightisawave.
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Project83
Howtomeasurethesizeofalightwave.
TheIdea
Lightisawave.Theinterferencepatterncreatedbyoverlappinglightwavesisdifferentfordifferentwavelengthsoflight.We
canusethistodeterminethiswavelength.
WhatYouNeed
diffractiongratingofknownseparationbetweenthelines
laserpointerofknownwavelength(low-costredlasersaretypically650–670nm,greenlasersareintherangeof
535nm)
apparatususedinthepreviousproject(includingameterstick,ruler,indexcard,andassociatedclampsandholders)
protractor
darkroom
Method
1.SetuptheapparatususedinProject81.
2.Determinethespacingbetween the linesof thediffractiongrating.Diffractiongratingsuppliers typically identify the
numberoflinesinagivendistance.Forinstance,ifadiffractiongratinghas15,000linesperinch,thespacingfromthe
center-to-centeroftherulelinesis1inch/15,000linesor0.000067inchesbetweenlinesor0.0026mbetweenlines.
3.Darkentheroom.(Caution:Aswithanyprojectinvolvingalaser,usealow-powerlaser,suchasalaserpointer,andbe
carefultoavoidcontactwithanyone’seyes.)
4. On either side of the central maximum, you should also find a much dimmer spot. This is called the first order
maximum.Withapencil,markthedistancetoeachofthefirstordermaxima.
5.Usingthemeterstickandprotractor,measuretheanglebetweenthepointwherethe laser lightpassesthroughthe
diffraction grating and the first order spot on the card.Measure both the angle to the right and to the left of the
centerline.Theangletotheleftandtotherightofthecenterspotshouldbeveryclosetoeachother.Repeatingthis
measurementandtakingtheaveragecangiveamoreaccuratevalue.
6.Iftheroomisdarkenoughandeverythingelseisworking,itislikelyyouwillbeabletoseethesecondand,possibly,
thethird-ordermaxima.NotethedistanceandsavethedatafortheOtherThingstoTrysection.
7.Repeatthisusingseveralcombinationsofscreendistance.
8.Thediffractiongratingequationis
whereλ(Greekletter“lambda”)isthewavelength(inmeters),nistheorderoftheband=1,2,3…Forthefirstorder,n=1,anddisthedistance(inmeters)betweenlinesonthediffractiongrating.
9.Usethisdatatabletoorganizeyourdata.Convertallyourdatatometers.Ifyourmeasurementsareincentimeters,
convertthemtometersbydividingby1000.
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10.Comparetheaveragewavelengthyoufindtotheexpectedwavelength.
11.Note,ifyoureallywanttonailthismeasurement,rememberthelinesthemselvestakeupsomeofthatdistance.The
distancebetweenthelines(whichiswhatwereallyneed)isslightlylessthanthecenter-to-centerdistancebetween
lines.Youcancalibrateforthisdiscrepancybyusingthepreviousdiffractiongratingwithalightsourcewithaknown
wavelength.Bymeasuringthedistancebetweencardandgrating,thelocationofthefirstordermaxima,andusing
theknownwavelength, youcansolve ford, thespacingbetween the lines.Although this gets you intoabit ofa
chickenandeggsituation,itdoesenablethemostaccurateresults.
ExpectedResults
Forcommonlyuseddiffractiongratings,theexpectedwavelengthcanbefoundbymeasuringabrightlightmaximumatthe
followingangle.
WhyItWorks
Thedistancebetweenthebrightspotsestablishedwhenlightofagivenfrequencypassesthroughadiffractiongratingcan
beused tomeasure thewavelengthofasourceof light. If thespacingof thegratingand thedistance to the imageare
known,thewavelengthcanbedetermined.
OtherThingstoTry
For simplicity, we only used the first ordermaximum. You can try the previousmeasurement also using the second and,
possibly,thethirdordermaxima.Thistechniqueshouldgivethesamewavelength,regardlessofwhichorderisbeingused,so
findingthesameorasimilarresultfromdifferentorderscangiveyouaconfirmationthatyouaredoingsomethingright.
Thespectralbreakdownof lightemittedbyahydrogenatomcanalsobedetectedusingahigh-sensitivity lightsensor,
suchasPASCOpartnumberPS-2176.AnexampleofthisisshowninProject120.
The optical tracks on aCDor the grooves on a vinyl recording are effectively diffraction gratings. Use the diffraction
gratingequationtofindoutthespacingofthetracksonaCDorrecord.Basically, thereflectionfromthecloselyspaced
tracksonaCDcangiveasimilarinterferencepattern,suchasthatproducedbytransmissionthroughadiffractiongrating.
Details canbe found inanarticle called “UsingaLaserPointer toMeasure theDataTrackSpacingonCDsandDVDs”
(www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p011.shtml?from…).
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ThePoint
Adiffractiongrating is a device that produces an interference pattern when a light is shined on it. If that light has one
frequency(orismonochromatic),suchasalaser,theinterferencepatterncantelluswhatthefrequencyis.Thiscapability
formsthebasisofmanyanalyticaltechniquesthatrequiremeasuringthefrequencyoflightwithgreatprecision.
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Project84
Thespeedoflightinyourkitchen.Visitingthelocalhotspots.
TheIdea
Lightisanelectromagneticwave.Becauseofitsextremelyhighspeed,it isdifficulttomeasurethespeedoflightdirectly.
Historically,astronomerssuchasO.Roemeruseddistancesonthescaleofplanetaryorbitstogetahandleonhowfastlight
traveledthroughspace.Inthisproject,youmeasurethespeedoflightrightinyourownkitchen.Thetechniqueissimilarin
principletotheapproachweusedinProject73wherewefoundthespeedofsoundbyfindingitsresonantwavelength.Here,
youuseamicrowaveoventoestablishastandingwavethatcanbeusedtoestimatethespeedoflight.
WhatYouNeed
microwaveoven
sheetsofslicedcheese,barsofchocolate,oraboutfiveeggs
sheetorplate to holdabove food itemswithout rotating in theoven—some ideas includea rectangularwoodor
plasticcuttingboard,arectangularPyrexbakingdish,arounddishthatfitsasclosewall-to-wallaspossible,ora
sheetofposterboardcuttosize.Obviously,remembernometalshouldgointhemicrowaveoven.
ruler
calculator
light,soyoucanseeinsidetheoven(theovenmayhaveanadequatelightbuiltin)
Method
1.Microwaveovensrotatetospreadoutthehotspotsintheoven.Inthisexperiment,wewanttodetectthesehotspots.
So,ifyourmicrowaveovenhasarotatingtray,removeitfromyourmicrowaveoven.
2.Putanonrotatingsheetorplateinthebottomofthemicrowaveoven.
3.Cover theplatewith themicrowavable food:cheeseslicesorchocolateslabs.The layershouldbeasuniformas
possible in thickness and composition. If you choose to use eggwhites, pour a thin layer into a suitable dish and
spreaditouttoformathin,uniformlayer.
4.Lookthroughtheglasswindowofthemicrowaveovenandstartthemicrowaveovenonthelowestavailablepower
setting.Usealightshiningfromoutsideifthathelpsyouobservewhatisgoingoninsidetheoven.Ifyoudon’thavea
window, you need to cook in increments. Becausemicrowavesdiffer somuch in power, you need to determinean
appropriateamountoftimetouseforthis:10to15secondsisagoodplacetostart.
5.Continuerunningthemicrowaveovenuntilyounoticethefirstsignsofmeltspotsorcooking.
6.Stopthemicrowaveovenandidentifythepatternofmeltspots.Unlessyouaresurethemicrowaveovenhasrunlong
enoughtoestablishaclearmeltspotpattern,donotmovethetrayintheovenyet.
7.Measure the center-to-center distance between adjacentmelts spots. An example forwhat you are looking for is
showninFigure84-1.
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Figure84-1Microwavestandingwavenodesareindicatedbyhotspotsinmeltedcheese.
8.Becauseone-halfofawavelengthfitsbetweeneachhotspot, thewavelengthsforthemicrowavesintheovenare
twicethecenter-to-centerdistancemeasured.
9.Lookfora labelorsearchonlineforthespecificmicrowavefrequencyused inyourmicrowaveoven. Ifyoucannot
easilyfindthisfrequency,youcanuse2450MHz,whichisthefrequencyatwhichmostcommercialmicrowaveovens
operate.
10.When you finish, you canmake grilled cheese sandwiches, s’mores, or egg-white omeletswith the leftover food
ingredients.
11.Calculatethespeedoflightusingtheequation:
c=λforspeedoflight=thewavelength/frequency
Forλusethewavelength(inmeters)fromtwicethecenter-to-centerhotspotdistance.Forf,use2450MHz,whichis2,450,000,000Hzor2.45×109Hz(unlessotherwiseindicatedonthemicrowaveoven).
ExpectedResults
Supposeyoufindtheaverageofthehot-spotdistanceis6cm.
Thewavelengthofthemicrowaveresonantinthemicrowaveovenis12cm.
Inmeters,thisis12cm×0.01m/cm=0.12m.Thespeedoflightisthen,c=0.12m×2,450,000,000Hz=2.94×108m/s.Thisisreasonablyclosetotheacceptedvalue,whichisjustunder3×108m/s(300,000,000m/s).Remember,microwaves
mayvaryinhowtheycreatestandingwavesandanerrorfactorisassociatedwithheatdistributionontheheatsurface.For
thisreason,thismeasurementcanbeonlyexpectedtogiveballpark,notpreciselyaccurate,values.
WhyItWorks
Amicrowaveovenproducesaresonantwaveintheovenchambersimilartothatofavibratingguitarstring.Thehotspots
arelikethenodesorthepointswheretheendsofthestringareheld.Acompletewaveisacycleupanddown,soonlyahalf
wave fits between the two nodes in both cases. From knowing the frequency of the microwaves and measuring its
wavelength,wecanfindthespeedoflight.
OtherThingstoTry
Amoresophisticated,butmoreprecisewaytomeasurethespeedoflightistodetecttheinterferencebetweenlightwaves
separatedbyameasurabledistance.Equipmenttodothisisavailablefromscientificsupplyvendors,suchasPASCO.
ThePoint
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Thespeedofawave,suchaslight,canbedeterminedfromitswavelengthandfrequency.Thewavelengthofamicrowave
ovencanbefoundbythedistancebetweenthenodesofaresonantstandingwave.
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Project85
Refraction.Howfastdoeslighttravelinairorwater?
TheIdea
Lighttravelsat itstopspeed inavacuumandat (nearly) itstopspeed inair.When lightmovesthroughothertransparent
materials,itslowsdown.Ifitgoesfromonematerialtoanotheratanangle,thelightwillbend.Themoreitslowsdown,the
moreitbends. Inthisprojectyouwillcomparehowmuchlightbendsinvariousmaterials.Thisbending iscalledrefraction
anditgivesusawaytodeterminehowfastlighttravelsinatransparentmaterial.
WhatYouNeed
squareorrectangularpieceofglassabout¼inchthickandafewinchesinlengthandwidth(atleasttwoopposing
sidesmustbeclear)
laserpointer
semicircularplasticcontainerfilledwithwater
protractor
Method
Laser
1.Placethepieceofglassonthepaper.
2.Tracetheshapeoftheglass.
3.Darkentheroom.
4.Putadotononesideoftheglasstoprovideatargetforthelaser.
5.Drawalineperpendiculartotheedgeoftheglassatthatpoint.Extendtheline,soitextendsundertheglass,aswell
asgoingintoit.
6.Placethelaser,soitsbeamformsananglewithrespecttotheperpendicularlineyoujustdrew.Markthepositionof
thelaser.
7.Darkentheroom.
8.Shine the laseranddirect itsbeamtoward the targetdot.Angle thebeamvertically, soyoucansee itspathboth
beforeenteringandafterexitingtheglass.(ItisOKifyoudon’tseetheentryandexitbeamsatthesametime.)
9.Placeadotwhereyouseethelaserbeamexitfromtheglassandoneortwodotsalongitspath.
10.Connectthedotwherethelightstrikestheglasswiththepointwherethelightrayemergesfromtheglassbackinto
theair.
11.Measuretheanglesthat:
–theincomingraymadewiththeperpendicularline(θi).–theraygoingthroughtheglassmadewiththeedgewherethelightenteredtheglass(θr).12.Trythiswithothertransparentmaterialssuchaswater(inaplasticcase).
ExpectedResults
Goingfromairintowater,thelightpathisbenttogiveasmalleranglewithrespecttotheperpendicularline.Specificresults
aregiveninthefollowingchart:
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WhyItWorks
TherelationshipbetweentheincidentandrefractedanglesisgivenbySnell’slaw,whichstates:
nisin(θi)=nrsin(θr)whereniistheindexofrefractionwheretherayisincidentandnristheindexofrefractionwheretherayisrefracted.Both
aremeasuresofthespeedoflightinthevariousmaterials,Theindexofrefractionforanymaterialisgivenbyn=c/v.The
physicalarrangementforthisisshowninFigure85-1.
Theindexofrefractionforair,whichis1.0,indicatesthatlightistravelingatitsmaximumspeed.
Becauselightslowsdowninglass,nforglassis1.45.
Figure85-1
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OtherThingstoTry
Findtheindexofrefractionfortheglassorwaterusingtheequation:
nisin(θi)=nrsin(θr)usingniforair=1.0andθIandθrasdefinedintheprevioussteptofindtheindexofrefractioninthematerialofinterest.Theindexofrefractionisgivenby:
n=c/v
Theindexofrefractionisameasureofthespeedoflightinaparticularmaterial,v,comparedtothespeedoflightina
vacuumwhichisgivenbyc=3.0×108m/s.Thespeedoflightinaparticularmediumisgivenbyv=c/nr.
ThePoint
Lighttravelsataslowervelocitywhenitgoesthroughmaterialsotherthanvacuumorair.Whenlighthitsaboundarygoing
fromamaterialwherethelightisfastertoonewhereitisslower,thelightbendstowardtheperpendicularline.
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Project86
Polarization.Sunglassesandcalculatordisplays.
TheIdea
Theorientationofthecrestsandtroughsoflightwavescanbehorizontal,vertical,oranythinginbetween.Unpolarizedlight
consistsofarandommixoforientations.Polarizedlighthasonlyonedirection.Thisgives it theuniquepropertiesused in
liquid crystal displays found inmany television screensandcomputermonitors. Sunglasses reduceglare byallowingonly
selectedorientationsofpolarizedlightthrough.Thisexperimentexploreshowtoidentifywhetherlightispolarizedandhow
thetransmissionofpolarizedlightcanbecontrolled.
WhatYouNeed
2polarizedsheets
calculatororotherLCDdisplay,suchasalaptopcomputer
polarizedsunglasses
lightsource
shallowtray
water
fewrocks
sheetofglass
optional:protractor,lightsensor
Method
Transmissionthroughpolarizedsheets
1. Takeoneofthepolarizedsheets.Holditinfrontofalightsource(alamporanopenwindow)androtateit.Turnthe
sheetafull360degrees,holdingthesheetsoitremainsroughlyperpendiculartoyourfieldofview.
2. Trythiswiththeothersheet.
3. Now,withbothsheets,holdtheminfrontofthelight,oneinfrontoftheother,androtateonlyoneofthem.Observe
whathappens.Addinothercombinations:rotatebothinthesamedirection,rotateboth,butindifferentdirections.
Describetheeffectofthesheets.Isthelightfromyourlightsourcepolarized?
4. Usinganondestructivemethod,suchasapplyingasmallpieceoftape,identifyanedgeoneach,whichwhenplaced
together,blocksthemaximumamountoflight.
5. Note:ThisisgoodtodousinganoverheadprojectororthelightfromanLCDprojector.
Reflections
1. Placeasmallflatmirrorfaceuponatable.
2. Placealightsourceononesideofthemirror.
3. View the reflected light throughoneof thepolarizedsheetsasyou rotate thesheet. Is that lightpolarized?View
througharangeofreflectedanglesfromnearlyperpendiculartoaveryglancingangletothemirror.
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4. Place the two sheets, one on top of the other, but with taped edges aligned, so both sheets have the same
polarizationplane.Whathappenswhenyourotatethesheets,bothwithrespecttothemirrorandtoeachother?
5. Repeat1–4,usinglightreflectedfromasquareofglass.
Laptop/sunglasses
1. HoldapolarizedsheetinfrontoftheLCD(liquidcrystaldisplay)ofalaptopcomputerordigitalcalculator.
2. Rotatethepolarizedsheet.WhatcanyouconcludeabouttheLCDofthelaptop?
3. Take the two lenses fromanold (no longerneeded)pairofpolarizedsunglasses.Hold them—one in frontof the
other—and view a light source. Are the glasses polarized? You also can try this with two pairs of polarized
sunglasses.
ExpectedResults
Lightwill pass throughpolarizedsheetswith little losswhen thedirectionsofpolarization forbothsheets lineup.As the
sheetsarerotated,moreandmoreofthelightisblocked.Withthedirectionofpolarizationofthetwosheetsatrightangles,
almostnolightcanpassthrough,asshowninFigure86-1.ThiscanbequantifiedinMalus’slaw,whichisaddressedlaterin
thissection.
Figure86-1
Figure86-2Percentageoflightblockedbypolarizingfilters.
Alightmeterisagoodwaytoquantifytheamountoflightpassingthroughafilter.Figure86-2providesanapproximate
visualreferencetoevaluatetheamountoflighttransmissionthroughasetofpolarizingfilters.
Reflected lightcanbepolarized.Thiscanbedeterminedbyobservingtheeffectofasinglepolarizedfilteronreflected
light.
ThelightfromaLCD,suchasalaptopscreen,isalsopolarized.Thiscanbeseenbyrotatingapolarizedfilter,suchas
polarizedsunglasses,infrontofanLCDscreen,asshowninFigure86-3andFigure86-4.
WhyItWorks
Lightisanelectromagneticwavethatpropagatesalongaline.Ifwecanimaginelookingdownthatline,wewouldseethe
wavesfrommostlightsourcesmovingupanddowninanydirection.Forunpolarizedlight,thewaveoscillationsarerandomly
distributed over 360 degrees. A polarized filter selects only one of the polarization planes. Reflection polarizes light by
favoringlightintheplaneofthereflectingsurface.
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Figure86-3Polarizedfilter(sunglasses)orientedtopasspolarizedlightfromlaptop.
OtherThingstoTry
Malus’slaw
Wesawhowthemorewerotatedthepolarizedsheets,thelesslighttheytransmitted.Here,wefindthephysicalmodelfor
thateffect.
1. Startwiththetwopolarizedsheetsoriented(withtapedsidesaligned)toallowthemaximumlighttobetransmitted.
2. Findawaytomeasureorestimatetheamountoflighttransmitted.Dependingonyourresources,thiscaninclude:
–Estimatingthetransmissionvisuallybyusingachartrangingfromwhite100percenttransmissiontoblack0percent
transmission.Figure86-5maybearoughguide.
–Comparingthetransmissionusingasetofcalibratedneutral-densityfilters(thatmaybeavailableinsomelabs).These
transmitaspecificamountoflightwithoutchangingthecolor,sotheymightserveasagoodvisualcomparison.
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Figure86-4Polarizedfilter(sunglasses)orientedtoblockpolarizedlightfromlaptop.
– Using a lightmeter tomeasure the light transmitted. The percent would be the ratio of the light transmitted at a
particularmisorientationangledividedby theamountof light transmitted through thepolarizedfilterswhen theyare
aligned.Thisworksbestiftheroomisdarkenedandthelightfromthesourceisisolatedfromthemeter.Onewayto
dothisistoputthelightinaboxandcutasquareholesmallerthanthefilters.Thelightmetercanbepurchasedfrom
asciencesupplycompanyormadefromasolarcellwithsolderwireleadsconnectedtoanammeter(asdescribedin
Project81).
3.Measureorestimatetheamountoflighttransmissionasafunctionofmisalignmentangleofthepolarizedsheets.Use
thefollowingdatatabletoorganizeyourdata.
TheexpectedresultsaredescribedbythisiscalledMalus’slaw.
Thegreaterthemisorientation,thelesslightistransmitted.Thedrop-off,however,isnotlinearbutis,instead,givenby:
Fractionoflighttransmitted,I/Io=cos2θ
TheexpectedresultsaregiveninFigure86-5.
FindBrewster’sangle
Previouslyinthissection,yousawthatlightreflectingfromapieceofglasscanbepolarizediftheangle(withrespecttothe
normal)isgreatenough.ThatangleiscalledBrewster’sangle.
1. Placeasheetofglassflatonatable.
2. Usingaprotractorasaguide, view the reflected lightatvariousangles.Useastraightedgepositionednear the
protractorasavisualguidetoestablishthereflectedangle.
3. Determine themaximum angle with respect to the perpendicular that results in reflected polarized light. That is
Brewster’sangle.
4. CompareyourresultwiththeexpectedvalueofBrewster’sanglegivenby:
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n=tanθpwherenistheindexofrefractionfortheglassandθpistheanglewherethereflectedlightiscompletelypolarized.
Figure86-5Malus’slaw.
Sometypicalvaluesaregiveninthefollowingtable:
Findinganobjectunderwater
1. Placeseveralobjects(coins,rocks)inapanofwater.
2. Covertheobjectswithseveralinchesofwater.
3. Establishalightsourceatanangle.
4. Findaposition toview thesurfaceof thewater,soyousee the reflected lightshimmeringat thesurfaceof the
waterobscuringtheobjectsbelow.
5. Viewthe lightusing thepolarizingfilter.Viewatanglesbothgreaterand lesser thanBrewster’sangle through the
polarizingfilter.Underwhatconditionsareyouabletoseetheunderwaterobjects?
ThePoint
Typical light sources, such as light bulbs or the sun, produce unpolarized light that has electromagnetic waves oriented
randomly.Lightcanbepolarizedbyfiltersorcertainreflectingsurfacesthatselectaspecificorientationofthelightwaves.
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Project87
Whatisthewireofafiber-opticnetwork?Totalinternalreflectionusingalaseranda
tankofwater.
TheIdea
Muchof thedigitalcommunicationthatcirculatesaroundtheworldonthe Internetconsistsof light travelingthousandsof
miles through glass threads thinner than human hair. Total internal reflection is the physical process that keeps these
informationpulsesconfinedwithinthesetinyopticalfibers. Inthisexperiment,youcansetupvariouswaystoexplorehow
transparentmaterialsguidelightbytotalinternalreflection.
WhatYouNeed
laserpointer
fishtank(preferablywithaglassbottom)
tablespoonofmilk
darkroom
sink
one2-Lclearplasticsodabottle
Method
Totalinternalreflectionfromthesurfaceofwater
1. Fillthetankwithwater.
2. Turnofftheroomlights.
3. Directthelaserfromthesideofthetankunderthelevelofthewatertowardthesurface.
4. Addenoughmilktothewaterinthetanksothepathofthelaserisvisibleasitpassesthroughthewater.
5. Ifthefishtankhasaglassbottom,directthelaserthroughthefishtankfromthebottomatvariousangles.
6. Determinethemaximumanglethatwillallowthelighttoemergefromthetank.
Aliquidlightpipe
1. Punchasmallholeabout1mmindiameterinthesideoftheplasticgalloncontainer.
2. Fillthecontainerwithwater.
3. Darkentheroom.
4. Asthewaterflowsfromtheholeintothesink,shinethelaserfromtheothersideofthebottle,butaimitatthehole.
5. Observehowthelightpassesthroughthebottleandisguidedthroughthewaterstreampouringoutofthebottle.
Thisisbecausethelightistrappedinthewaterstreambytotalinternalreflection.Withanindexofrefractionof1.33
forwater,any light incidenton thesurfaceatananglegreater than48.7degreeswillbe totally reflected.This is
muchlowerthantheanglesthelightmakeswiththewaterstream.
Acryliccylinderlightguide
299
An acrylic (or other transparent material) makes a good demonstration of light trapped in a medium by total internal
reflection. Send the beam through one of the flat ends. Regardless ofwhat angle you direct the beam, the lightwill not
refractoutthroughthesidesofthecylinder.
Observinglightfibers
Opticalfibersshowveryconvincinglyhowlighttravelsthroughathintransparentmaterial.Opticalfibersareavailablefrom
scientificsupplycompaniesandnoveltylightingstores.
ExpectedResults
Lightpassingthroughthewaterandstrikingthesurfacepassesthroughtotheairiftheangleisabovethecriticalanglefor
water.
Figure87-1shows lightpassing throughplasticatanangle less than thecriticalangle.Notice thatmostof the light is
refracted(orgoesthrough)thelenswithasmallerpartofthelightbeingreflectedattheflatsurface.
However, once the incident angle coming from the plastic back into theair is greater than the critical angle for those
materials,thelightexperiencestotalinternalreflection,asshowninFigure87-2.Here,lightiseffectivelytrappedinsidethe
plasticandcannotemergebackintotheair.
Figure87-1Incidentlightisrefractedandreflected.
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Figure87-2Totalinternalreflectionofincidentlight.
WhyItWorks
When light enters a material where it goes faster, the angle approaches 90 degrees as the incident angle increases.
Becausetheangleofrefractioncannotbegreaterthan90degrees,lightabovethecriticalangleistotallyreflected.
OtherThingstoTry
Variable index of refraction. (Based on a lecture demonstration posted at the UCB web site:
www.mip.berkeley.edu/physics/E+60+40.html.)
Refraction takesplacewhen light goes fromonematerial to another. Fiber-optic cableandother optical devices take
advantageofavariableindexofrefractiontoguidethelightinachannel.Todothis:
1. Coverthebottomofanemptyfishtankevenlywithabout1cm(about½inch)ofgranularsugar.
2. Addwatertothetankasslowlyandcarefullyasyoucan,soyoudisturbthelayerofthesugaraslittleaspossible.
Warmwateratabout70degreesCwillenablethesugartodissolvemorequickly.
3. Fillthetankwithafewinchesorsoofwater.
4. Letthetankremainundisturbedforafewdays,allowingthesugartoslowlydissolve.Theconcentrationofthesugar
solution—and,asaresult,theindexofrefraction—willvarywiththeheightabovethebottomofthetank.
5. Darkentheroom.
6. Directa laserfromthesideof thetankatananglewithrespecttothebottomof thetank.Thebeamshouldbe
guided,asifthroughaninvisiblelightpipeinthetank.Thisuseofavariableindexofrefractionissimilartotheway
afiber-opticcableguidesalightbeam.Ifthelaserisdirectedatanangle,thelightmaygothroughseveralbounces
ifthetankislongenoughandthedistributionofthesugarisuniform.Thisalsoillustrateshowmiragesform.When
lightpassesthroughcoolerairtowarmerairoveraroadsurface,thevariableindexofrefractionguidesthelightina
waythatcreatestheillusionofwaterlyingontheroad.
Lightguides
Opticalfiberscanbefoundintoyandnoveltystores,andasapartofcertain lamps.Theseworkontheprincipleoftotal
internalreflectionandtheyshowhowlightcanbe“piped”aroundcorners.Asimilarwaytoexplorethisistoshinealaserinto
anacryliccylinder.Althoughagoodbitofscatteringiswithintheacrylic,thelightistrappedinsideinasimilarmannertoan
opticalfiber,asshowninFigure87-3.
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Figure87-3Lightcominginonesideofthetubeistrappedbytotalinternalreflectionandemergesfromtheotherside.
ThePoint
Iftheanglethatalightraystrikesasurfaceistoolarge,thelightwillnotpassthroughtotheothermedium.Thiscanonly
happenifthespeedoflightisfasterinthesecondmedium(oriftheindexofrefractioninthesecondmediumissmaller).For
anglesgreaterthanthatcriticalangle,nolightisrefracted,butisinsteadtotallyreflectedbackintothematerialfromwhichit
originated.
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Project88
Thedisappearingbeaker.
TheIdea
Thisdemonstrationletsyousetupacloakingshieldthatmakesaglassobjectdisappear.
WhatYouNeed
Pyrexbeaker
otherglassobjectssuchasPyrexstirringrodsandmagnifyingglasses
transparentcontainerlargeenoughtoholdthebeaker
cookingoil(suchasWesson,babyoil,Karosyrup,orlightandheavymineraloil)
Method
1. Placethebeakerinthelargercontainer.
2. Fillthecontainerwiththeoil.
3. Immersethebeakerintheoilandslowlypourtheoilintothebeaker.
4. Observewhathappenswhenotherglassobjectsareplacedintheoil(Figure88-1).
ExpectedResults
Astheoillevelrisesabovethebeaker,theglasscannolongerbeseen.Ifanymarkingsareonthesideofthebeaker,they
willstillbenoticeable,asseeninFigure88-2.
Ifyouuseotherliquids,similarresultsmaybeobtained,butyoumayhavetodosomefinetuning.Othertypesofglassand
other oils (including the “lite” version of cooking oils) may be less perfect, leaving some ghost images that are less
noticeable the fartherawayyour “audience” is.Amixtureofaheavyand lightmineraloil (ina ratioofabout2:1 tostart)
shouldmatchPyrexandbeadjustableforothertypesofglass.KarosyrupisaclosematchtoPyrexandcanbedilutedwith
watertomatchothertypesofglass.
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Figure88-1
Figure88-2Disappearingbeaker.
Themagnifyingglasswillnotenlargeimageswhensubmerged.
Thepreciseindexofrefractionforthesematerialsmayvaryslightlywithtemperature.Also,imperfectionsintheglassmay
makeitdifficulttomaketheverylasttracedisappearonsomesamples.
WhyItWorks
Objectsarevisibletotheextentthattheyareabletoreflectlight.Ifanobjectimmersedinaliquidhasanindexofrefraction
thatisdifferentthantheobject,someofthelightisrefractedthroughtheobjectandsomeisreflectedbacktotheobserver.
However, if the object has exactly the same index of refraction as the immersed object, the light will neither reflect nor
refractattheinterfacebetweentheobjectandtheliquiditisimmersedin.Inthatcase,theobjectwillappeartobeinvisible.
Lenses,suchasmagnifyingglasses,workbyvirtueoftheirindexofrefractionbeingdifferentthantheindexofthemedium
aroundit. Iftheindexofrefractionsurroundingthelensis increasedfrom1.0,whichistheindexofrefractionofair,toan
indexveryclosetoglass,thelightrayswillnotbebentthroughafocalpointandmagnificationwillnotoccur.
BothWesson cookingoil andPyrex glass havea nearly identical index of refraction of about n=1.474,making them
particularlywellmatchedforthisdemonstration.
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OtherThingstoTry
Asimilarexperimentalongtheselinesisfirsttopourawater-alcoholmixturetoabeaker,andthencoveritwithcookingoil.If
asmallenoughamountofalcoholisinthemixture(lessthantwiceasmuchoilaswater),theoilwillfloatanditwillalsonot
mixwiththealcohol-waterlayer.Ifyouaddafewdropsoffoodcoloringtothewater-alcoholmixture,theeffectiseasierto
see.Viewing from the top, thewater-alcohol layer is invisible.This is the resultof total internal reflectionat the interface
betweenthelayers.
ThePoint
Transparentobjectsarevisiblebecauseofreflectionfromtheirsurface.Transparentobjectswillpartiallyreflectandpartially
refractlightifthereisadifferencebetweentheirindexofrefractionandthatoftheirsurroundings.Iftheindexofthematerial
andtheirsurroundingsisthesame,theobjectwillappeartobeinvisible.
305
Section8
HotandCold
Project89
HowmuchheatisneededtomeltGreenland?Heatoffusion.
TheIdea
Iceanywhererequiresacertainspecificamountofheattomelt.Icemeltsat0°C.Onceatthattemperature,theamountofheatneededdependsonlyonhowmuchiceyouhave.Heatcaneitherchangethetemperatureofsomethingorcauseitto
changefromonestatetoanother.Inthisexperiment,thatchangeisfromsolidtoliquid.Youwilldeterminehowmuchheatis
neededtomeltagivenmassoficebycarefullykeepingtrackoftemperaturechangesandheatflows.
WhatYouNeed
Styrofoamcup
cubeofice
graduatedcylinder(250mL)
water
thermometer
stirringrod
scale
Method
1. Fillthebeakerwithexactly150mLofwateratatemperatureofatleast25degreescentigrade.Thisresultsina
massofthewater,mw,of150g.
2. Removeanicecubefromthefreezerandletitsitoutuntilitjustbeginstomelt.Thisestablishesitstemperatureat
(verycloseto)0degreescentigrade.
3. Measurethemassoftheicecube,mice,ingrams.Ifsignificantmeltinghasoccurred,youcanuseapapertowelto
absorbanyexcessliquidwaterbeforemeasuringthemass.
4. Measuretheinitialtemperatureofthewater,Ti,beforetheicecubeisadded.
5. Dropintheicecube.Stirgently.Measurethefinaltemperature,Tf,assoonastheicecubehascompletelymelted.
6. Calculatehowmuchheatwasneededtomelttheicethroughthefollowingsteps(seeFigure89-1):
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Figure89-1Heatistransferredfromthewatertoraisethetemperatureoftheiceandwaterandtomelttheice.
–Heatextractedfromthewater
GivenbyQw=mwCw(Tf−Ti)whereCwisthespecificheatofwater=4.18J/g°C.Thismeansthat4.18joulesofenergy(whichishowenergyismeasured)areneededtoraiseeachgramofwaterevery1degreecentigrade.
–Heatneededtobringthemeltedicefrom0°CtothefinalliquidtemperatureGivenbyQmeltedice=miceCw(Tf−0)–Heatneededtomelt1gramofice
Hf=(Qw–Qmeltedice)/mice
ExpectedResults
TheexpectedresultisHf=334J/g.Thismeans334joulesofheatenergyareneededtomelt1gramofice.
WhyItWorks
Whenacubeoficeisplacedinabeakerofwater,someheatistakenfromthewater.Thislossofheatresultsinthewater
beingbrought toa lowerequilibriumtemperature,which is lower thanthestartingtemperature.Theheat lostby thewater
accomplishes two things:1) itmelts the ice,and2) itbrings the liquid resulting from themelting iceup to theequilibrium
temperature.Thisgivestheoverallequation:
Qw=Qmeltedice+miceHf
SolvingforHfgivestheequationusedtofindtheheatoffusionforice.
OtherThingstoTry
Determinethetemperatureofafreezer.Asbefore,placeanicecube(thistimeimmediatelyremovedfromthefreezer)ina
Styrofoamcupfilledwithwaterofaknowntemperature.Dothisbyusingtheknownvaluefortheheatoffusionoficeand
theheattransferequationusedpreviously.
Determinethetemperatureofahotobject(suchasared-hotnail)bymeasuringthetemperaturebeforeandtheequilibrium
temperatureafterimmersionoftheobject.Thensolvetheheatequationsfortheinitialtemperatureoftheobject.
CalculatetheamountofheatneededtomelttheGreenlandicecaps:Greenlandcontains2.85millioncubickilometersof
iceor1.4×1014icecubeseachwithamassof20g.Basedontheheatoffusionforice(0degreesC)determinedinthisexperiment,theGreenlandicecapswouldrequire9.5×1023Joulesofheatenergytomelt.
ThePoint
307
Whenobjectsatdifferenttemperaturesaremixed,theyresultinanequilibriumtemperaturethatisbetweenthehighestand
lowesttemperaturesinthemixture.Theamountofheatneededtocauseacertaintemperaturechangeforagivenmassof
materialischaracterizedbythespecificheatforthatmaterial.Inadditiontocausingtemperaturechangeinamaterial,some
heat(calledlatentheat)resultsinachangeofphasefromsolidtoliquid.
308
Project90
Awaterthermometer.
TheIdea
Allmaterials(withtheonenotableexceptionoficeataround4°C)expandwhenheated.Itishardtonoticethedifferenceinvolumebetweenahotcupofteaandthevolumeinthecupwhentheteacools.Thisexperimentgivesawaytointensifythe
effectofthethermalexpansion,soitcanbemeasuredandcomparedtoaknownvalue.
WhatYouNeed
250mLflask
2-holerubberstopperthatfitsintheflask
hotplate
1000mLbeaker(oronelargeenoughforyoutoplacetheflaskin)
glasstubethatfitsthroughtherubberstopper(about15incheslong)
water
glassthermometerthatfitsthroughthesecondholeofthestopper(ifyoudon’thaveathermometerthatworks,then
youneedaone-holestopper)
Vaseline(orglycerin)andatoweltohelpslidetheglassandthethermometerintothestopper
ruler
ringstandwithabeakerortesttubeclamp
Method
1.Determinetheradiusoftheglasstubeby:
–Partiallyfillingtheglasstubewithwater.
Placeyourfingeroverthetopofthetubetokeeptheliquidfromslidingoutwhileyouaremakingthismeasurement.
–Measuretheheight,ho,ofthewatercolumn.
–Releasethevolumeintothegraduatedcylinderandmeasurethevolume.
–ThevolumeoftheliquidmeasuredV=πhr2.–Theradiusofthetubeisr=(V/πho)½.2.Carefullyslidetheglasstubeintothestopper.UsealittleVaselineorglycerinasalubricantandprotectyourhands
withatowelasyoupush.Don’tforceit.Afewinchesofthetubeshouldextendbelowthestopperwiththereststicking
outabove.
3.Slidethethermometerintotheotherhole,sothebottomofthethermometerispositionednearthecenteroftheflask.
4.Completelyfilltheflaskwithwater.(Addfoodcoloringifyoulike—yourchoiceofcolor.)
5.Insertthestopper.Asmallamountofliquidmayspilloutoverthesideoftheflaskandsomemaybeforcedupthe
tube.
6.Placetheflaskwiththestopperinthebeaker.
7.Fillthebeakerwithwatertocovertheflask.
8.Placethebeakeronthehotplate.
9.Turnonthehotplate.TheapparatusforthisexperimentispicturedinFigure90-1.
10.Recordthetemperatureintheflaskandnotethepositionoftheliquidintheglasstube.(IfyouhaveaSharpiehandy,
markitontheglass.)
11.When the temperature in the flask risesa fewdegrees, record the temperatureandmeasure the increase in the
309
heightoftheliquidintheflask.
12.Theincreaseinvolumeforagiventemperature increaseisgivenbyV=πhr2,whereh isthemeasuredheight(inmeters)andristheinnerradiusoftheglasspreviously.Insettingthisup,someliquidlikelywillextendintothetube
atyourstartingtemperature.Ifthisisthecase,definethisasyourzeropointandtakehasthedistancethe liquid
rises intothetube. (Thesmalldifference in volume resulting from the liquid that initially rises into the tube isnot
significantforthismeasurement,butifyouareverypicky,youcancorrectforthisonprinciple.)
Figure90-1Waterthermometer.
ExpectedResults
Agivenvolumeofwaterexpandsbya factor that is0.000207 (or2.07×10−4)of itsoriginalvolumeforevery1degreeincreasecentigrade.Thisvolumeisdistributedbetweentheflaskandthetube.
WhyItWorks
310
Nearly all materials expand when they are heated. The amount of expansion is characterized by something called the
coefficientofexpansion. Inthecaseofsolids, theexpansion inonedirection iscalledthecoefficientof linearexpansion.
Multiplyingtheoriginallengthbythecoefficientoflinearexpansiongiveshowmuchlongertheobjectis.
Volumeworksalmostthesameway,exceptinthethreedimensions.Thecoefficientofvolumeexpansion indicateshow
muchvolumeisaddedtoa(solidorliquid)materialforeverydegreethetemperatureincreases.
OtherThingstoTry
Design and calibrate a water thermometer using the coefficient of volume expansion for water and the dimensions you
determinedfortheglasstube.
ThePoint
Theamountamaterialexpandswhenheatediscalledthecoefficientofvolumeexpansion.Weconstrainedtheexpansionof
alargervolumeofwaterintheflasktoprimarilyonedimensioninthetube.Thismagnifiedtheeffectoftheexpansion,sowe
wereabletomeasureit.
311
Project91
Whatisthecoldestpossibletemperature?Estimatingabsolutezero.
TheIdea
What is thecoldest thingpossible?Somepeoplemightsay it isgivingaphysics testonaFridayafternoonbeforewinter
break. (Now that’scold!)But, thecoldest temperaturepossible isabsolutezero.Thisexperiment isanice, simpleway to
estimatethisfundamentalpropertyofnature.Withsomeextracare,amoreaccuratevaluecanbeobtained.Weknowthat
mattercontractsasitgetscold.Thebasicideahereistodeterminewhatwouldbethetemperatureifthevolumewereto
contracttothepointwhereitapproachedzero.Wecan’tgettothatpoint.Infact,wecan’tevengetcloseinanordinarylab.
But,wecanmeasurehowmuchthevolumechangesforagivenchangeintemperatureandmakeagraphtodetermineat
whattemperaturethevolumewouldbezero.Thattemperatureisabsolutezero.
WhatYouNeed
Toestimateabsolutezero
250mLPyrexflask
pairoftongssuitableforsafelyhandlingahotflask
beaker(largeenoughtofullyimmersetheflask)
hotplate
thermometer
bucket
graduatedcylinder
Tomeasureabsolutezerowithgreaterprecision
Atemperaturevolumeorpressure-volumeapparatus,suchasshowninFigure91-1.
Method
1.Putthebeakeronthehotplate.
2.Fillthebeakerwithwatertoalevelthatwillallowtheflasktobeimmersedwithoutcausingthewatertooverflow.
3.Turnonthehotplate.
4.Placetheemptyflask inthebeaker,so it isheatedfromoutside,butwithouthavingtheheatedwaterspill intothe
flask.
5. After the air in the flask has had a chance to reach equilibriumwith the heatedwater (about 5–10minutes at a
constanttemperature),measurethetemperatureofthewater.Theboilingpointisagoodstablemeasurementpoint,
butatemperaturelessthanthiscanbeusedifitisstable.
6.Fillthebucketwithcoldwater.Youcanuseicetobringthetemperaturedown.
312
Figure91-1CourtesyPASCO.
7.Removetheflaskandimmediatelyplaceitnecksidedowninthebucket.Holdtheneckoftheflaskunderwaterasit
cools.Youmayfindithelpfultolightlyinsertarubberstopperwhileyouaretransferringtheflask.Youcanalsotryto
useaone-holestoppertemporarilypluggedwithashortsectionofastirringrod.
8.Once(inyourjudgment)itreachesequilibrium,measurethetemperatureofthewaterinthebucket.Thisshouldtake
lessthanoneminute.
9.Theairhascontractedandsomewaterhasentered the flask.Measure thevolumeof thewater in the flask. (The
mostaccuratereadingoccurswhentheairpressureaboutthewaterisinequilibriumwiththeoutsideair.Thiscanbe
establishedbyraisingthebottomoftheflasksothatthe liquid level intheflask isatthesameheightasthe liquid
levelinthebucket.)SeeFigure91-2.
10.Subtractthevolumeofwaterfromthetotalcapacityoftheflask.
11.Plotthetwopointsyoumeasuredonagraphwithvolumeonthey-axisandtemperatureonthex-axis.Leaveenough
roomonbothaxessothatthepointwherethe lineconnectingthepointsextrapolatestozerovolumefitson the
graph.Drawthatlineanddeterminethetemperaturewherethevolumewouldbezero.
Figure91-2WhenthetemperaturecoolsfromT1toT2thevolumechangesfromV1toV2.
ExpectedResults
Theacceptedvalueforabsolutezerois0Kor−273°Cor−459.7°F.However,becausethefirstpartofthisexperimentisaballparkmeasurement,valuesanywherefrom−175to−350°Carereasonableextrapolations.Althoughthisisawiderange,theconceptthatextrapolatingthevolumeversustemperaturecurveuntilthevolumegoestozeroissignificant.Statistically,
weknowweareonveryshakygroundbecausewearegeneratingdatapointsthatarefarremovedfromthetemperaturewe
areextrapolatingto.
WhyItWorks
Charles’slawstatesthatT1/V1=T2/V2.Thiscanbeinterpretedassayingthatthevolumeofagasisdirectlyproportionalto
313
thetemperature.Thelowesttemperatureconceivableisthetemperaturewhenthegascontractstoazerovolume.Thiscan
never actually occur. If we extrapolate the linear relationship between temperature and volume to zero volume, you can
determineavalueforabsolutezero.
Similarly,Gay-Lussac’s lawstatesthatT1/P1=T2/P2.Absolutezero isthetemperaturewherethetemperaturepressure
lineisextrapolatedtozeropressure.
OtherThingstoTry
The accuracy of this measurement can be improved on by using the Gay-Lussac’s apparatus and extrapolating the
temperatureversuspressurecurvetozeropressure,asshowninFigure91-3.
TwodifferentsetsofmeasurementsoftemperatureversuspressureareshowninFigure91-4.
Thepointwherethepressureextrapolatestozeroisinterpretedasabsolutezero,asshowninFigure91-5.
Figure91-3TheGay-Lussacapparatusisusedtomeasuretherelationshipbetweenpressureandtemperature.
Onesourceoferrorindeterminingthechangeinvolumewithtemperatureisthepresenseofwatervaporintheflask.Use
ofoil insteadofwater to immerse theflask inavoids thisproblem.This isamessierbutmoreaccurateway toestimate
absolutezero.
Absolutezerocanbedeterminedbymeasuringthespeedofsoundatdifferenttemperatures,asdescribedin“Determining
AbsoluteZeroUsingaTuningFork,”byJeffreyD.Goldader(ThePhysicsTeacher46,April2008,206–209).
314
Figure91-4Measurementoftemperatureversuspressure.
Figure91-5Extrapolationoftemperatureversuspressuredatatozeropressuretofindabsolutezero.CourtesyPASCO.
ThePoint
Absolute zero cannot be measured directly. It can be determined by extrapolating measurements of pressure versus
temperaturetozeropressure.Similarly,absolutezerocanbedeterminedbyextrapolatingmeasurementsofvolumeversus
temperaturetozerovolume.
315
Project92
Liquidnitrogen.
TheIdea
Theairwebreath isabout78%nitrogen.Typically this isagasbutwhenbroughtdowntoanextremelycoldtemperature
nitrogenbecomesaliquid.Notonlyisliquidnitrogenfuntoplaywith,butitgivesyouanopportunitytobegintoexplorelow-
temperaturephysics.
WhatYouNeed
safetygoggles
tongsandthermalmitt
dewar(specificallydesignedtocontainliquidnitrogen)
sampleofliquidnitrogeninasecurecontainer
plasticbeaker
tableorothersurfacethatwillnotbeharmedbyverycoldtemperatures
Pyrexbowllargeenoughtoholdasmallquantityofliquidnitrogenandimmersetheotherobjectslistedhere
12inches(approximately)ofleadtinorothersolderwire
20ghookedmass
flowers
banana
hammer
metaltubewithoneendopenandtheothersealed
medicinebottlewitheasysnapon/snapofflidora35mmfilmcanister
corkthatlooselyfitsintotheopenendofthemetaltube
balloon
Method
Safety
1. Liquid nitrogenmust be handled safely. Thismeans itmust be stored in a specially designed container called a
dewar,whichisintendedforthispurpose.Donotputliquidnitrogeninatypicallunchboxthermos,whichshouldnever
beusedforliquidnitrogen.
2. Liquidnitrogenissocold,itcanfreezehumanskininaveryshorttime.Foralltheseactivities,allparticipantsshould
wear safety goggles and avoid any sustained contact with skin. Be especially carefully to avoid splashing liquid
nitrogen, which could get trapped under clothing and cause freezing. Also, remember, objects that have been
immersed in liquid nitrogen have themselves been brought to a very low temperature and should be handled
appropriately.
Splittingabanana
316
1. CarefullypoursomeliquidnitrogenintothePyrexbowl.
2. Using the tongs and thermal mitt, immerse the banana into the liquid nitrogen for about 15–30 seconds. Initial
bubblingandvaporizationdiminishasthebananaapproachesequilibriumwiththeliquidnitrogen,asshowninFigure
92-1.
Figure92-1Freezingabananainliquidnitrogen.CourtesyPASCO.
3. Removethebananaandplaceitonthetable.
4. Take the hammer and strike the banana, as shown in Figures 92-2 and 92-3. (For contrast, you can strike an
unchilledbananaeitherbeforeorafter,showingtheeffectofthemuch-more-brittlefrozenversion.)
Frozenflowers
1. Usingthesamebowlasthepreviousexperiment,immersesomefreshflowersintheliquidnitrogen.
2. Dropthebouquetonthefloororstrikethemonthetable.
Figure92-2Strikingadeep-frozenbananawithahammer.CourtesyPASCO.
317
Figure92-3Normallysoftandpliableobjectswhendeepfrozenbecomebrittle.CourtesyPASCO.
Solderspring
1. Formthepieceofsolderintoacoilroughly¾inch(1–2centimeters)indiameter.
2. Noticethelackofstiffnessinthespring.
3. Immersethespringintheliquidnitrogenforroughly15–30seconds.
4. Hang a 20 g (or so) hooked mass from the frozen spring and compare its stiffness with that of the room-
temperatureversion.
Balloon—filledwithair
1. Blowuptheballoonandtieaknotintheopenend.
2. Immersetheballoonintheliquidnitrogen.
3. Observewhathappensastheballooniscooled.
4. Removetheballoonfromtheliquidnitrogenandagainobservewhathappens.
Balloon—filledwithliquidnitrogen
1. Pourasmallamount(startwithabout10mL)ofliquidnitrogeninaballoon.
2. Tieaknotintheopenend.
3. Settheballoononatable.
4. Stepbackandmakesurenooneisnearthe(expanding)balloonandespeciallymakesurenoone’sfaceiscloseto
theballoon.
5. Observewhathappensastheballoonisexposedtothewarmerairtemperature.
Prescriptioncontainer/Filmcanister
1. Placethefilmcanister(oraplasticprescriptioncontainerwithasnap-offlid)onatabletoporonthefloor.Donot
useaprescriptioncontainerwithascrew-onorachild-prooflidthatdoesnoteasilysnapoffwithmoderateforce.
2. Poursomeoftheliquidnitrogenintotheplasticbeaker.
3. Poursomeoftheliquidnitrogenfromtheplasticbeakerintothefilmcanister.Fillthefilmcanisterabout¼fullwith
liquidnitrogen.
318
4. Snaponthetop.
5. Standbackaspressurebuildsupinthecontainer.
Corkgun
1. Placethecorkgunwhereitisaiminginasafedirection(andspecificallynotdirectedtowardanyone’sface).
2. Pourabout50mLofliquidnitrogenintothecylinder.
3. Lightlyplacethecorkintheopenendofthecylinder.Donotjamthecorkinsotightlythatitcannotbepushedout
bythepressurethatwillbuildupinthecylinder.
4. Standback.Pressurewillbuildupastheliquidnitrogenevaporates.
ExpectedResults
Thefrozenbananaandflowerswillshatter.Thesolderwilltemporarilybecomemuchmorespring-like.Theair-filledballoon
will shrink as the air inside contracts from the extreme cold, and then it will re-inflate as it warms up again. The liquid
nitrogen-filledballoonwillexpandandpossiblyburst.Thelidsofthefilmcanister/prescriptionbottlewillpopoff.Thecorkwill
shootoutofthemetalcylinder.
WhyItWorks
Objectsbecomemorebrittleandcontractfromtheextremecold.Astheliquidnitrogenevaporates,itoccupiesamuchlarger
volume.Foragivenvolume,thegashasamuchlargerpressure.
OtherThingstoTry
For many experimenters, liquid nitrogen may not be easily available on a daily basis. While you have a supply of liquid
nitrogenavailable,youmaywanttoconsiderdoingtheotherprojectsthatalsorequireliquidnitrogen,suchasProject101
(effectoftemperatureonresistance)andProject106(superconductivity).
ThePoint
Liquidnitrogenprovidesanopportunitytoexplorelow-temperaturephysics.This includesmakingnormallyelasticmaterials
brittle.Materialscooledbyliquidnitrogencontract.Asliquidnitrogenevaporates,itexpands.
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Project93
Boilingwaterinapapercup.
TheIdea
Isitpossibletoboilwateroveraflameinapapercup?Thisprojectletsyoufindoutwhythisispossible.
WhatYouNeed
2 paper cups—most “paper” cups have a thin coating ofwax, which can still be used, but if you can get them,
uncoatedcupsarepreferable
water
flame—amatchoraBunsenburner
thermometerordigitaltemperaturesensor
Styrofoamcup
sand(enoughtopartiallyfillapapercup)
waterballoon
paperbag
Method
1. Fillthepapercupnearlytothetopwithwater.
2. Holdthecupovertheflame.
3. Continuedoingthisuntileitherthepaperburnsorthewaterboils.Optional:measurethetemperatureasitisheating
up.
4. Fillthesecondpapercupwithsand.
5. Holdthiscupovertheflameandobservetheeffectoftheflameonthecup.
6. FilltheStyrofoamcupnearlytothetopwithwater.
7. Holdthiscupoftheflameandobservetheeffectoftheflameonthecup,asshowninFigure93-1.
ExpectedResults
Thewaterwillboilinthepapercup.Ifthecupiscoatedwithwax,thewaxmaymelt,especiallyabovethewaterline.Ifthere
isacircularrimonthebottom, itmayburnwithoutburningthroughthecup.Thepapercupfilledwithsandwillchar,but it
won’tnecessarilyburstintoflames.TheStyrofoamwillmeltand,wheretheflameisapplied,possiblyleaveaholeintheside
ofthecup.
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Figure93-1Boilingwaterinapapercup.
WhyItWorks
When heat is added to water, its temperature increases until it reaches the boiling point of water at 100°C. The paperdoesn’tburnbecauseheatisconductedawayfromthepaperbeforeitcanreachitskindlingpoint(thetemperaturewhereit
beginstoburn).Paperbeginstoburnataround233°C(whichisclosetothenominalvalue451°Fforpaper,madefamousinRay Bradbury’s novel Fahrenheit 451). The water temperature can increase until it boils and still remain well below the
kindlingtemperatureofpaper.
Sandconductsheatawayfromthepaper.However,unlikethepaper,sanddoesnotundergoaphasechangesaswater
doesatitsboilingpoint.Thetemperatureincreasesabove100°C.Thisiswhyweseecharringinthepapercupcontainingsand.
TheStyrofoamisaninsulator.Asaresult,thewaterdoesnotconductheatawayfromtheStyrofoamcupasitdoeswith
thepapercup,whichconductsheatmuchmorereadily.ThisexplainswhytheflamemeltstheStyrofoam.
OtherThingstoTry
Analternativeapproach is towrapapieceof paperaroundametal pipeand note its response toa flame. Ina similar
manner,themetalpipeconductsheatawayfromthepaperbeforeitcanstarttoburn.
Fillthepaperbagwithwaterandholditovertheflame.Thewaterconductsheatawayfromthepaperatafastenough
ratetokeepitfromburning.
ThePoint
Phasechangesinmatter,suchasthetransitionfromliquidtovapor,takeplaceataconstanttemperaturecalledtheboiling
point.Aliquidcannotexceedtheboilingpointuntilalltheliquidhasevaporated.Materialssuchassandconductheatmuch
betterthanair.SomematerialssuchasStyrofoamaremuchbetterinsulatorsthanothermaterials,suchaspaper.
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Project94
Boilingwaterwithice.
TheIdea
Inthisproject,youuseapieceoficetocauseacontainerofverywarmwatertostartboiling.Thisisdefinitelynotwhatmost
peoplewouldexpect.
WhatYouNeed
PyrexErlenmeyerflask(oraFlorenceflaskwithapartiallyflatbottom)
rubberstopper(withoutholes)
beakertongs(orovenmitt)
water
fewicecubes
hotplate
ringstandwitharingsmallenoughtosupporttheflaskupsidedown
optional:belljarandvacuumpump,beaker
Method
1. Partiallyfill theflaskwithwater.Thereshouldbeagapofan inchortwoabovethewater levelwhenit isupside
down.
2. Placetheflaskonthehotplate,asshowninFigure94-1.
3. Keeptheflaskonthehotplateuntilthewaterboils.
4. Removetheflaskfromthehotplate.
5. Withoutdelay,puttherubberstopper(snuggly)intheflask,carefullyturnitupsidedown,andplaceitinthering.Use
anovenmittortongstohandletheflask.
6. Thewater(havingcooledslightly)shouldnowbestillquitehot,butnolongerboiling.
7. Positionafewicecubesontheflatoftheflaskandobserve.
ExpectedResults
Shortlyaftertheicecubesareplacedonthebottomoftheflask,bubblesstarttoemergefromthetop(nearthestopper).
These bubbles continue and the water in the flask boils for a short time. Careful observation should convince anyone
watchingthatthebubblesarecomingfromtheliquiditselfandarenotaleakintherubberstopper.SeeFigure94-2.
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Figure94-1Bringingaflaskfilledwithwaterto(justunder)boling.
WhyItWorks
When a vapor (such as the air/water vapor mixture) is cooled, it contracts. As the volume of gas above the hot water
decreases, thepressurealsodecreases.Waterboilsat100°C(212°F)atstandardatmosphericpressure,butataslightlylowertemperaturewhenthepressureabovetheliquidisreduced.
Figure94-2Boilingwaterwithice.
OtherThingstoTry
Youcantrythisanotherway:
1. Fillabeakerwithwater.
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2. Placeitonahotplateandbringittoaboil.
3. Removethebeakerfromthehotplateandletitcooluntiltheboilingjuststops.
4. Placethebeakerinavacuumchamber(belljaronavacuumplate).
5. Attachandturnonthevacuumpumptoevacuatethechamber.
6. Comparetheeffectofdirectlyapplyingavacuumtothereducedpressurecausedbytheice.
ThePoint
Waterboilsatalowertemperaturewhenthepressureoftheairaboveitislowered.
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Project95
Seebeckeffect/Peltiereffect.Semiconductorheating.
TheIdea
Muchofphysicsconcernsitselfwithhowoneformofenergyischangedintoanother.Thisexperimentexploreshowheatcan
causeanelectricalcurrenttoflow.Althoughthisisnotyetefficientenoughtobeusedasasignificantsourceofelectrical
power,itiswidelyusedintheformofthermocouplestomeasuretemperature.ThisisknownastheSeebeckeffect.
Thereverse—whereelectricalcurrentflowingthroughcertainmaterialsresultsinonepartofthecircuitgettinghotandthe
other part getting cold—is known as the Peltier effect. Unwanted heat is dissipated by electronic components. These
componentsmustbecooledtofunctioncorrectly.Peltiercoolershavenomovingpartsandhavebeenusedtocoolhigh-
speedcomputermicroprocessors.Theyarealsousedinsteadofdryiceincloudchambers.(SeeProject125.)
WhatYouNeed
voltmeter(ormultimeterconfiguredasanvoltmeter)
ammeter(ormultimeterconfiguredasanammeter)
variableDCpowersupply
jumperswithalligatorclips
1000ohmresistor
24-inchlengthsofvarioustypesof(uninsulated)metalwire,includingiron,copper,constantan,andaluminum
heatsource,suchasacandle,Bunsenburner,orasolderingiron
icecubes
optional:2thermocouplestobeusedastemperaturesensors
Method
Seebeckeffect
1. Selecttwodifferentwirematerials.Taketwopiecesofthefirstmaterialandonepieceofthesecondmaterial.Let’s
saywestartwithtwopiecesofironandonepieceofcopper.
2. Attacheachendofthecopperwiretoeachofthetwopiecesofironwirebytwistingaboutaone-halfinchlengthof
thewiretogether.
3. Connectthetwounattachedendsoftheironwiretothepositiveandnegativeterminalsofthevoltmeter.SeeFigure
95-1.Setthevoltmeteronthemostsensitivesetting.The250mV(0.250V)rangeisagoodplacetostart.
4. Measurethevoltageatroomtemperature.(Momentarilydisconnectoneofthevoltmeterconnectionstoverifythat
thevoltageyouarereadingistheresultofthecircuityousetup,ratherthanasmallstrayvoltagereading.)
5. Touchonejunction(twistedwireconnection)totheice,leavingthesecondjunctionatroomtemperature.Howdoes
thataffectthevoltagereading?
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Figure95-1WiringarrangementformeasuringtheSeebeckeffect.
6. Placethesecond junction in theheatsourceandseewhathappens.Becarefulbecausethevariousmetalwires
conductheatandcanburnanythingthatcomesincontactwithit.
7. Trythiswithasmanymaterialcombinationsasyoucan.
8. Placeatemperaturesensoroneachofthetwistedmetaljunctions.Varythejunctiontemperatures.Plotthevoltage
asafunctionofthedifferencebetweenthetwojunctiontemperatures.
Peltiereffect
1. Asbefore,connecteachendofonepieceofwiretoapieceofasecondtypeofmetalwire.
2. Connect the components as a series circuit consisting of thewires, the ammeter, a 1000 ohm resistor, and an
ammeter.ThiscircuitisshowninFigure95-2.
3. AdjusttheDCpowersupply,soabout10mA(10milliampsor0.01amps)isflowingthroughthecircuit.(Youcanuse
a9-voltbattery insteadofanadjustableDCpowersupply,which results inslightly less than thiscurrentwith the
1000ohmresistor.)
4. Putwateroneachofthejunctions.Whathappens?Reversethedirectionofthecurrentflowbyexchangingthewire
connectedtotheDCpowersupply.Howdoesthataffectwhatyoufind?
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Figure95-2ApparatusforthePeltiereffect.
5. Monitor the temperature of each of the junctions as you vary the current flowing through the circuit. Plot the
temperaturesofeachjunctionandthedifferenceversusthecurrent.
ExpectedResults
IntheSeebeckeffect,atemperaturedifferenceatthetwojunctionsresultsinavoltagegeneratedthroughthecircuit.
ThePeltiereffectresultsintemperaturedifferencesatthejunctionswhenacurrentflowsthroughthecircuit.
WhyItWorks
A temperature difference between two dissimilarmetals results in an electrical potential that drives a current through a
circuit.Thereverseeffectcausesatemperaturedifferencewhenacurrentflows.
OtherThingstoTry
Commercial thermocouples that employ dissimilarmetals are based on the Peltier effect and can be used to study this
principle. Some temperature control devices that serve as a means of studying the Seebeck effect are available
commercially.
ThePoint
The Seebeck effect and Peltier effect describe a set of interactions between the thermal properties and the electrical
propertiesofmatter.
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Section9
ElectricityandMagnetism
Project96
Staticcharges.
TheIdea
AccordingtoNewton’slawofuniversalgravitation,anymassexertsaforceonanyothermass.Electricchargesworkina
verysimilarway.Thefartherawayyouget,theweakertheforce.Becausetheelectricforceissomuchstrongerthanthe
gravitational force, it is much easier to measure. This experiment explores the nature of the electrostatic force and
establishesthebasisforCoulomb’slaw.
WhatYouNeed
2pithballsorconductivelycoatedStyrofoamballs(conductivelycoatedping-pongballsarealsoanoption)
2piecesofstringabout16inchesinlength
movableringstandwithapendulumclamp(orotherhorizontalsupport)
smallnonconductivepostonastand(thepostshouldbeafewinchesinlengthandconsistofathinwoodendowel
orashortglassorplasticrod)
ruler
rubberrod/woolpair(orequivalent)toapplyachargetothepithballs
optional:lightsourcetoprojecttheimageofthepithballsontoascreen(anoverheadprojectorLCDprojectorcan
servethispurpose)
Method
1. Attachonesideofeachofthetwostringstothepithball.
2. Attachtheothersidesofthestringtothependulumclampseparatedbyafewinches,sothepithballcanswingin
onlyonedirection,asshowninFigure96-1.
3. Attachtheotherpithballtothenonconductivestand.
4. Theswingingpithballshouldbepositionedsoitcanonlyswingclosertoandfurtherfromthestationaryball.
5. Drawareferencemarkonthebottomoftheringstandtoindicatetherestpositionoftheswingingpithballwithout
beingsubjectedtoanyforceotherthangravity.
6. Vigorouslyrubthewoolagainsttherubberrodtochargeitup.Toucheachofthepithballstoapplythesamecharge
tothem.Touchingthetwoballstogetherwillmakethechargesnearlyequal,butitisnotnecessarytodothis.
7. Startwithadistancebetweenthepithballsthatallowstheswingingballtohangvertically.
8. Slowlybringtheswingingpithballcloseruntiltherepulsionbetweenthetwopithballscausestheswingingpithball
tomoveawayfromthestationaryball.
9. Measurehowfartheswingingpithballmoveshorizontally.Youmaydothisbyobservingfromaboveandmeasuring
thedistancetheballhasmovedfromthereferencepoint.
10. Recordthehorizontaldistancebetweenthecentersofeachofthepithballs.
11. Repeatthismeasurementafewtimesbymovingtheswingingpithballinalittlecloser.
12. Thehorizontalseparation,x,betweentheunconstrainedpithballanditsequilibriumpositionisagoodindicationof
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theforce.(Thiscanactuallybeworkedoutintermsoftheforce,butthisisunnecessarytoexplorethekeypointof
this experiment.) For small angles that the pith ball makes with the vertical, the electrostatic force is directly
proportionaltotheseparationfromequilibrium.
13. Theseparationbetweenthestationaryballandtheequilibriumpositionsisdesignatedasd,asshowninFigure96-2.
Thetotaldistancebetweenthetwopithballsisgivenbyd+x.Makeagraphoftheseparationfromequilibrium,x,
andthedistance,d+x,betweentheballs.
Figure96-1Twounchargedballsinequilibriumposition.
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Figure96-2Twochargedballsshowdisplacementfromequilibriumposition.
ExpectedResults
Thecloserthetwoballsget,thegreatertheforce.
Thisrelationshipisnotlinear.
Theclosertheballsget,thefastertheincreaseinforcebetweentheballs.
Specifically,thisisaninversesquarerelationship.
Overall,thisexperimentworksbestonadaywithlowhumidity.
WhyItWorks
Coulomb’s law states that the force (in newtons) between two charges, q1 and q2 (in Coulombs or C), separated by a
distance,d(inmeters),isgivenby:
wherekistheCoulombconstant=9.0×109m2/C2.
OtherThingstoTry
Findinghowmanyelectronsareonachargedballoon.
Hangtwoballoonsafterfirstdeterminingtheirmass.Chargethemandtouchthemtogether,sotheyhaveroughlythesame
charge.TheCoulombforceresultsintheballoonsrepellingandseparating,asshowninFigure96-3.
Thenumber,n,ofelectronsoneachoftheballoonscanthenbedeterminedfrom:
whereqisthechargeon1electron
=1.6×10−19CkisCoulomb’sconstant=9.0×109m2/C2
misthemassofeachballoon
andθistheanglethestringofeachballoonmakeswithaverticalline.
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Figure96-3Twoballoonswithlikechargesrepel.
TheCoulombforcecanalsobeexploredinthefollowingsimpledemonstrations:
Chasingacan
Achargedrubberrod,suchastheonepreviouslyusedtochargethepithballs,inducesacurrentinacan.Thisenablesyou
torollthecanbackandforthacrossthetable,asiftherodwereamagicwand.
Bendingwater
Athinstreamofwaterfromafacetcanbebentbyachargedrod.
Tape
Thesimplestofallistotakesometransparenttapeandadhereittoatable.Afterpullingitup,thetapewillhaveacquireda
chargethatwillbeattractedorrepelledbyothernearbyobjects.Twosimilarpiecesoftapeacquiresimilarchargesandare,
therefore,repelled.
Plasmaglobe/Sunderball
Thisisatrue“evilgenius”propthatlookslikesomethingoutofaFrankensteinmovie.Asmallteslacoilproducesa large
voltagedifferenceinsideaglassbulb.Thisissimilartothewaythatchargebuildsupinclouds.Minilightningboltsdischarge
throughaninertgasinthebulb,producinganeerieglow.Theelectronsinthegasflowtotheelectricalgroundharmlessly
providedbyafingertouchingtheouteredgeoftheglassasifthepersontouchingtheoutsideoftheglobewasahuman
lightningrod.Thisissafetodobecausethecurrent(amps)flowingisverysmall.SeeFigure96-4.
FurtherAnalysis
ApplyanExcelcurvefitforthegraphoftheseparationfromequilibrium,x,versustheseparation(d+x)betweentheballs.A
scatterplotwiththepoweroptionselectedshouldindicatethebestfitclosestto–2,whichisaninversesquarerelationship.
Youcouldalsoplotxversus1/(d+x)2.Alinearfittothisgraphwouldindicateaninversesquarerelationshipbetweenx
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(whichisanindicatorofthemagnitudeoftheforce)andd.
Figure96-4Plasmaglobe.
ThePoint
The force between two charges is directly proportional to the product of the charges and inversely proportional to the
distanceseparatingthechargesasgivenbyCoulomb’slaw.
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Project97
Makinglightning.ThevandeGraaffgenerator.
TheIdea
AvandeGraaffgeneratorbuildsupstaticelectriccharges,whichwhendischarged,producevisiblelightning-likesparks.This
isoneofthemorememorablephysicsexperimentsandprovidesagreatintroductiontothebasicideasofelectricity.
WhatYouNeed
vandeGraaffgenerator
groundingsphere
groundingwire—withalligatorclipterminationsorjustplaininsulatedwirewiththeendsstripped
confetti,paperholesfromaholepuncher,RiceKrispies
stripsofpaper
scotchtape
afewaluminumpiepans(thesmallonesthatareabout4inchesindiameterarepreferable)
electroscope
glassrodandsilk,rubberrod,andwoolorfur
short(12inchorso)neonlightbulb
insulated(plastic)crate
othervandeGraafftoys:spinner,sparkgap
electroscope
Method
Awordaboutsafety
When used as intended and according to manufacturer’s specifications, this is a safe experiment. The van de Graaff
generator produceshigh voltages.Thesecanbeover20,000 volts,whichmay soundhigh.However, similar voltagesare
producedbyscrapingyourshoesacrossacarpetonadayoflowrelativehumidity.Thevoltageishigh,butthecurrentisvery
low,sothehighvoltageisnothazardousbecauseveryfewelectronsareinvolved.
Removeall electrical devices from your pockets orwrist. Set up a safe areawith unobstructed access to the van de
Graaffgenerator.
Herearesomeconsiderations:
Sparkscandamageelectronicdevices,includingcellphones,audiodevices,calculators,computers,digitalwatches,
andpacemakers.
Thisactivityisfunbecauseofthedramaticandsuddenstaticelectricdischarges.However,makesurenooneisput
atriskbyanyone’ssuddenreactionstothisapparatus.
Becarefulnottobuilduphigher-than-intendedchargesusinglonghumanchainsorotherstoragedevices,suchas
capacitorsorLeydenjars.
Makesuresparksarenotnearflammablematerials,suchasnaturalgaspipesorcombustiblelaboratorychemicals.
Lightning
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1. PlacethevandeGraaffgeneratoronatableandplugintheelectricalchord.
2. PositionagroundingelectrodeafewcentimetersfromtheconductingsphereofthevandeGraaffgenerator.Ifyou
don’t havea discharge sphere purchased for this purpose, you can improvise using ametal rod, such as a ring
stand.
3. Attachawirebetweenthegroundingelectrodeandanelectricalground,suchasawaterpipeorametalbeamthat
ispartofthebuildingstructure.
4. TurnonthevandeGraaffgenerator.
5. Darkentheroom.
6. Move the conducting sphere of the van deGraaff generator back and forth, and observewhat is themaximum
distanceadischargewillcross.
7. Placeasheetofpaperinthepathofthespark.Doesasheetofpaperstopthespark?
8. TurnoffthegeneratorandtouchthegroundingspheretotheconductingsphereofthevandeGraaffgeneratorto
removeanyresidualcharge.
Paperstrips
1. Groundtheconductingsphere.
2. UsetapetoattachstripsofpapertothetopoftheconductingsphereofthevandeGraaffgenerator.
3. Turnonthegeneratorandobservethepaperhairsseparatingandstandingonend,asshowninFigure97-1.
4. Turnthegeneratoroffandgroundtheconductingspherewiththegroundelectrodetoremoveanyresidualcharge.
Ahair-raisingexperience
1. Groundtheconductingsphere.
2. PlaceaninsulatingsurfaceonthefloornearthevandeGraaffgenerator.Aninvertedplasticcrateworkswellfor
thispurpose.Thereasonfordoing this is tomakesurenodischargeoccurs toconductors,suchaswaterpipes,
underthefloor.
Figure97-1Likechargesrepel,causingthepiecesofpapertoseparate.
3. Placeyourhandontopofthegeneratorwiththepalmofyourhandfacedown.
4. Have someone turn on the generator. You can do it yourself, but be prepared for the possibility of a mild and
harmlessshock.
5. Thisworksbestwithpeoplewithlong,finehaironlowhumiditydays.Ifsomeonecomesclose,theycouldbemildly
334
shocked.
6. Whenyouarefinished,turnoffthevandeGraaffgenerator,stepoffthecrate,anddischargetheconductingsphere.
Levitatingpiepan
1. Groundtheconductingsphere.
2. Placeanaluminumpietinontheconductingsphere.
3. Turnonthegeneratorandobservetheresult.
4. Trythiswithseveralpiepansstackedontopoftheconductingsphere.
5. Turnthegeneratoroffandgroundtheconductingspherewiththegroundelectrodetoremoveanyresidualcharge.
Positiveornegative?
1. Groundtheconductingsphere.
2. Turnonthegeneratorandbringtheelectroscopeneartheconductingsphere.Don’tbetotallysurprisedifyougeta
spark.
3. Rubtheglassrodwiththesilktoproduceanegativechargeontheglassrod.
4. Bringthenegativelychargedglassrodtothetopoftheelectroscopetoseparatetheleaves.
5. Bring the negatively charged electroscope near the van de Graaff generator and observe whether the leaves
separatefurtherormoveclosertogether.
6. Rubtherubberrodwiththewool(orfur)toproduceapositivechargeontheglassrod.
7. Bringthepositivelychargedrubberrodtothetopoftheelectroscopetoseparatetheleaves.
8. Bring the positively charged electroscope near the van de Graaff generator and observe whether the leaves
separatefurtherormoveclosertogether.
9. Based on the response of the electroscope, what do you conclude about the type of charge produced on the
conductingsphereofthevandeGraaffgenerator?
Neonbulb
1.TurnonthevandeGraaffgenerator.
2.Darkentheroom.
3.Bringasmallneonbulb(withnoelectricalconnectionstoeitherend)neartheconductingsphere.Ifyougettooclose,
some sparks will likely discharge harmlessly in your hand. If you prefer for this not to happen, you can rig up a
nonconductingholdertosupporttheneonbulbduringthisexercise.Becarefultoavoidsuddenmovesthatmightresult
indroppingthebulb.
4.Positiontheneonbulbparalleltotheflooronalinepointingtowardthecenteroftheconductingsphere.Moveitcloser
andfurtherfromthevandeGraaffandobserve.
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Figure97-2Lightinganeonbulbbyexposingittoanelectricfield.
5.Position theneonbulbparallel to the floorona linepointingperpendicular to thecircumferenceof theconducting
sphere,asshowninFigure97-2.MoveitcloserandfurtherfromthevandeGraaffandobserve.
6.Turnthegeneratoroffandgroundtheconductingspherewiththegroundelectrodetoremoveanyresidualcharge.
ExpectedResults
Sparkswilldischargethroughtheair.Longersparksaregeneratedifthevoltageishighandthehumidityislow.Best-case
sparklengthisshowninFigure97-3.
Figure97-3Sparklength.BasedondatafromA.D.Moore,Electrostatics:Exploring,Controlling,andUsingStaticElectricity
(NewYork:Doubleday-Anchor,1968).
WhyItWorks
Anelectricalmotordrivesanonconductingbeltthatseparatespositiveandnegativecharges.Negativechargesaredrawn
awayfromtheconductingmetalsphereatthetopofthedevice,leavingastaticpositivechargeonthesphere.Bringinga
neutralornegativelychargedobjectclosetotheconductingsphereresultsinadischargeintheformofalightning-likespark
throughtheair.Themaximumlengthofthesparkdependsontherelativehumidityintheair.Asaruleofthumb,thespark
jumpsabout1centimeterforevery10,000voltsthatbuildup.
Objectsthatcomeintocontactwiththeconductingsphere,themselvesbecomecharged.Thiscausesrepulsionbetween
piecesofpapertapedtotheconductingsphere,ofthehairofapersontouchingthesphere(whilestandingonaninsulating
surface),andbetweensmallobjects,suchasStyrofoamchipsorRiceKrispiesthatcomeintocontactwiththesphere.
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OtherThingstoTry
Chargesseparatedby thevandeGraaffgeneratorcanbeconcentratedon thebulbofanelectroscope.Thesignof the
chargecanbedeterminedbyobserving theeffectofachargedrodbroughtnear thebulb. If thecharge is thesame, the
leaves of the electroscope are driven further apart. If the charge is different, the leaves are drawn closer together. A
positivelychargedrodresultsbyrubbingwoolorfuronrubber.Anegativelychargedrodresultsbyrubbingsilkonglass.
Useofateslacoil isanotherway togeneratesparks that jump through theair.Thesecanbepurchasedashand-held
units.
ThePoint
Thisexperimentshowshow, through themovementofdissimilarmaterialsagainsteachother,staticelectricchargescan
buildup.Anelectricfieldisestablishedintheregionseparatingtheelectricalchargeswhichcanforcetheelectronstomove.
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Project98
TheWimshurstmachine.Separatingandstoringcharges.
TheIdea
The Wimshurst machine, like the van de Graaff generator, is capable of throwing long sparks as much as several
centimeters between two small conductive spheres. The Wimshurst machine is usually also tied to a Leyden jar, which
presentsagoodopportunitytoexplorecapacitanceandchargestorage.
WhatYouNeed
Wimshurstmachine
Method
1. CAUTION:Electricalcircuitryincludingpacemakers,hearingaids,cellphones,flashdrives,electroniccardoorlocks,
andcomputersmaybedamagedbythesparksgeneratedinthisexperiment.Inaddition,followallsafetyinstructions
providedbythemanufacturerofthisdevice.
2. SettheWimshurstapparatusonatable.
3. Darkentheroom.
4. Makesureallelectricaljumpersareinplaceforyourparticularsetup.Checkwiththemanufacturer’sinstructionsto
makesuretheapparatusissetupproperlywithcorrectelectricalpathstotheLeydenjarsanddischargespheres.
YoucandothisbothwiththeLeydenjarsconnectedornotconnectedtoyourcircuit.
5. Separatethetwodischargespheresbymorethan8cm.
6. Turnthehandleforfivesecondsorso,asshowninFigure98-1.
7. Holdingonlytheinsulatedwoodenhandlesforthedischargespheres,slowlybringthemtogether.
8. Notethedistancebetweenthedischargesphereswhenthefirstdischargeoccurs.
9. Setthedischargespheresatroughlythesameslightlycloserandslightlyfurtherdistances.
10. IftheLeydenjarswereinyourcircuit,repeattoseewhathappenswhentheyarenotconnected.
11. Touch the two spheres together for a few secondswhen finished tomake sure no residual charges are on the
electrodes.
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Figure98-1ChrisAleodemonstratestheoperationofaWimshurstmachine.
ExpectedResults
Withthedischargedspheresseparatedbyalargedistance,nothingshouldhappen.
Asthespheresapproachtowithinafewcentimetersseparatingthem,alightningboltwilljumpacrossthegap,asshownin
Figure98-2.
WhyItWorks
TheWimshurstmachineisconstructedfromtwoparallelplatesmadefrominsulatingmaterialsuchasLuciteorglass.The
platesarearrangedtobeturnedbyhandinoppositedirections.Narrowmetalstripsaremountedontheplatesandoriented
along the radius. Charges are transferred bymetal brushes that sweep across themetal strips as the plates rotate. In
contrasttothevandeGraaffgenerator,theWimshurstmachineseparateschargebytheprincipleofinductionratherthan
friction.Positiveandnegativechargesaccumulate,andtheycaneitherchargeaLeydenjarordischargeacrossagap.
Figure98-2Wimshurstmachineelectricaldischarge.
OtherThingstoTry
Charges separated by the Wimshurst machine can be determined using an electroscope, as described in the previous
experiment.
ThePoint
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Thisexperimentshowshow,throughthemovementoftwoinsulatingplatesneareachother,staticelectricchargescanbuild
up.Theseparatedchargescanbestoredordischargedacrossasmallnonconductivegap.
340
Project99
Runningintoresistance.Ohm’slaw.
TheIdea
Ohm’s law forms thebasis for understanding howelectricity flows throughcircuits.This isa very simple relationship that
involvesthreethings:1)thevoltageorthepushthatmoveelectronsthroughthecircuit,2)thecurrent(oramps),whichisa
measureofhowmuchelectricityisflowingthroughthatcircuitasaresultofthatpush,and3)theresistance(inohms),which
doesallitcantomakeitdifficultfortheelectricitytoflow.
Because of its simplicity, this experiment is a good one for you to discover the law for yourself, based on your
measurements.
WhatYouNeed
one100ohmresistorratedfor0.5watt(otherresistorvaluescanwork,buttheresistormustberatedtohandlethe
wattagethatwillbeappliedtoit;thewattageissuppliedbytheresistormanufacturerandisoftenmarkedonthe
resistor)
ammeter
voltmeter
DCpowersupply(orbattery)
wirestoconnecttobatteryterminals
Method
1. Connectacircuit,asshowninFigure99-1.ThisisacircuitconsistingofaresistorinserieswithaDCpowersupply
andanammeterwithavoltmeterconnectedbyjumperwirestoeachoftheendsoftheresistor.Adrawingcalledan
electrical schematic is shown in Figure 99-2. This is equivalent to Figure 99-1, but it shows the electrical
connectionswithoutregardtotheactualphysicallayoutofthecomponents.
2. TurntheDCpowersupplytozero.
3. Settheammetertoreadmilliamps.Setthevoltmetertoread0–10volts.
4. IncreasetheDCpowersupplytogiveavoltagereadingof0.2volt.
5. Readthecurrent.
6. Dothesamewithavoltageof0.4,0.6,and0.8volts.
7. Graphcurrentversusvoltage.Drawalinethatbestfitsthedata.Whatisthesignificanceoftheslopeoftheline?
8. Repeatthiswitha200anda300ohmresistor.
ExpectedResults
Foragivenresistor,thegreaterthevoltage,themorecurrentflows.
Asresistanceincreases,lesscurrentflowsforagivenvoltage.
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Figure99-1CircuitformeasuringOhm’slaw.
Figure99-2SchematicformeasuringOhm’slaw.
Voltageincreaseslinearlywithcurrent.Theslopeofthelineistheresistancethecurrentisflowingthrough.
WhyItWorks
Ohm’slawisgivenbyvolts=resistance(ohms)×current(amps).Fromthis,youcanseethattheslopeofthevoltsversusthecurrentgraphisresistance.
OtherThingstoTry
Whathappensifyouhavetwoorthreeresistorsofthesameresistanceinarow,oneconnectedtothenext?Thisiscalleda
seriescircuitandisshowninFigure99-3.Foragivenvoltage,isthecurrentgreaterorlessthanforasingleresistor?
Whathappensifyoutakethosesamethreeresistorsandconnecttheminaparallelcircuit,asshowninFigure99-4?
ThePoint
Ohm’slawrelatesthevoltage,current,andresistanceofacircuit.Thevoltageatanyparticulartimeequalsthecurrenttimes
theresistance.
342
Project100
Circuits:Bulbsandbuzzers.
TheIdea
Ifyouhaveneverbuiltacircuitbeforewithyourownhands,thisisyourchance.Likemanyoftheexperimentsinthisbook,
various levelsofcomplexityexistandyoucantaketheexperimentasfarasyoucareto.Youstartwithbuildingasimple
circuit, suchasmakingabell ring.Then, youbuildabasic telegraphsystem.Youbranchoutandaddseriesandparallel
pathstosimplecircuits.Next,youmeasurethecurrentandvoltageatvariouspoints inthecircuit.Finally,youlookathow
Ohm’slawcanbeappliedtomorecomplicatedcircuits.
WhatYouNeed
jumperwires
6Christmastreebulbs(orlow-voltagebulbsandsockets)
various(low-voltage)electricaldevicessuchasbells,buzzers,LEDs
DCpowersupply(orbatteryasinthepreviousproject)
knifeswitch
ammeter(ormultimetersetupasanammeter)
voltmeter(ormultimetersetupasanvoltmeter)
for the telegraph:5–10feetof insulatedwire, ironnail, twoblocksofwoodroughly3×6×¾ inches,asecondblockofwood¼inchtallerthanthenailafterbeingnailedintotheblock,a“tin”can,tinsnips,andafewsmallnails
Method
Buildingacircuit
1. LookatthecircuitdiagraminFigure100-1andmaketheappropriateconnections.
2. IfyouhaveanadjustableDCpowersupply,setavoltageof2–3voltsandkeepitconstantthroughoutthetest.You
mayneedtoadjustthis,dependingonthecircuityouareworkingwith.
3. Thecircuitdiagramshouldgiveyoualltheinformationyouneed.Hereareafewdetailsthatmaybehelpful:
–AttachajumperwiretothepositiveandnegativeterminalsoftheDCpowersupplyorbattery.(Notthattheelectrons
care,butredisgenerallyusedforpositiveandblackisusedfornegativeforclarityinassemblingthecircuits.)
–Theremustbeacompletepathfromthepositiveofthepowersupplyandbacktothenegative.
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Figure100-1Basicelectricalcircuitconsistingofabattery,bulbandaswitch.
–All connectionsmust bemetal-to-metal. If insulation is on thewires, youeither need to usea bare-metal alligator
connectororremovetheinsulation.
Makingatelegraph
1. Wind25–50turnsofinsulatedwirearoundalargeironnail.Leavethetwoendsofthewirefreeandremoveabout¾
inchofinsulation.
2. Hammerthenailintothewoodenblock.
3. Cuttwostripsfromyourcan,roughly2½incheslong×½inchwide.Bothpiecesshouldbeflexible.4. Attachoneofthemetalstripstothewoodenblock.Theheightofthewoodenblockshouldbe¼inchhigherthan
thenail.
5. Attachtheblockwiththemetalstriptothebaseblock,sothemetalisabovetheheadofthenail,butnottouching.
6. Buildthe“key”bynailingthesecondmetalstriptothesecondblockononeside,andthenputtinganailunderneath
theotherendofthemetalstrip.Leaveenoughofthenailheadexposedabovethewoodsurface,soyoucanwrap
wirearoundit.
7. OK.Let’shookeverythingup.WhatyouhaveisaseriescircuitfromtheDCpowersupplythroughtheelectromagnet
tothekey.Thekey issimplyaswitch.When itcloses, theelectromagnetpulls themetalstripdown,asshown in
Figure 100-2. Short and long durations are the dots and dashes of Morse code. If you have enough wire, you
separatethekeyandthereceiverbysomedistance.(Note:ifyouusethistocheatontestsinschool,pleasemake
sureyoudon’tsayyougottheideatodoithere.)
Seriesandparallelcircuits
1. AttacheachofthetwoendsofaChristmastreebulb(oralow-voltagebulbinasocket)acrossthepowersupply.
(Thismeans oneof thewires attached to the bulb goes to the positive terminal and the other end goes to the
negativelead.)
2. Connectthree(ormore)bulbsinseries.Comparethebrightnessofthesebulbswiththebrightnessofasinglebulb.
3. Connectthreebulbsinparallelandcomparewiththebrightnessofbulbsinaseriesandasinglebulb.
Measuringthecircuit
1.Repeattheprevioussetofmeasurements,butthistime,includeanammeterinserieswiththecircuitandavoltmeter
inparallelwith thecircuit,asshown inFigure100-2. It helpswith thecomparison if youkeep thevoltageconstant
throughoutthesemeasurementsandcomparethecurrentflowinginthecircuits.
2.Comparethecurrentflowingineachthesituations.
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Figure100-2Inatelegraphanelectromagnetisactivatedwhenaswitchisclosedtocompletethecircuit.
3.ApplyOhm’slaw(intheformR=V/I)tofindtheresistanceofeachofthecircuitsyoumeasured.
ExpectedResults
Currentwillflowinacircuitifacontinuouspathexistsfromthepositiveterminalofthepowersupplythroughallcomponents
ofthecircuit,andthenbacktothenegativeterminalofthepowersupply.
Componentsinseriesreducethecurrentthatcanflowbyeffectivelyaddingresistancetothecircuit.
Components in parallel result in increased current flowing through the circuit. The resistance of the overall circuit is
reducedwhencomponentsareaddedinparallel.
WhyItWorks
Whencomponentsareaddedinseries,thevoltageisdistributedoverallthecomponents.Asaresult,lesscurrentisableto
flow.
Whencomponentsareadded inparallel,alternatepathsareprovided for thecurrent to flowback to thebattery.Fora
givenvoltage,thepushfromthebatteryisabletoforcemorecurrentthroughthelargernumberofpaths.
OtherThingstoTry
Anextlogicalstepistocreateandtestmorecomplexnetworksofresistors.Thefollowingshowssomeexamples.These
canbeanalyzedusingthefollowingprinciples:
Resistorsinseriessimplyadd:Rseries=R1+R2
Resistorsinparalleladdinamorecomplexfashion.Resistorsinparallelcanbethoughtofasonesingleequivalent
resistancegivenby:1/Rparallel=1/R1+1/R2+…Thesecircuitscanthenbesimplifiedbycombiningseriesandparallelcircuits,andthenapplyingOhm’s law in its
variousforms(V=RI,R=VI,andI=V/R).
ThePoint
Ohm’s lawdetermineshowmuchcurrent (oramps) flows throughacircuit.Foragiven resistance (ohms), thegreater the
voltage,thegreaterthecurrent.
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Project101
Howdoesheataffectresistance?
TheIdea
Whenmatterheatsup,theatomsstartmovingfaster,likecarsinrush-hourtraffic.Thehotteritgets,themoredifficultitis
forelectronstomakeitthroughawire.Inthisexperiment,youexplorewhathappenswhenaconductorgetshot.
WhatYouNeed
one10-ohmresistorratedfor1Worgreater
DCpowersupplyorbattery
(optional) digital temperature sensor (some multimeters come with a thermocouple and setting to read the
temperature)
stopwatch
Method
1. Setupthecircuit,asshowninFigure101-1.
2. Attachthetemperaturesensortotheresistor.(Nottoworry.Ifyoudon’thaveathermocouple,thereisstillawayfor
youtodothis.)
3. Setavoltageofabout5V.
4. Measurethevoltage,current,andtemperature.
5. Continuetakingreadingsofvoltage,current,andtemperatureatregular intervals. Ifyoudon’thaveatemperature
sensor, you can still proceed, taking note of the fact that the resistor is heating up qualitatively. A relationship
betweenresistanceandtime(ratherthantemperature)canstillbeestablished.
6. UseOhm’slawtodeterminetheresistancebydividingthevoltagebythecurrent(inamps).
7. Whathappenstoresistanceastheresistorheatsup?
ExpectedResults
The higher the temperature, the higher the resistance. Resistance increases linearlywith temperature. See Figure101-2,
whichshowstheresistanceofa5centimeter(0.05m)sectionof20AWGcopperwireoverarangeoftemperatures.
WhyItWorks
Whenaconductor is heated, themoleculesmove inplacemore rapidly. Likeacarmovingonahighwaywith increasing
traffic,theelectronscannotmoveasfreelythroughtheconductor.Theresultistheresistanceincreases.
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Figure101-1Circuitformeasuringtheeffectofheatofresistance.
Figure101-2Resistanceversustemperaturefor5cmlengthof20AWGcopper.
OtherThingstoTry
Useanexternalsourceofheat,suchasahotplateoraBunsenburner,toheatthe(uninsulated)wire.
Use ice, dry ice, or liquid nitrogen to produce low temperatures. Your thermocouple may not read over the entire
temperaturerangeofyoursample,butyoucanstillobtainsomeextremelylow-temperaturereadingsasthesamplewarms.
ThePoint
Electricalresistanceincreaseswithtemperature.Thisrelationshipislinearoverabroadrangeoftemperatures.
348
Project102
Resistivity.Canironconductelectricitybetterthancopper?
TheIdea
Yes,ifthewireislongerorthicker.Copperiswellknownasagoodconductorofelectricity.Thissameisnotusuallysaid
aboutiron.Thisprojectdealswithtwoideasthatsoundsimilar,butthatarequitedifferent:resistanceandresistivity.
WhatYouNeed
uninsulatedcopperwire25cminlength
uninsulatedironwire25cminlengthofthesamediameter(thiscanbeindicatedbythewiregaugeorAWG)
(othermaterialcombinations,suchasaluminumorsilverwirecanbeusedinsteadof,orinadditionto,copperand
iron)
DCpowersupply
ammeter
voltmeter
(ifyouhaveadigitalmultimeter,youmaybeabletousetheohmmetersettingdirectly)
connectingwire
ruler
Method
1. SetupthecircuitasshowninFigure102-1.MarkthewirewithaSharpiein2cm(orotherconvenient)lengths.
2. Theammeterisattachedacrosstheentirelengthofthewire.Thecurrentfromthepowersupplyflowsthroughthe
entirelengthofthewire.Thevoltmeterisattachedonlyacrosstheselectedlength(2cm,4cmandsoon).
3. Readvoltage,current,anddistance.
4. Find the electrical resistance fromOhm’s law by dividing the voltage (volts) by the current (amps). This gives a
resistancereadinginohms.Thiscanalsobedirectlyreadfromanohmmeterifyouhaveone.
5. Comparetheresistanceyoumeasurefordifferentlengths.
6. Foragivendiameter,multiplyingtheresistancebythelengthgivesameasureofthewire’sresistivity.Whatdoyou
findhappenstothisvalueasthelengthincreases?
ExpectedResults
Thelongerthewire,thegreatertheresistance.
Thegreaterthecross-sectionalareaofthewire,thelowertheresistance.
Resistanceincreases(linearly)withlength.
Resistanceisinverselyproportionaltocross-sectionalarea.ThisisrepresentedinFigure102-2.
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Figure102-1Circuitformeasuringresistivity.
Figure102-2Resistanceofvariouslengthsofcopperwire.
Thecross-sectionalareasofthevariousAmericanwiregauges(AWG)areshowninTable102-1.
Table102-1
Resistivity at 20 degrees C for various materials used to make wires is shown in Table 102-2. This tells howmuch
resistanceiscontributedbyeverymeterofwire.
Table102-2
350
WhyItWorks
Foragivenwiresize,resistanceisproportionaltothematerial’sresistivity,accordingtotheequation:
R=ρL/AwhereRisresistanceinohms
ρistheresistivityinohm-cm(ρistheGreekletter“rho”)Lislengthincentimeters
Aiscross-sectionalareaincentimeters.
OtherThingstoTry
Alessprecise,butpossiblymorefun,approachtothisexperiment istousewirescutfromfooditems,suchaspicklesor
fruit,orbyformingwiresfromPlayDough.
Thewirecanbeslicedinsectionsasitismeasuredtoshortenitslength.Thisapproachmayrequiretheuseoftwometers
becausetheohmmetermaynotbestable.
Thiscanbetakenastepfurtherbycomparingtheresistancetotheresistivity.Youcangettheresistivitybymultiplyingthe
resistancebythelengthofthewire(incm)andtheareaofthewire(incm2).Youcangettheareaofthewirefromusinga
measuredorlooked-upvalueforthewirediameterandusingtheequation:
A=πr2
whereristheradiusofthewire.
ThePoint
Resistanceisameasureofhowdifficultitisforagivenvoltagetoforceelectronsthroughaconductor.Itdoesn’tmatterhow
bigorsmallthepieceofconductor.Allthatmattersistheoveralleffectithasintheelectricalcircuit.
On theother hand, resistivity is ameasure of how effective a particularmaterial is in impeding the flow of electrons.
Resistivityisthesameforanyparticularmaterial.
Resistancecombinestheeffectofthematerial’sresistivity,aswellasitslengthandcross-section.
351
Project103
Storingcharge.Capacitors.
TheIdea
Acapacitor isanelectroniccomponent thatcanstoreanelectricalcharge.Unlikeabattery thatstoreselectricalcharge
throughchemical reactions, thecapacitorholdselectronsonconductiveplatesseparatedbyan insulator.Capacitorsare
present in numerous electronic circuits. They are also gaining attention recently as a possible means of supplementing
batteriesinelectriccars.Thisexperimentexploreshowcapacitorscanbechargedanddischarged.
WhatYouNeed
1000μF(micro-Farad)capacitor50kΩ(kilo-Ohm)resistor(noteothercapacitor/resistorcombinationsthatcanworkarelistedinTable103-1)DCvoltmeter(ormultimeterconfiguredasavoltmeter)
10-voltDCpowersupply
DCammeter(with0–1.0mArange)
3knifeswitches(SW1,SW2,andSW3)
jumperwire
stopwatch
2LEDs
Method
Charging
1.SetupthecircuitshowninFigure103-1.Payattentiontothepositiveandnegativepolaritymarkings,especiallyifyour
capacitorhasadesignatedpositiveside(somedoandsomedon’t).Startwithallswitchesopen.
2.CloseSW2.LeaveopenSW3.
3.CloseSW1andstartthetimer.
352
Figure103-1Circuitforstudyingcapacitors.
4.RecordthecurrentinmAeveryfiveseconds(thisiseasierwithpartners).Ifyoumissareading,keepgoingandcatch
the next five-second interval. Keep going until the current becomes too small to read. If other capacitor/resistor
combinationsareused,adifferenttimeintervalthanfivesecondsmaybemoreappropriate.
Discharging
1. Whenthechargingpartiscomplete,openalltheswitches.
2. CloseSW1andleaveSW2open.
3. CloseSW3andstartthetimer.
4. Asbefore,recordthecurrentinfive-secondintervals.
ExpectedResults
With SW2 closed, the capacitor will charge. LED2 will light, but slowly fades as the voltage builds and the current flow
decreases.For the10kΩ resistorand the1000μFcapacitorgiven in theparts list, thechargingwillbeabout two-thirdscompletein50seconds,asshowninFigure103-2.
WithSW3closed,thecapacitorwilldischargeasindicatedinFigure103-3.After50secondsthevoltagewillhavedropped
from10voltstoaround3.7volts.LED3willlightandwillslowlyfadeasthecapacitordischarges.
353
Figure103-2Capacitorvoltageversustimefora1000μFcapacitorchargingthrough10kΩand50kΩresistors.
Figure103-3Capacitorvoltageversustimefora1000μFcapacitordischargingthrough10kΩand50kΩresistors.Ingeneral,thetimetochargeordischargetwo-thirdsofcapacityischaracterizedbythetimeconstant.ForacapacitorC
(inFarads)andaresistorR(inohms),thetimeconstant,τ(inseconds),isgivenbyτ=RC.Thetimeconstantrepresentsthetimewherethecurrentduringchargingor thevoltageduringdischarginghasdecreasedbyabout two-thirds.Thefollowing
combinations of resistor and capacitor (Table 103-1) give a reasonable time constant of 30 seconds, which gives
measurableresultsinthisexperiment.
Table103-1
354
WhyItWorks
ThecurrentforachargingcapacitorisgivenbyI=Ioe−t/RC
ThevoltageforachargingcapacitorisgivenbyV=Vo(1–e−t/RC)
ThecurrentforadischargingcapacitorisgivenbyI=Ioe−t/RC
ThevoltageforadischargingcapacitorisgivenbyV=Voe−t/RC
Whent=thetimeconstant,RC,thene−t/RC=e−1=0.37.Thismeanadischargingcapacitorhasdroppedtoaboutone-
thirdofitsoriginalvalueorhasdischargedabouttwo-thirds.
OtherThingstoTry
Ifyouhaveotherresistorsandcapacitorsavailable,try(small)increasesordecreasesinvalues,andthendeterminehowit
affects the time to charge and discharge. The previous Table 103-1 gives combinations that result in reasonable time
constantsandservesasagoodstartingpoint.Adjustyourmeasurementintervalasneeded.
Usea current and voltage sensor that displays theseparametersasa functionof timeona computer. A combination
voltage/current sensor (part number PS-2115) is available from PASCO that displays both parameters simultaneously in
DataStudiosoftware.
Makeagraphof voltage (orcurrent) versus time for yourdischargedatawith voltageona linearscaleand timeona
logarithmicscale.UseanexponentialcurvefittoanExcelscatterplottofindtheargumentoftheexponent.Comparethat
with–1/RC.
ThePoint
A capacitor is a device that stores electrical energy. The rate of charging and discharging depends on the size of the
capacitorandtheresistorit ischargingordischargingthrough.Thebiggerthecapacitorandtheresistor,thelongerthese
processestake.Thecharginganddischargingisanexponentialfunctionoftimethatapproachesasaturationvalue.
355
Project104
Isthemagneticforcemorepowerfulthangravity?
TheIdea
Inthisexperiment,youuseamagneticfieldtodefygravityandholdamagneticobjectsuspendedintheair.Youalsoexplore
theeffectivenessofvariousmaterialsinshieldingtheeffectsofthemagneticfield.
WhatYouNeed
powerfulpermanentmagnet
ringstandwithclamp
paperclip
12inchesof(lowmass)string
materialstotestasashield:glass,paper,copper
pieceoftape
Method
1.Securethemagnettotheringstand,sothemostpowerfulmagneticfieldisdirecteddownward.
2.Tiethestringtothepaperclip.
3.Bringthepaperclipneartheoverheadmagnet.Itshouldbecloseenoughforthemagneticfieldtoexertaforceon
theclip,asshowninFigure104-1.
4.Tapetheotherendofthestringtothetable.Usingtapeenablesyoutoeasilymakeslightadjustmentsinthestring
length.
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Figure104-1PhotobyS.Grabowski.
5.Atthispoint,ifyouaregoingtoshowthistosomeone,thiswouldbeagoodpointtohavethemcomeintotheroom.
6.Observewhathappenswhenyoubringthepaperclipcloser,andthenfurtherfromthemagnet.
7.Tryblockingthemagneticfieldbyusinganyofthefollowingpotentialshieldingmaterials:glass,paper,copper,iron.
ExpectedResults
Thepaperclipappearstodefygravityandwillbeheldsuspendedabovethetable.Dependingonthestrengthofthemagnet,
agapofafewmillimeterscanbeestablishedbetweenthepaperclipandthemagnet.
Themagneticfieldcanbeshowntopenetratethroughmaterials,suchasglass,paper,wood,orcopper.SeeFigures104-
2and104-3.
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Figure104-2Doesamagneticfieldpassthroughaconductor?Thisshouldleavelittledoubt.PhotobyS.Grabowski.
Figure104-3Doesamagneticfieldpassthroughaninsulator?PhotobyS.Grabowski.
WhyItWorks
358
Theforceexertedbythemagnetisgreaterthantheforceofgravity.
OtherThingstoTry
Useaverysensitivespringscaleoraforcegaugetomeasurethemagneticforceexertedonthepaperclip.
ThePoint
Magneticfieldsexertaforceonmagneticobjects.Thisforcedecreaseswithdistance.Themagneticfieldpenetratesboth
electricalinsulatorsandconductors.
359
Project105
Magneticlevitationusinginduction.Electromagneticringtosser.
TheIdea
Thisisafundemowithsomewhatsurprisingresults.Youwilluseapowerfulmagneticfieldtoexertaforceonamaterialthat
is not normally magnetic. You will generate a circulating current using electromagnetic induction. The result is that the
magneticrepulsioncausesametalobjecttobeforcefullythrownintotheair.
WhatYouNeed
ringlauncherapparatus(ElihuThomsonapparatus).PicturedinFigure105-1isPASCOEM-8661.
coppercollar
aluminumring
splitaluminumring
copperring
Figure105-1CourtesyPASCO.
leadring
coilofinsulatedwireconnectedinserieswithalow-wattagelightbulb
ACvoltmeter(ormultimeterconfiguredasanACvoltmeter)
tongs
optional:Pyrexbowlwithliquidnitrogen
Method
1. Safety:Allwiringtothelaunchershouldbeappropriatelyenclosedandinsulatedtoavoidapotentialshockhazard.
Without giving away the results of this experiment yet, it should come as no surprise thatmetal objects will be
launched, sometimes at significant velocities.Make sure no one and nothing of value can be hit by flying rings.
Cautionshouldbeexercisedwhenworkingwithlow-temperaturerings.Avoidconstraininganyofthecollarsforany
prolongedperiod,whichcouldresult inelevatedtemperaturesandburninghazard.Thecurrentshouldflowthrough
thecoilofthelauncherforalimitedtime.Becarefultoavoidoverheatingthecoilbyflowingcurrentforanexcessive
360
time.
2. Slidethealuminumringovertheironcoreoftheringlauncherapparatusandslideindownoverthecoil.
3. Activatethelaunchswitchforafewsecondstoapply120Valternatingcurrenttothecoil.
4. Repeatwiththeotherringsandcollars.
5. ConnectanACvoltmeteracrossthetwosidesofthesplitringtomeasurethecurrentwhilethecurrentisflowingin
thecoreofthelauncher.Similarly,putacoilofwirearoundthecore.ComparetheACvoltagedevelopedinone,two,
ormultiplecoilsofwire.
6. Placethecoilofwireattachedtothelightbulboverthelaunchercoilandapplycurrenttothelauncher,asshownin
Figure105-2.
7. Holdthecopperringoverthecollarforafewsecondswiththelauncherturnedonandfeelthecollar’stemperature.
(Becarefulnottoholdittoolongoritmaygettoohottohandle.)
8. For this next part, make sure the ceiling is high enough. Immerse the rings in liquid nitrogen and activate the
launcher.
ExpectedResults
Closedconductiveringsandcollarswillbethrowverticallybytheringtosser,asshowninFigure105-3.Thecopperring is
thrownthehighest,followedbyaluminum.Thecoppercollarisraised,butitismoresluggish.Thesplitringsarenotlifted.An
ACvoltageofafewmillivoltscanbemeasuredacrossthesplitring.Aringthatishelddownwhilethecurrentisflowingin
thecoilwillheatupsignificantly.Theringscooled in liquidnitrogenaremuchmoreresponsethantheir roomtemperature
counterparts.Thecooledcopperringwillflythehighestandcanlikelydamageastandard8to10foot(2meter)ceiling.The
lightbulbwillbeilluminatedwhenheldoverthecurrent-carryingcoil.
Figure105-2Inducedcurrentcauseslighttobeilluminated.CourtesyPASCO.
WhyItWorks
This is a demonstration of electromagnetic induction based on an apparatus developed by the prolific inventor Elihu
Thomson.Aconstantlychangingmagneticfieldproducedbytheappliedalternatingcurrentcausesanopposingcurrent,and
361
voltageintheringsandcollars.ThegenerationofanopposingcurrentisanillustrationofLenz’slaw.
Figure105-3Ringtosser.CourtesyPASCO.
Thisinducedcurrentgivesrisetoamagneticfieldorientedtorepelagainstthefieldthatformsintheringlaunchercoils.
Therepulsionbetweenthesemagneticfieldscausestheringtobetossed.
Becausecopperisabetterconductorthanaluminumorlead,morecurrentflowsandtheringistossedhigher.Thecollars
areheavierandarenotthrownasfar.Thesplitringsdonotprovideacompletecurrentpath,sotheinducedcurrentdoesnot
flowinacompletecircuit.Thebulblightsbecauseacurrentisinducedinthecoilconnectedtothebulb.Theliquidnitrogen
reduces the resistance of the rings.With lower resistance,more current can flow. The higher current creates a stronger
magneticfield,whichlaunchestheringhigher.
OtherThingstoTry
ThecurrentgeneratedinthesplitringcanbemeasuredbyattachinganACvoltmeteroramultimeterconfiguredasanAC
voltmeter.
ThePoint
Acurrentflowinginaconductorproducesamagneticfield.Achangingmagneticfieldcaninduceacurrentinaconductor.
Theinducedcurrentcanthengenerateacurrent.ThesecurrentsaccordingtoLenz’slawwillalwaysopposeeachother.
362
Project106
Magneticlevitationusingsuperconductivity.TheMeissnereffect.
TheIdea
Typically,whenthetemperatureofaconductorisreduced,theresistanceisalsolowered.Wesawinthepreviousexperiment
howamagnetic field cancauseanobject to levitate. For somematerials, ifwecontinue to lower their temperature, the
resistancecontinues todropuntil itdisappearsentirely.When thishappens,wehavewhat isknownasasuperconductor.
Superconductorshaveamazingpropertiesandarebeginningtofindtheirwayintopracticalapplications.
WhatYouNeed
liquidnitrogen
thinpieceofcork(about¼inchthick)
Styrofoamdish(formedbycuttingaStyrofoamcup;tThetotalheightshouldbeabout2mm)
cube-shapedneodymiummagnet(seeFigure106-1)
plastictongs
superconductordiskconsistingofYBa2Cu3O7ceramic(seeFigure106-2)
optional:videocameraorPCcamconnectedtoaTVmonitor(toshowthistoalargergroup)
optional:thermocouple,voltmeter,DCpowersupply,superconductorcoil,superconductorsamplewithmeasurement
leadsattached
Figure106-1Neodymiummagnetcube.
Figure106-2YBa2Cu3OO7ceramicdisk.
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Method
1. PlacetheYBa2Cu3O7ceramicdiskonthetableandsettheneodymiummagnetontopof it toshownorepulsive
forceisoccurringatroomtemperature.
2. PlacethecorkinthecenteroftheStyrofoamdish.
3. PlacetheblackYBa2Cu3O7ceramicdiskonthepieceofcork.
4. CarefullypourliquidnitrogenintotheStyrofoamdishtopartiallycovertheceramicdisk.
5. Theliquidnitrogenwillboilforashortwhile.Whentheboilingsubsides,thediskhassufficientlycooled,asshownin
Figure106-3.
6. Usingtheplastictongs,pickuptheneodymiummagnet.Carefullyplacethemagnetovertheceramicdisk.
7. Whenthemagnetisobservedtohoverovertheceramicdisk,usethetongstogiveitaspin,asshowninFigure106-
4.
8. Becausethepartsinthisprojectaresmall,iftheintentionistoshowthistoalargergroup,avideocameraorPC
camcanbeusedtodisplaythisonamonitor.
ExpectedResults
Themagnet is held suspendedabove the ceramic superconductingmaterial. If themagnet is spun, it continues spinning
withoutnoticeableresistance.Eventually,theceramicwillwarmupandthesuperconductingeffectwillfade.
Figure106-3SuperconductingdiskbeingbroughtbelowCurietemperature.
364
Figure106-4Magneticcubespinningabovesuperconductingceramicdisk.
WhyItWorks
Normally,attemperaturesabovewhat isknownasthecriticaltemperatureofamaterial, thematerialhassomeelectrical
resistance. This means a voltage must be applied across the material to push the electrons through the material. The
voltageisneededtodrivetheelectronsthroughwhatislikeanatomicobstaclecourse,consistingofotheratomsvibrating
randomly.As(normalnonsuperconducting)resistorscooldown,theirresistancegetslower.However,superconductorshave
zeroresistance.Notjustlower,butzero!Thismeanstheelectronsnolongerneedavoltagetopushthem.Thisalsomeans
theelectronscanmoveaboutfreelythroughoutthesuperconductorwithoutenergylosses.
Differentmaterialsbecomesuperconductingatcharacteristictemperaturesthatdifferforeachmaterial,asshowninthe
followingtable:
Noticethatall themetals listedmustbecooledtobelow4.2K.Toaccomplishthis, it isnecessarytouseliquidhelium,
whichremainsliquiduptothattemperature,asshowninthefollowingtable. In1987,abreakthroughwasachievedbythe
discoverythatYBa2Cu3O7ceramicbecamesuperconductingaround90K(andbelow),whichcanbeachievedbyimmersion
inliquidnitrogen.Thisisfarlessexpensiveandeasiertoworkwiththanliquidhelium.Scientistsarepursuingmaterialsthat
canbesuperconductingattemperaturesclosertoroomtemperature,whichcouldopenthedoortoitsapplicationinmany
newareas.
TheactualdetailsofhowsuperconductivityworkswilltakeusfurtherintoquantummechanicsthanIthinkmostreaders
would care to go. The theory known as BCS theory was named after three American physicists: Bardeen, Cooper, and
Schrieffer. (Very) basically, theBCStheory describes how electrons are able tomore easily navigate through the crystal
latticeofmatter in amanner that is somewhat analogous toa racecar encountering lessaerodynamic resistanceas it
closely follows another car in front of it. As the critical temperature is reached, the electrons are able to go through a
materialby“tunneling”rightthroughanelectricalfieldinitsway.Asaresult,superconductorshavezeroresistance.Ifdigital
electronicswerebasedonsuperconductorstheywouldfunctiontentimesfasterthanstandardsemiconductorelectronics.
Magnetic fields can pass through and be present in most materials, including superconductors above their critical
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temperature.However,asasuperconductingmaterial isbroughtbelowitscriticaltemperature,themagneticfield isforced
out in a process known as the Meissner effect, which serves as the basis for the effect we saw here. To enable the
magnetic field to be pushed out of the superconductor, it becomes necessary for a counter current to flow in the
superconductor.Withnoresistance,electricalcurrentsareinducedinthesuperconductingceramic,which,inturn,createsa
magneticfieldthatrepelsagainstthatofthepermanentmagnet.
Superconductorsarebeinglookedattoaddresssomeofthefollowingchallengesintechnology:
1. Muchoftheelectricalpowertransmittedthroughouttheworld’selectricalpowergridisdissipatedasresistiveheat
losses. If superconductors could be used for power transmission and generation, some of the losses could be
reduced.
2. Magneticresonanceimaging(MRI)equipmentusesextremelypowerfulmagnetstohelpcreatedetailed imagesof
thebody.Superconductorsallowstrongermagnetstobebuilt.
3. Maglev trains use superconductors to help produce powerful magnetic fields that raise trains above the track,
enormouslyeliminatingfriction.
4. Theextremelypowerfulmagnetsusedtoguidebeamsofsubatomicparticlesinresearchfacilities(suchasCERN)
usesuperconductors.
5. Superconductorsholdthepromiseofenablingfasterprocessingofdigitalinformationincomputers.
OtherThingstoTry
Someadditionalexperimentsinclude:
Measurethecriticaltemperature
Attach a thermocouple to the superconductor tomeasure the critical temperature. This is the temperature at which the
magnetfirstbeginstolevitateaboutthecooledceramicdisk.Thethermocoupleshouldnotconstrainthemagnetfrombeing
liftedandshouldnotbeimmersedintheliquidnitrogenoritwillunderstatethecriticaltemperature.
Resistanceversustemperaturecurve
BasicallytodothisyouwilluseOhm’slaw(resistance=voltage/current)tomeasuretheresistanceofthesuperconductoras
itstemperaturechanges.Itiseasiertomeasurethesechangesasthesuperconductorwarmsfromtheinitialimmersioninto
liquidnitrogenuntilitpassesthroughthecriticaltemperature.Twowiresforcurrentandtwowiresforvoltageareattachedto
the superconductor. This is called a four-point probe, which eliminates the effect of contact resistance that would be
encounteredifbothvoltageandcurrentweremeasuredusingasinglesetofcontacts.Thecontactscanbeformedusing
very high gauge (thin) silver or copper wire and attaching them to the superconductor using silver paint. A sample with
contactsattachedcanbeobtainedaspartofanexperimentkitbysuperconductorexperimentsuppliers.
ThePoint
Superconductors arematerials that have no electrical resistancewhen they are brought below their critical temperature.
SuperconductorscanexertofforceonapermanentmagnetasaresultoftheMeissnereffect,inwhichacirculatingcurrent
is established in response to exclusion of the magnetic field. This current generates a magnetic field that repels the
permanentmagnet. Superconductors have significant technological applications, includingMRIs,maglev trains, subatomic
particleresearch,andultrafastdigitalelectronics.
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Project107
Movingelectronsproduceamagneticfield.Oersted’sexperiment.Themagneticfieldof
acurrent-carryingwire.
TheIdea
Whatcausesamagneticfield?In1820,HansOersteddiscoveredthatelectricityflowinginawirecausedacompassneedle
tobedeflected.Thisestablishedoneoftheearliestconnectionsbetweenelectricityandmagnetism.Thisinvestigationre-
createssomeofthethingsOersteddid.
WhatYouNeed
DCpowersupplyorbattery
aboutameter(afewfeet)ofinsulatedwire
compass,preferablyonemountedonapivot
ringstandorothersupportforthewire
optional:ammeter
optional:knifeswitchtocompletethecircuit.Youcanactivatethecircuitsimplybycompletingthefinalconnection
tothepowersupply.
Method
1.Connectoneendofthewiretothepositiveterminalofthepowersupply(orbattery).
2.Routethewirethroughthesupport,soalengthofabout0.25m(oraboutafoot)isrunningupanddown.Thecurrent
flowingfromthepositiveterminalshouldflowupthroughthewire.
3.Theothersideofthewireshouldeithergotooneoftheterminalsoftheswitchorbeplacedreadytoattachtothe
negativeterminal.Ifyouareusingtheknifeswitch,keeptheswitchintheopenpositionandattachtheotherterminal
tothenegativeterminal.
4.Makesurenoothermagnetsareintheimmediatevicinityoftheapparatus.
5.Placethecompassclosetothewire.(ThecompasswillpointinthedirectionoftheEarth’smagneticfield.Imaginea
circleformedaroundthewirewhenviewedfromabove.Toexperiencetheforcegeneratedbythemagneticfieldof
thewire,thecompassneedleshouldnotbeatatangenttothatcircle,butitshouldformsomeangletothetangentat
thatpoint.ThisisshowninFigure107-1.)
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Figure107-1Measuringtheeffectofcurrentonamagnet.
6.Completethecircuit(eitherbyclosingtheswitchorbyattachingthewiretothenegativeterminal).Ifyouareusingan
adjustablepowersupply,itmaybehelpfultoputanammeterinserieswiththepowersupplytomakesurethecurrent
flowdoesn’tgomuchabove1amp.Thiscanalsoletyouquantifytheeffectofincreasingcurrentonthestrengthof
thegeneratedmagneticfield.
ExpectedResults
Withacurrent flowing through thewire, thecompass isdeflected.Themagnetic fielddeflects thecompassneedle in the
directionofthetangentofthecircle,asshowninFigure107-1.
WhyItWorks
Amagneticfieldisproducedbymovingelectriccharges.
OtherThingstoTry
Measuretheeffectofincreasingthecurrentandmovingthecompassfurtherfromthewireontheresponseofthecompass
needle.
ThePoint
Anelectricalcurrentflowinginaconductorproducesamagneticfield.
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Project108
Faraday’sexperiment.Currentgeneratedbyamagnet.
TheIdea
MichaelFaradaydiscoveredthatamovingmagneticfieldcausesanelectricalcurrenttoflowinawire.Mostoftheelectricity
generatedthroughouttheworldtodayisbaseduponthishistoricdiscovery.Powerplantsroutinelyconvertmechanicalenergy
intoelectricalenergy.Thisexperimentexploresthephysicalprinciplethatmakesthispossible.
WhatYouNeed
barmagnet
coilof insulatedwire—themorecoils, themorepronounced theeffect.Thin “magnet”wire insulatedwithclearor
coloredenamelcanworkfine.
galvanometer(averysensitiveammeter)
Method
1. Wraptheinsulatedwireinacoilaroundacylindricalcardboardform.Usethesmallestdiameterthatwillenablethe
barmagnettopassthrough.Prewoundcoilsareavailable.
2. Connectthetwoendsofthewiretothepositiveandnegativeterminalsofthegalvanometer.
3. Predictwhatyouthinkwillhappenifthemagneticisplacedinsidethecoil.Tryitandobservetheresponseonthe
galvanometer.
4. Movethemagnetbackandforthinthecoil.Observethedeflectiononthegalvanometer.
5. Movethemagnetbackandforthoutsidethecoilandobservetheeffect.Whathappensifthecoilmoveswhilethe
magnetisstationary?
6. If it ispossibletoincreaseordecreasethenumberofcoils,youcanevaluateitseffectontheamountofcurrent
thatcanbegenerated.
7. Basedonyourobservations,describehowamagnetcanproduceanelectriccurrent.
TheapparatusisshowninFigure108-1.
ExpectedResults
Amagnetproducesacurrentinawireonlywhenthemagnetismoving.Astationarymagnetwillnotgenerateacurrent.
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Figure108-1Amagnetmovingthroughacoilofwire.
Thefastertherelativemotionbetweenthemagnetandthecoil,thegreaterthecurrent.Thelargerthenumberofcoils—
withallelseequal—thegreaterthecurrent.Amorepowerfulmagnetproducesagreatercurrent.
WhyItWorks
Amagneticfield itselfdoesnotproduceanelectriccurrent.Achangingmagneticfield isrequiredtoproduceanelectrical
current.ThisisaddressedinmathematicaldetailbyMaxwell’slawsforthosewhowanttopursueitfurther.
OtherThingstoTry
Aniceway todisplay these results is toattach thecoil toavoltagesensoranduse this togenerateagraphofvoltage
versustime.Movingthemagnetbackandforthinthecoilresultsinanalternatingcurrent(AC).Ifyouhangthemagnetona
springandhaveitoscillateupanddowninthecoil,youwillhaveasimplemodelofanACgenerator.
Agoodfollow-upistoinvestigateamodelelectricalgenerator,whichcanalsogenerateasimilarACcurrent.
ThePoint
Thesignificanceofthisprojectistoshowhowmechanicalenergyisconvertedintoelectricalenergy.Thekeypartsofan
electricalgeneratorareamagnetandacoilofwire.Electricityflowswhenthecoilandmagnetmoverelativetoeachother.
370
Project109
Ifcopperisnotmagnetic,howcanitaffectafallingmagnet?Lenz’slaw.
TheIdea
Whenamagnetmovesnearaconductor,electricalcurrentscanbeproducedintheconductor.Whencurrentscirculateina
pieceofbulkmaterial, ratherthanawirethatformsacompletecircuit, thecurrentsarecallededdycurrents.Theseeddy
currentsaremorelikewaterswirlinginatidepoolratherthanflowinginastream.Eddycurrentscanreducetheefficiencyof
electrical devices, such as transformers, because the circulating current results in a loss of power. Eddy currents have
severaluses,which includemagneticdampingofsensitivemeters,andtheyareused inmagneticbrakingforrapidtransit
trains.ThisprojectexploresanaspectofeddycurrentscalledLenz’slaw.
WhatYouNeed
3neodymiumdiscmagnets
copperpipewhosediameterisslightlylargerthanthemagnet
plasticpipeofsimilardimensions
Method
1. Holdbothpipesvertically.
2. Checkthemagneticattractionbetweenthemagnetsandeachofthepipes.
3. Positionthemagnetovertheopentopofeachofthepipes.
4. Dropthemagnetthroughthepipesatthesametime.
5. Comparehowfastthemagnetsfallthrougheachofthepipes,asshowninFigures109-1and109-2.
ExpectedResults
Themagnetfallsthroughtheplasticpipefasterthanthroughthecopperpipe.
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Figure109-2Themagnetgoingthroughthenon-conductivetube(ontheleft)emergesfirst.
WhyItWorks
Whenamagnetmoveswithrespecttoaconductor(suchascopper),itcreates(induces)anelectriccurrentintheconductor.
Thiscurrent,inturn,producesamagneticfield.AccordingtoLenz’slaw,thismagneticfieldwillbealignedinsuchawaythat
it is pointed in the opposite direction as themagnetic field that originally produced it. This results in an attractive force
between themagnetand thecopperpipe inwhichacurrent is inducedby the fallingmagnet.Because theplastic is not
conductive,nomagneticfieldisproducedtocreatetheLenzeffect.
OtherThingstoTry
Oneotherway todo this is to usediscmagnetswith holes in their centers.Then, themagnetsareplacedover copper,
plastic,andironrodswhosediameterisslightlysmallerthantheinnerdiameteroftheholeinthemagnet.
Analuminumdisc isnotmagnetic. If thedisc isspunandastrongmagnet isbroughtnear,eddycurrentsareproduced
whoseeffect istoslowthespinningdisc.This isknownasmagneticbraking,and it isshowninFigures109-3andFigure
109-4.
ThePoint
Lenz’slawdescribeshoweddycurrentsareformedinanonmagneticmaterial.Theseeddycurrentsinteractwithamagnetin
awaythatopposestheeffectofthatmagneticfield.
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Figure109-3Aneodymiummagnetisbroughtnearaspinningnon-conductingplate.
Figure109-4Magneticbraking(andnotfriction)stopstheplate.
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Project110
Effectofamagnetonanelectronbeam.Theright-handruleformagneticforce.
TheIdea
OneofthegreataccomplishmentsofphysicsinthetwentiethcenturywasthediscoveryoftheelectronbyJ.J.Thomson.In
thisproject,yourevisitsomeofthestepsthatledThomsontohisdiscovery.
WhatYouNeed
cathode ray tube (CRT)—this can be any tube-type video monitor (TV or computer). If you have access to an
oscilloscope,youcanusethat.Liquidcrystaldisplay(LCD)orplasmascreendisplaysdonothaveelectronbeams
andwill notwork here. A stand-aloneCRT (such as aCrooke’s tube available from scientific supply companies
excitedbyaninductioncoil)canbeused.
strongmagnet
yourrighthand
miniPost-itnotes
Method
1.CAUTION:Ifyouareusingahigh-voltageinductioncoiltoproducetheelectronbeamintheCRT,beverycarefulnot
totouchtheexposedterminalswhileitisoperating.Becertainyouexactlyfollowthemanufacturer’s instructionsfor
usingthisequipment.
2.Careful:ItistypicallynotrecommendedtoexposeTVorcomputerscreenstomagneticfields.Excessiveorprolonged
exposurecancauseunintendeddamage.
3.TurnontheCRT.
4.Makeanyadjustmentsneededtofocustheelectronbeam.
–Foranoscilloscope,disabletheverticalandhorizontalsweeps,leavingasingledotatthefocus
–Withthecomputer,findapointoffocus,includingtextoraperiodonthescreen
–WiththeTV,findastationaryimagetofocuson
5.Identifythenorthpoleofyourelectronmagnet.
6.Bringthemagnetnear(butnottouching)theCRTscreen.
7.Observetheeffectofthemagnetontheelectronbeam.
ExpectedResults
Themagneticfieldcausestheelectronbeamtobend.
Ifthebeamismovingtoyourrightandthemagneticfield,northtosouth, ispointedinwardacrossthetube,theelectron
beamwillbebentdown.SeeFigure110-1.(Notethatsinceelectronshaveanegativecharge,thisistheoppositedirection
specifiedbytheright-handruleforpositivecharges.)
Figure110-2showsanelectronbeammovingfromlefttorightinacathoderaytube.Intheabsenceofamagneticfield,
thebeamishorizontal.
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Figure110-1Effectofamagneticfieldonanelectronbeam.
Figure110-2Cathoderaytube.PhotobyS.Grabowski.
If a magnetic field is placed across the beam (with the north pole indicated by tape in front), the beam is deflected
downwardasshown(bySteveGrabowski)inFigure110-3.
Ifthemagneticfieldisreversed(sothatthenorthpoleisintheback)thebeamisdeflectedupwardasshowninFigure
110-4.
WhyItWorks
Amagnetic field does not exert a force on a stationary electron. However, amagnetic field does producea force on a
movingelectron.Theelectron’smotion,themagneticfield,andtheforceareallatrightanglestoeachother.
Figure110-3Cathoderaytubewithmagneticfieldfronttoback.
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Figure110-4Cathoderaytubewithmagneticfieldbacktofront.PhotobyS.Grabowski.
OtherThingstoTry
Thedirectionoftheforceontheelectronfollowstheright-handrule.Ifyourindexfingerpointsinthedirectionofthebeam,
andyourotherthreefingerspointinthedirectionofthemagneticfield(northtosouth),thenyourthumbshowsthedirection
ofaforceonapositiveparticle (or theoppositedirectionforanegativeparticle,suchasanelectron).Youcan label the
fingersofyourrighthandwithPost-itnotestohelpkeeptrackoftheelectronmotion,thefield,andtheresultingforce.(This
iswhyPost-itnotesareontheWhatYouNeedlist.)
Youcantakethisastepfurther.Thomsonappliedanelectricfieldtodeflecttheelectronbeambyameasurableamount.
Then,byapplyingamagneticfieldatarightangletotheelectricfield,Thomsonwasabletodeterminethechargetothe
massratiooftheelectron.Thiscanbeperformedusingcommerciallyavailableequipment.
ThePoint
Propertiesoftheelectroncanbedeterminedbyobservingitsbehaviorinelectricandmagneticfields.
Theelectronisnegativelycharged.
Theforceproducedbyamagneticfieldonamovingbeamofelectronscanbedescribedbytheright-handrule, inwhich
thethumbindicatesthedirectionoftheforce,theindexfingerindicatesthedirectionofthemotionoftheelectrons,andthe
restofthefingersindicatethedirectionofthemagneticfield.
Carefulanalysisofelectricandmagneticfieldsonanelectronbeamdeterminesthechargetomassratiooftheelectron.
377
Project111
Whatistheshapeofamagneticfield?
TheIdea
Youcannotseeamagneticfield.Butyoucandefinetheshapeofthefieldbymeasuringitseffects.Inthisproject,youtrace
theshapeofthemagneticfieldcreatedbyvariousarrangementsofpermanentmagnets.
WhatYouNeed
2barmagnets
U-magnet
severalsheetsofpaper
ironfilings
Method
1. Laythebarmagnetonthetable.
2. Placethesheetofpaperoverthemagnet.
3. Tracetheoutlineofthemagnet,showingthenorthandsouthpoles.
4. Evenlysprinkleironfilingsoverthepaper.Distributethefilingssotheshapeofthepatternonallsidesofthemagnet
isdelineatedbytheironfilings.
5. Repeatwiththefollowingcases.
6. Theironfilingscanbeeasilypouredbackintothecontainer.Iftheycomeintodirectcontactwiththemagnet,itis
muchhardertocleanup.
–Twonorthpolesfacingeachother
–Anorthandasouthpolefacingeachother
–Ahorseshoemagnet
–Anyothershape—yourchoice
ExpectedResults
Theelectricfieldsurroundingabarmagnetfollowslinesthatgofromthenorthpoletothesouthpole,asshowninFigure
111-1.
Withanorthpoledirectlyoppositeasouthpole,thelinesofforcearedirectedfromthenorthpoletothesouthpole,as
showninFigure111-2.
Withtwonorthpolesfacingeachother,theelectricfieldisdirectedawayfromeachofthepoles.Linesofforcecanbe
seendirectedperpendiculartoeachofthetwomagnets,asshowninFigure111-3.
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Figure111-1Barmagnet.
Figure111-2Northpoleoppositesouthpole.
WhyItWorks
Themagneticfieldcausesferromagneticmaterials,suchasironfilings,toalignwiththefieldlines.
OtherThingstoTry
Ahighertechapproachwouldbetouseamagneticfieldsensortomapouttheshapeofthesemagneticfields.
Figure111-3Northpoleoppositeanothernorthpole.
ThePoint
Magneticfieldsshowtheforceamagnetwouldexertonthenorthpoleofanothermagnet.Magneticfieldspointfromnorth
tosouth.Magneticfieldspointawayfromnorthpoles(oppositesrepel)andtowardsouthpoles(likesattract).
379
Project112
Whathappenstoacurrent-carryingwireinamagneticfield?
TheIdea
Theheartandsoulofanelectricalmotorismovementcreatedwhenmagnetsrepeleachother.ThediscoverybyMichael
Faradaythataforceisproducedwhencurrentflowsthroughamagneticfieldwasagroundbreakingdiscovery,whichpaved
thewayfortheeventualdevelopmentoftheelectricmotor.
WhatYouNeed
powerfulhorseshoemagnet
DCvoltagesource,suchasanadjustablepowersupply,amotorcyclebattery,oracarbattery
about1meter(afewfeet)ofinsulatedwire
ringstandwithclampstopositionthewire
Method
1. Setthehorseshoemagnetonthetable.
2. Positionthewiremidwaybetweenthenorthandsouthpolesofthemagnet.Thewireshouldrunperpendiculartothe
twoendsofthemagnetanditshouldbeabletomove.
3. Attachoneendofthewiretothenegativeterminalofthepowersupply,asshowninFigure112-1.
4. Brieflytouchtheotherendofthewiretothepositiveterminalandobservethewirepassingbetweenthepolesofthe
magnet.Ifyouareusinganadjustablepowersupply,startwithalower-currentoutputsettingandslowlyincreaseit
until thewireresponds.Becausethere isnoresistancebesidesthe littleresistancethewireoffers,ahighcurrent
mayflowthatmaycauseafuseorcircuitbreakertoblow.
ExpectedResults
Withcurrentflowinginthewire,themagnetpushesthewireawayfromthemagnet.
WhyItWorks
Aforceisexertedonamovingcharge(orcurrent)inawiremovingperpendiculartoamagneticfield.
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Figure112-1Forcebetweentwocurrent-carryingwires.
OtherThingstoTry
Repeatthiswithatightcoilofthewireinthemagneticfield.Comparewiththeresponseofanuncoiledwire.
ThePoint
Amagneticfieldexertsaforceonacurrent-carryingwire.Thedirectionofthatforcedependsonthedirectionofcurrentflow
andtheorientationofthemagneticfieldaccordingtotheright-handrule.
381
Project113
Ano-frillsmotor.
TheIdea
Inthisprojectyouwillbuildaverybasicelectricmotor.Thisprojecthasbeenbrokendownintoanumberofstepsforclarity,
buttheoveralldeviceissimple.It’slikeassemblingabarbequegrill—thefirsttimeyoudoitmaytakealittlelonger,butonce
yougettheoverallidea,itgetseasiereachtime.Ittakesjustafewminutestobuild,butitcankeeprunninguntilthebattery
runsout.
WhatYouNeed
CorDcellbattery
ceramicdiscmagnet
1meterofenamel-coated(thin)22AmericanWireGauge(AWG)wire. It ismucheasiertoworkwithredorgreen
coatedenamel,ratherthanclear-coated
2paperclipsorafewinchesofatleast20AWGwire
Figure113-1Partstoassemblea“no-frills”motor.
electricaltape
optional:batteryholder,Styrofoamcup
Method
1. Windabout25–30turnsofthe22gaugewirearoundacylindricalcoilform,suchasaballpointpenorasmallAAA
battery.
2. Leaveafewofinchesofwirefreeateachend.
3. Pull thecoil off the formyouwound itaround.Becarefulandhold thewire, so it doesn’t springoutof shape (it
doesn’thavetobeperfecttowork).
4. Weave each of the ends of the wire around the coil a few times to hold the coil together. This becomes the
armatureofthemotor.Ifyouprefer,youcanalsousetapetohelpkeepthecoiltogether.
5. Theendsofthewireshouldbeplacedinastraightlinetomakeagoodaxle.Itcanhelpifyoudoubleback,sothe
endsectionsconsistofmorethanonethicknessofwire.Italsohelpstooverwraptheendswiththelastsegmentof
wireortape.
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6. Usingautilityknife, removethe insulationfromthetophalfofthe22gaugewireatbothends.Youcanalsouse
sandpapertodothis.Ifthewireiscoatedwithacoloredlayer,youcanseewhentheinsulationhasbeenremoved.If
thewireisclear-coated,youmustbemorecarefulandkeeptrackofwhereyouareremovingtheinsulation.Donot
removetheinsulationfromthebottomhalfofthewire.
7. Whenyoufinish,thesidewiththeinsulationremovedmustremainfacinguponbothends.
8. Makeanarmaturesupportbyfirstformingthepaperclipsintoaloop.Ifyouareusingwire,removeinsulationfrom
eachoftwo1½-inchsectionsofwireandformasmallcircularloopabout1millimeterindiameterinthecenterof
eachwire.Anailcanserveasagoodformtowraptheloop.
9. Bendthewirestoformashapelikeawishbonewiththewireendsseparatedbyafewmillimeters.
10. Thetwoendsofthecoilsshouldeasilyfitintothearmaturesupportsandshouldbeabletoturnfreely.
11. Securethearmaturesupportwirestothebatteryholderwithtape.
12. Establishelectricalcontactbetweenthearmaturesupportsandthepositiveandnegative terminalsof thebattery
holder.Youmayneedtousejumperwirestodothis.
13. Insert the endsof thearmature (coil) into the holes of thearmature supports. Thearmature supports should be
spacedfarenoughapartsothecoilissupportedatbothends.
14. Tapethebatterytothetopofthecuporinsertthebatteryintotheholder.
15. Attachthemagnettothetopofthebatteryholderjustunderneaththecoil.UsetapeorVelcrotodothis.Makesure
thecoilcanstillspineasilyandthatitisjustabovethemagnet.Itmaybenecessarytoraiseorlowerthearmature
supportstoattainthecorrectheightabovethemagnet.
16. Spinthearmaturegentlytogetthemotorstarted.Ifitdoesn’tstartspinning,tryspinningitintheotherdirection.It
willonlyspininonedirection.
Thismaysoundlikealotofsteps,butitisverysimple,asshownbyFigure113-2,whichshowswhatthismotorlookslike
whenitisallassembled.
Figure113-2BasicDCmotor.
ExpectedResults
Themotorshouldkeepturninginonedirection.
If itdoesnotrun,checkallelectricalconnections.Besureonesupporttouchesthenegativeendofthebatteryandthe
othersupporttouchesthepositiveend.Besurethearmaturecanspinfreely.It isessentialthattheinsulationberemoved
fromonlyone-halfoftheturnsandtheuninsulatedsideofthewireisfacingthesamedirection.
WhyItWorks
383
Thebasicconceptofamotoristherepulsionoftwomagneticfields,resultinginarepetitiveturningmotion.Onemagnetisa
permanentmagnet.Theotherisanelectromagnetformedbyacoilofwirethroughwhichanelectricalcurrentisflowing.The
trickisonlytohavethemagneticfieldsrepel,butnotattract.Ifwehadtakentheinsulationoffthetopandbottomsidesof
theenamel-coatedwireused for thecoil, themotorwouldgonomore thanone-half turn,and thenstopas thecoil and
permanentmagnetattractedeachother.By leavingthe insulationonthebottomhalvesof thecoilwires,nocurrent flows
throughthecircuitatatimewhenthemagnetswouldattract.Inourcase,themomentumofthecoilkeepsitrotatinguntilthe
uninsulatedwiresemerge just in time for thepermanentmagnet to repel thecoiland rotate throughanothercycle.Other
motordesignshavewhatiscalledasplitcommutator,whichgoesonestepbetterbychangingthedirectionofthecurrent
flowingthroughthewire,sothemagnetsarealwaysrepulsive.
OtherThingstoTry
Double the spinning power by constructing a split-ring commutator. Try this bymaking the followingmodifications to the
simplemotorconceptpreviouslydescribed:
1. Insulatethetophalfoftheloopofonearmaturesupportandinsulatethebottomhalfoftheotherarmatureloop.
2. Startingwith insulatedenamel-coatedendsofthe22gaugewire, removethe insulationfromthetopononeside
andthebottomontheotherside.
3. Onceyoustartthemotor,thecontactshavebeensetuptomakesurecurrentflowsthroughthecoilatatimeandin
adirectionthatresultsinacontinuousrepulsiveforce.
ThePoint
Amotorconsistsofthefollowingfundamentalcomponentsillustratedinthisproject:Theseincludeapermanentmagnetand
anelectromagnetthatreceivesDCcurrentonlyduringthoseportionsofitscyclewhenitwillberepelledbythepermanent
magnet.
384
Project114
Magneticaccelerator.
TheIdea
This is a simple experiment with a very unexpected outcome. A steel ball is rolling in a track drawn by amagnet. The
seeminglygentleforceproducesapowerfulaccelerationthatpropelstheballathighvelocity.Theresultsarequiteamazing
andprovideaninterestinginsightintothenatureoflinearmomentum,aswellasmagneticfields.
WhatYouNeed
4stainlesssteelballs
1neodeumcylindricalmagnet
tracktoguidethesteelballs(agroovedmountingbracketforcurtainsworkswell,andithastheaddedadvantageof
providingahandyend“bumper”)
Method
1. Placethesteelballsinthetrack.
2. Groupthreeballstogether.
3. Rollthefourthballtowardtheotherthree.
4. Noticewhathappens.(Thisisnotthesurprisingpart,butitestablishesabaselineofexpectation.)
5. Placethreeballsonthetrack.Then,placetheneodymiummagnettotherightofthethreeballs.
6. RollthefourthballfromtherightsideofthemagnetwithaboutthesamespeedastheballinNumber3.
ExpectedResults
Withoutthemagnet,theincomingsteelballstopsandknocksoutanotherball.Thedislodgedballcontinueswiththesame
velocityoftheincomingball.Thisisthefamiliarcaseofconservationofmomentumduringanelasticcollision,asshownin
Figure114-1.
Withthemagnetinplace,asingleballisalsoknockedout,asshowninFigure114-2.However,theballthatisknockedout
surprisinglymovesatturbospeed—muchfasterthanthevelocityoftheincomingball.Themagnetincreasesthevelocityof
the incomingball.Thismuchhighermomentumat the last instant is imparted to theoutgoingball,whichshootsoffata
surprisinglyhigherspeed.
Figure114-1Theincomingballdislodgesoneballthatexitswiththesamevelocityastheincomingball.
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Figure114-2Themagnetdramaticallyincreasesthemomentumoftheballatthelastminute.
WhyItWorks
Inbothcases, linearmomentumisconserved.Withthemagnet, the incomingball isacceleratedandachievesaveryhigh
instantaneousvelocityjustbeforeithitsthemagnet.Conservationofmomentumrequiresthattheoutgoingballmovesatthat
samehighvelocity.
Linearmomentum is always conserved if no force is doing work. In physics, work is force applied over a distance. A
principleofphysicscalledthework-energytheoremstatesthatifaforceisexertedoveradistance,thekineticenergyofan
object(and,asaresult,itsvelocity)changes.Inthiscase,amagneticforceisdoingwork,whichacceleratesthesteelball.
Becausethemagneticforceincreasesastheballapproachesthemagnet,thespeedpicksupatanevengreaterratethan
aconstantforce.
OtherThingstoTry
Repeatwithothercombinationsofballsoneithersideofthemagnet.
ThePoint
Linearmomentumisthesamebeforeandafteracollision.Becausethesteelballisacceleratedrapidlybythemagnet,the
velocityoftheball(anditsmomentum)isveryhighjustbeforethecollision.Conservationoflinearmomentumrequiresthe
velocityoftheballafterthecollisionalsobeveryhigh.
386
Project115
Alternatingcurrent.
TheIdea
Inthissection,youexploresomeofthebasicaspectsofACcurrent.
Theelectricalpowerweget fromabattery iscalleddirectcurrent (DC).A9-voltbatteryproducesavoltageof9volts,
whichdoesn’tchangeuntilthebatteryisusedup.Theelectricitywegetdeliveredfromtheelectricalpowercompanyfrom
thewallsocketisAC(alternatingcurrent).Thisisdifferentthanabatterybecausethevoltageandcurrentcomingfromour
wallsocketsiscontinuouslychanging.Thevoltagereversesdirection60timeseverysecondinNorthAmerica(and50times
eachsecondinmostofEuropeandmuchofAsia).
ACishowelectricityisdistributedthroughouttheworld’spowergrid.SometimesDCneedstobeconvertedtoAC,suchas
solarelectricpanelsusedtoprovidepowerforanelectricalutility.SometimeACneedstobechangedtoDCatadifferent
voltage,suchasisdoneincellphonebatterychargers.
WhatYouNeed
Displayinganalternatingcurrent
waveformgeneratorandanoscilloscope
connectorfortheoscilloscope(consistingofaBNCconnectorwithtwowireleadsattached)
diode
alternative: a source of sound, amicrophone, and a computer-based, sound-card oscilloscope.CAUTION: Sound
cardoscilloscopescanhandleonlylow-voltageinputs,suchasfrommicrophones.Attemptingtouseasound-card
oscilloscopeforlargerelectricalsignalmaydamageyoursoundcard.Ahigh-impedancecircuitthatwillenableusing
a sound-card oscilloscope for higher voltages can be found at
www.geocities.com/~uWezi/electronics/projects/soundcard_osci.html.
Buildingatransformer
2-footlengthofinsulatedwire
4-footlengthofinsulatedwire
largeironnail
ACpowersupply,waveformgenerator,orkeyboardoutput
2ACvoltmeters(ormultimetersconfiguredasanACvoltmeter)
Method
Whata60-cycleACsignalsoundslike
1. IfyouhaveanadjustableACpowersupply,attachoneoftheterminalsofthespeakertothepositiveterminalofthe
ACpowersupplyandtheotherspeakerterminaltothenegativeterminalofthepowersupply.
2. Slowlyturnupthevoltageandyouwillstarttohearthecharacteristic60-cyclehumcomingfromthespeaker.This
maybeafamiliarsoundtorockmusiciansworkingwithpreownedPAsystems,whichoftenleaksintoaudiosystems.
387
Whatan60-cycleACsignallookslike
1. ConnectthepositiveandnegativeterminalsoftheACpowersupplytoa1000ohmresistor.
2. Attach the two wire leads of the oscilloscope input to the two ends of the resistor. (Do not use a PC-based
oscilloscope,whichweusedinotherexperiments,unlessyouhaveaspecialcircuittoadapttheACsignalforthis
purpose.)
3. TurnontheACpowersupplywithjustenoughvoltagetoproduceadisplayontheoscilloscope.
4. Adjust the amplitude, time sweep, and, if necessary, trigger setting to display the AC signal on the oscilloscope
screen.Figure115-1showshowtheelectricalcomponentsareconnectedtomakethismeasurement. (Thediode
usedinthenextsetofstepsisshownconnected.)
Whatadiodedoestoanalternatingcurrent
1. Removeoneoftheconnectionstothepowersupply.
2. Attachadiodeinthecircuitgoingfromthepowersupplythroughtheresistor.
3. TurnontheACpowersupply.
4. Reattachtheleadsfromtheoscilloscopetotheendsoftheresistor.
5. DisplaytheACsignalontheoscilloscopescreen.
Figure115-1
6. TurndowntheACpowersupply.
7. Removethediode.Reversethedirectionoftheleadandreattachthediodeinthecircuit.
8. WiththeACpowersupplyturnedon,observehowthesignalchanges.
Buildingatransformer
1. Windthe2-footsectionofwirearoundthenail.Leaveapproximately6-inchlengthsofwireateachend,withabout
¾oftheinsulationremovedfromtheendsofthewire.Keeptrackofhowmanyturnsyouapply.
2. Dothesamewiththe4-footsectionofwire.Thereshouldbetwiceasmanyturnsonthissection.
3. AttachthepositiveandnegativeofanACpowersupplytothetwoleadsofthe2-footsectionofwire.(Wecancall
thistheprimarycoil.)
4. AttachthetwoendsofanACvoltmetertothepointsofcontactbetweenthepowersupplyandthe2-footsectionof
thetransformerwire.
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5. AttachtheotherACvoltmetertothetwoleadsofthe4-footsectionofwire.Whatdoyouread?
6. IfyouhaveaDCpowersupplyavailable,applyasimilarvoltagetotheprimarywindings.Howisthevoltageofthe
secondaryaffected?
ExpectedResults
A60-cycleACsignalisdisplayedonanoscilloscopewithafullwavelengthrepeatingevery0.017seconds.AnACsignalhas
theformshowninFigure115-2.
Insertingthediodeinthecircuitresultsinonlyone-halfofthewaveformflowinginthecircuit.Thismeansonlythepositive
(ornegative)halfofthecycleisdisplayed,asshowninFigure115-3foradiodeplacedinonedirection,orasinFigure115-4
foradiodeplacedintheotherdirection.
Figure115-2Alternatingcurrentwaveform.
Figure115-3Alternatingcurrentwithadiode.
Figure115-4Alternatingcurrentwithadiodefacingtheotherway.
WhyItWorks
Alternatingcurrentisconstantlychangingdirection.
Adiodeisadevicethatpassesthecurrentinonlyonedirection.
A transformerchanges theACvoltageofan incomingsignalbasedon the ratioof turnsbetween the inputandoutput
sidesofatransformer.AtransformeronlyletsACcurrentthrough,butitwillnotpassDCcurrent.
Theratiooftheprimary(in)tothesecondary(out)voltageofatransformeristheratiooftheturnsofthesecondarytothe
primary.Thisisgivenbytheequation whereVrepresentsthevoltage,Nthenumberofwindings,p
theprimary,andsthesecondarywindings.
OtherThingstoTry
Ifyoudon’thaveastand-aloneoscilloscope,herearesomeotheroptions:
1. Buildanadapterforthesoundcardoscilloscope.
2. Useanaudibletone,suchasfromanelectronicsynthesizerkeyboard,toproduceasignalthatiscompatiblewitha
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soundcardoscilloscope.
3. YoucanalsogenerateanACsignalusingamagnetsuspendedbyaspringoveracoil.Thesignalcanbemonitored
byasoundcardoscilloscopeorPASCOvoltagesensor,andtheeffectsofthediodescanbestudied.
ThePoint
Alternatingcurrentconsistsofa flowofelectronscontinuously reversingdirection.Thevoltageofacommon formofAC
followstherisingandfallingpatternofasinewave.
390
Project116
Thediode.Anelectronicone-wayvalve.
TheIdea
Adiodeisanelectronicdevicethatletscurrentflowinonlyonedirection.Diodesarefoundinelectroniccircuitsandformthe
basisformorecomplicateddevices,suchastransistorsandintegratedcircuits.LEDs(light-emittingdiodes)andsolarcells
arediodes.
Unliketheresistorswestudiedinpreviousexperiments,diodesdonotfollowOhm’slaw.Theyarecallednonlineardevices,
whichgivesthempropertiesthatareusefulinawidevarietyofelectronicapplications.
WhatYouNeed
diode
DCpowersupply
voltmeter
ammeter
jumperwires
Method
1. Setupthecircuit,asshowninFigure116-1.Thisconsistsofthepositiveterminalofthepowersupplyconnectedto
thepositiveendofthediode(identifiedbythelongerofthetwoleads).Theammeterisconnectedinserieswiththe
diodeand,together,theyareattachedtothepowersupply.Thevoltmeterisconnectedtothetwoterminalsofthe
diode.
2. Startwiththepowersupplyatthelowestlevelandmakesurethevoltageandcurrentmetersreadzero.
3. Very slowly, walk the voltage up, taking current and voltage readings at each step. Continue until the current
suddenlygoesupsignificantlyhigherthanpreviouslevels.Donotallowtoomuchcurrenttofloworthediodecanbe
damaged.
ExpectedResults
Therelationshipbetweenvoltageandcurrentisnotlinear.
Asthevoltageincreases,athresholdisreachedwhereasmallincreaseinvoltageresultsinahugeincreaseincurrent.
391
Figure116-1Diodetestcircuit.
Thisrelationshipbetweencurrentandvoltageisexponential.
WhyItWorks
Thecurrentthatpassesthroughadiodeisrelatedtothevoltageappliedacrossitbythediodeequation:
I=IoeqV/kT
whereI isthecurrentandV isthevoltage(qandkareconstants,T isthediodetemperature,andIo isapropertyof the
diode).
Thisequationshowsthatthecurrentincreasesexponentiallyasthevoltageisincreased.Atfirstthechangeisslow.But
afterabout0.7V,thediodeofferslittleresistancetotheflowofcurrent.
OtherThingstoTry
Current-voltagecharacteristics
Plotthecurrentversusvoltageonalinearplot.Itsshapeisexponentialwitha“knee”around0.7Vdefiningaregionwherea
small increaseinvoltagecausesavery largeincreaseincurrent. Ifyouplotthelogofthecurrentversusthevoltage,you
shouldgetastraightlineatleastoveramajorpartofthedatarange.Ifvoltageisalogarithmicfunctionofcurrent,currentis
anexponentialfunctionofvoltage.Plottingthisconfirmsthenonlinearbehaviorofthediodecharacteristic.
Voltageinthereversedirection
Whathappens ifyouswapthetwo leadsofthediode?Thisappliesavoltage intheoppositedirectionas intheprevious
case.Asaone-wayvalve,thediodedoesnotallowanymeasurablecurrenttoflowinthereversedirection.Ifyoutrytoforce
theissueandcontinuetoincreasethevoltage(goingthewrongway),youmay(dependingonthediode)reachacondition
calledthebreakdownvoltage.Whenthishappens,theoppositiontothecurrentflowbreaksdownandthediodeallowsthe
currenttoflow.Inmanydiodes,thisisareversiblecondition,whichcanbeusedtoestablishasetvoltagelevelinacircuit.
Goingintobreakdownmaydamagesomediodes,sobecarefulifyoutrytomeasurethisinyourcircuit.
ThePoint
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Adiodeisanonlineardevice.Asmallincreaseinvoltageproducesalargeincreaseincurrent,whichgrowsexponentiallywith
voltage.
393
Section10
TheEarth
Project117
MeasuringtheEarth’smagneticfield.
TheIdea
TheEarthhasamagneticfieldthatgoesfromtheSouthPoletotheNorthPole.ThemagneticSouthPoleisactuallycloseto
the geographic North Pole. We can measure how strong the horizontal component of the Earth’s magnetic field is by
comparingitseffecttothatofamagneticfieldproducedbythecurrentflowinginacoilofwire.
WhatYouNeed
insulatedwireseveralmetersinlength
compass,preferablyonemountedonalow-frictionpivot
ruler
protractor
cylindricalshapetowrapthecoil (Thediameteroftheshapedependsonthe lengthofthecompassneedle.The
diameterofthecoilneedstobelargerthanthelengthofthecompassneedle.)
ringstandorothersupporttoholdthecoilofwire
DCpowersupplycapableofcurrentintherangeof1.0amporhigher
DC-ammeteroramultimeterconfiguredasanammeterinthe0–10Arange
roomwithnonferroustablesandfreeofstraymagneticfields
Method
1.Setupthecompass.Makesureitisfree-spinningandpointingtothenorth.Metaldeskscontainingironorsteelmay
interferewiththis.Also,motorsorloudspeakersmayhavesignificantmagneticfieldsthatcouldaffecttheoutcomeof
thismeasurement.
2. Form a coil of 15 turns using the cylindrical shape to form the coil. (For a small hand-held compass, a 1½ inch
diameterpipeisagoodform.Forthepivottypecompass,asoupcanorcoffeecanismoreappropriate.)Afterthe
coilisformed,withdrawtheobjectusedtowindthecoil.Leavesomewireatthestartandendofthecoiltoallowitto
beconnectedintoacircuit.
3.Supportthecoilusingaringstandorothersupport.Thecoilisorientedverticallywiththeplaneofthecoilfacingeast
andwest.Thecompassshouldbecontainedinsidetheplaneofthecoil,asshowninFigure117-1.Atopviewofthis
isshowninFigure117-2forclarity.Noticetheendsofthecompasspointstotheturnsofthecoil.
4.MakesuretheDCpowersupplyisturnedoffandtheammeterissettoreadcurrentsintherangeof1–10amps.
5.Afterstrippingtheinsulationfromtheendsofthecoil,attachoneendtothepositiveterminaloftheammeterandthe
otherendtothenegativeterminaloftheDCpowersupply.Youcanusejumperwiresorattachthecoildirectly.Refer
toFigures117-1and117-2fortheappropriateconnections.
6.CompletetheelectricalcircuitbyconnectingthenegativeterminaloftheammetertothepositiveterminaloftheDC
powersupply.
7.Placetheprotractorsothezerodegreeline insalignedwiththedirectionthecompassexposedonlytotheEarth’s
magneticfield.
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Figure117-2SetupformeasuringtheEarth’smagneticfield(topview).
8.Slowlyandcarefully turnon theDCpowersupply. Increase thecurrent readingon theammeteruntil thecompass
needledeflects45degreesfromitsstartingposition.
9.Atthispoint,thehorizontalcomponentoftheEarth’smagneticfieldisbalancedbyandequaltothemagneticfieldof
thecoil.
TheEarth’smagneticfieldis:
(1.26×10−6isthesameas0.0000126andyoucanmultiplyinchesby0.00254togetmeters.)
ExpectedResults
TheEarth’smagneticfieldvarieswithlocation,butitisintheballparkofabout5microTeslasor5μTor5×10−7T.Thefollowingtablesummarizestheresultsfordifferent latitudes,and it includesthescientificnotationanddecimalformsthat
396
areequivalent.
WhyItWorks
Themagneticfieldofthecoil isperpendiculartotheplaneofthecoil. Inthisexperiment, themagneticfieldofthecoil is
perpendiculartothehorizontalcomponentofthemagneticfieldoftheEarth.Whenthecoil’smagneticfieldjustequalsthe
horizontalcomponentof theEarth’smagnetic field, the resultantpointsata45-degreeanglebetweenthe two.When this
occurs,themagneticfieldoftheEarthisgivenbythatofthecoilaccordingtotheequation:
whereBisthecoil’smagneticfieldinTeslas
Nisthenumberofturnsinthecoil
μo isameasureofhowstrongamagneticfield isproducedbyagivencurrent,calledthepermeabilityoffreespace,and
equals1.26×10−6TeslasIisthecurrentinamps
Ristheradiusofthecoilinmeters.
Asanexample:A15-turncoil that is2 inchesindiameter(or0.051meters)requiresacurrentof0.28ampstoturnthe
compass45degrees.
Themagneticfieldis:
B=(15turns×1.26×10−6T-m/A×0.28A)/(2×0.051m)=0.00000052Tor5.2×10−5TThisisintheballparkoftheexpectedrangefortheEarth’smagneticfieldformiddlelatitudes.
OtherThingstoTry
The previously measured value is the horizontal component of the Earth’s magnetic field. Near the equator, the Earth’s
magnetic field isall horizontal.Asyouapproach thepoles, thedirectionof themagnetic fieldwith respect to theEarth’s
surface increases.Theangle the fieldmakeswith theEarth’ssurfacecanbemeasuredusingacompass that is free to
rotateintheverticalplane.Thetotalfield(ortheoverallfieldstrengthvector)atthatlocationcanbedeterminedfrom:
totalfield(Teslas)=horizontalcomponent(Teslas)/cosine(angletohorizontal)
Aswithmanyexperiments,itiscomfortingtoknowthattheeffectweintendtomeasureis,infact,whatourexperimental
resultsaregivingus.Onewaytoincreaseconfidenceinourresultsistorepeatitunderdifferentconditionandverifywehave
thesameoutcome.Accordingtoourmodel,itshouldnotmatterhowmanycoilswehave.Repeatingthemeasurementtosee
howmuchcurrentisneededtoturnthecompass45degreesusing5,10,or20coilsshouldgiveaconsistentresultasthe
measurementdescribedaboutusing15coils.
ThePoint
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ThemagneticfieldoftheEarthcanbemeasuredbybalancingitwithaknownmagneticfield.Ifthatmagneticfieldisatright
anglestothehorizontalcomponentoftheEarth’smagneticfield,thecompasswillpointinanewdirectionthatis45degrees
fromtheoriginalposition.Awayfromtheequator, theEarth’smagneticfield isatanangletothehorizontal,whichcanbe
measured.Theoverallmagneticfieldwillbeslightlyhigherthanthehorizontalcomponent.
398
Project118
WeighingtheEarth.
TheIdea
ShortlyafterSputnikwaslaunchedbytheformerUSSR,PresidentDwightDavidEisenhower,askedhisgeneralstotellhim,
based on its orbit, howmassive the satellite was. Unfortunately, they were unable to provide the U.S. president with the
informationherequested.However,theywouldhavebeenable,instead,totellhimthemassoftheEarth(whichEisenhower
wasn’tconcernedabout). In thisproject, youuseadifferentsatellite—themoon—todetermine themassof theEarth.You
alsoexplorehowthescientistCavendishperformedsomepainstakingcalculationsofgravitationalattractionandwasable
toaccomplishthesamething.
WhatYouNeed
moon
calendar
Method
1. DeterminehowlongittakesforthemoontocircletheEarth.
2. Acalendarcangiveareasonableresult.Amoreaccuratevalueisthesiderealperiod,whichindicatesonlythetime
ittakesforthemoontocircletheEarth,withoutconsiderationforhowlongittakestoreturntoaparticularphase.
This can beobtained froma sidereal table or by subtracting2.2 days from the valueobtained by observing the
numberofdaysfromonefullmoontoanother.
3. Calculatethevelocityofthemooninitsorbitbasedonitsaverageradius,r,of384,400kilometers(3.844×108m).Youcandothisusingtheequation:
1. CalculatethemassoftheEarthusingtheequation
whereGistheconstantofUniversalGravitation=6.67×10−11m3/kgs2
ExpectedResults
Usingthefollowingvalues:
T=27.322days=2,360,621seconds
v=2πr/T=1,023meters/secondr=3.844×108m
399
Thisiswithin1percentoftheacceptedvalueforthemassoftheEarthof5.97×1024kilograms.
WhyItWorks
Newton’s law of universal gravitation states there is an attractive force between any two masses in the universe. The
attractiveforceisrelatedtohowmassivetheobjectsareandhowfaraparttheyarefromeachother.Thegravitationalforce
is linkedtothemassanddistancebyaconstant,“bigG,”calledtheuniversalgravitationconstant.Since thegravitational
forceistheforcethatprovidesthecentripetalforcethatkeepsasatelliteinorbit,wecansolveforthemassoftheEarthif
weknowtheothervariablesintheequation.Similarly,knowingthatthegravitationalforceequalstheweightofanobject,we
cansolveforthemassoftheEarth.
OtherThingstoTry
Cavendish’s famousexperiment is oneof our “wish-list” experiments that canbe used to determine the bigGand, asa
result,themassoftheEarth.GravitationalforcebetweentwomassescanbemeasuredusinganapparatusshowninFigures
118-1and118-2.Therelativelysmallforceisdetectedbymeasuringthetorsionitproducesinathinfilamentbetweenthe
masses.
ThePoint
Themassofabodythatasatelliterotatesaroundcanbedeterminedbytheorbitalperiodofthatsatellite.Akeycomponent
oftheforceistheuniversalgravitationalconstant,G.ByknowingG,itispossibletodeterminethemassoftheEarth,using
eithertheweightofobjectsontheEarth’ssurfaceortheorbitalperiodofsatellitescirclingaroundtheEarth.
Figure118-1Cavendishapparatus.
400
Section11
TheTwentiethCentury
Project119
Whatisthesizeofaphoton?
TheIdea
One of the pivotal discoveries of the twentieth century was the recognition that light ismade of photons, which can be
thoughtofasminuteparticlesof light.Lightbehaves inmanyways likeawave,but italsobehaves inmanywaysas if it
consistedofparticles.Justhowbig(orsmall)aretheseparticlesoflight?
WhatYouNeed
severalLEDs(light-emittingdiodes)ofknownwavelength
variablepowersupply
jumperwires
voltmeter(ormultimeterconfiguredasamultimeter)
darkroom
Method
1. Attach the positive end of the voltmeter to the positive end of the power supply, and the negative end of the
voltmetertothenegativeendofthepowersupply.
2. Adjustthepowersupplytogiveareadingofzerovolts.
3. SelectanLED.UsejumperwirestoconnectthepositivesideofthepowersupplytothepositiveterminaloftheLED.
(ThepositiveterminaloftheLEDisthelongerone.)
4. ConnectthenegativesideofthepowersupplytotheLED.
5. Darkentheroom.
6. SlowlyincreasethevoltagefromthepowersupplyuntiltheLEDjustbeginstogiveofflight.Forvisiblelight,thiswill
bebetween1.2voltsand2.5volts.
7. Writedownthevoltagethatresultsinlightjustbeingproduced.
8. RepeatthisprocessforalltheLEDsyouhave.
9. Makeagraphofvoltageversusfrequency.
TheschematicforthisexperimentisshowninFigure119-1.
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Figure119-1CircuittomeasureLEDturn-onvoltage.
ExpectedResults
Thehigher thefrequency, thehigher thevoltageneededto turnon theLED.Therelationship is linear,asshown inFigure
119-2.
WhyItWorks
Accordingtoquantumtheory,theenergyofaphotondependsonitsfrequency.Higherfrequencylight(orlightclosertothe
bluesideof the visible spectrum)hasmoreenergy. Lower frequency light (closer to the redside) has lessenergy. Fora
photonofagivenfrequency,f,orcolor,theenergyisgivenbyhf,wherehiscalledPlanck’sconstant.
Figure119-2LEDvoltageversusfrequency.
403
OtherThingstoTry
TheamountofenergyneededtoturnonanLEDisgivenbyqV,whereqisthechargeofanelectron=1.6×10−19CandVis theappliedvoltage.Fromtheslopeof thegraph,youcanestimatePlanck’sconstant (fromtheslopeof thepreviously
plottedequation, v= (h/q)f).Planck’sconstantcanbedeterminedbydividing theslopeof thegraphby thechargeofan
electron.TheacceptedvalueforPlanck’sconstantis6.63×10−34J-s.TheslopeofthegraphinFigure119-2isabout7×10−34J-s,whichprovidesareasonableorderofmagnitudeestimateofPlanck’sconstant.
Sohowsmallisaphoton?Let’stakea60Wlight.Thismeansthatatabout5percentefficiency,thereareabout3Joules
ofenergycomingfromthebulbeverysecond.AccordingtoPlanck’sconstantthismeansthateverysecond3J/6.63×10−34
J-s = 4.5× 1033 photons are coming from the light bulb. This incredibly large number of photons gives an idea of theextremelysmallsizeofthephoton.
ThePoint
Theturn-onvoltageforanLEDgivesanindicationofhowmuchenergyiscontainedinasinglephoton.Photonswithhigher
frequency(shorterwavelength)havemoreenergythanphotonswithlowerfrequency.
404
Project120
HowisahydrogenatomliketheNewJerseyTurnpike?Seeingtheenergylevelsofthe
Bohratom.
TheIdea
In this experiment, you look at the colors of the light that the atoms of a particular element give off when excited by
electricity.Thisisthesametypeofdatathatledsomeofthegreatestscientificmindsofthetwentiethcenturytodevelop
theconceptoftheatom.Thepatternsofthosecolorsgiveusinsightintothemysteriesofthestructureoftheatom.Likethe
NewJerseyTurnpike,theelectronsinthevariousenergylevelsofthehydrogenatomcanexitonlyincertainspecificways.
WhatYouNeed
diffractiongrating
tubeofhydrogen
high-voltagepowersupplytoexcitethehydrogen
Method
1. Insert thehydrogen tube into thehigh-voltagepowersupply.Makesure thegoodelectricalcontact isestablished
betweentheelectrodesofthehydrogentubeandthepowersupply.
2. CAUTION:Do not touch the electrical contacts of the high-voltage power supply once it is activated. Follow all
manufacturer’sinstructionsforsafeuseofthisequipment.
3. Darkentheroom.
4. Turnonthepowersupplyandobserveaviolet-blueglowinthetube.
5. Holdadiffractiongratingwiththescribedlinesparalleltothetubeinfrontofyoureyes,asindicatedinFigure120-1.
6. Observetheimageoftheglowinghydrogentubebrokendownbythediffractiongrating.Ifyouhaveaspectrometer,
observe the light from the hydrogen tube and identify the positions of each of the lines you see. Look for the
transmittedlighttotheleftandrightofthecentralimagefromwhichtheglowinghydrogentubeislocated.Youmay
needtouseyourperipheralvisiontoseetheentireeffect.
ExpectedResults
Thelighttransmittedthroughthediffractiongratingisnotacontinuousrainbow.
Thelightisbrokendownintoafewbrightverticallines.
ThedetailsofthelinesyouseearesummarizedinTable120-1.
WhyItWorks
OntheNewJerseyTurnpike,ifyougetonatExit6andgotoExit7,youpaya$0.80toll.IfyougofromExit6toExit8,you
pay$1.20.Inahydrogenatom,ifanelectrongoesfromthethirdenergyleveltothesecondenergylevel,onlyredphotons
(withawavelengthof656.3nanometers)arereleased.But, ifanelectrongoesfromthefourthenergyleveltothesecond
energylevel,onlyblue-greenphotons(withawavelengthof486.1nm)areemitted.
405
Figure120-1Measuringthespectrumofthehydrogenatom.
OntheNewJerseyTurnpike,nothingisbetweenExit6and7,andyouneverhavetopayatollbetween$1.20and0.80.
Thehydrogenatomdoesnotproduceaphotonwhosecolorisbetweenredandblue-green.
Einstein’sinterpretationofthephotoelectriceffectleadsustotheconclusionthatphotonshaveacertainspecificenergy
basedontheirfrequency.NielsBohrdevelopedamodelofthehydrogenatombasedontheideathattheelectronsarefound
incertainspecificenergylevels,butnotinbetween.Aparticularchangeinenergylevelsresultsinaphotonofaparticular
color.
Whenviewedthroughadiffractiongrating,thelightfromtheexcitedhydrogenatomsdoesnotresult inafullrainbow.It,
instead,producesonlyspecificbrightlycoloredlines,correspondingtospecificwavelengths.Eachwavelengthisassociated
withachangefromoneenergyleveltoanother.Thebiggerthejump,theshorterthewavelength.
OtherThingstoTry
Thespectralbreakdownoflightemittedbyahydrogenatomcanalsobedetectedusingahigh-sensitivitylightsensor,such
asPASCOpartnumberPS-2176.TheresultforthisisshowninFigure120-2.
Table120-1
406
Figure120-2Hydrogenemissionspectrum.CourtesyPASCO.
ThePoint
ObservationofseparatecolorsfromglowinghydrogengasconfirmsthemodeloftheatomdevelopedbyNielsBohr,inwhich
electronsoccupyspecificenergylevels.Becauseelectronscannotbebetweentheestablishedenergylevels,manycolors(or
photonfrequencies)arenotproduced.
407
Project121
Photoelectriceffect.
TheIdea
In1905,duringhis “miracle year,”AlbertEinsteinpublished fivepapers.These includedspecial relativity,whichdealtwith
spaceandtime,aswellasgeneralrelativity,whichrelatedmassandenergythroughtheequationE=mc2.However,Einstein
wonhisonlyNobelPrizeforworkhedidthatsameyearonthephotoelectriceffect.
Atthetime,itwasknownthatlightshiningoncertainmaterialscouldknockoutelectronstoproduceacurrent.Itstoodto
reasonthatthestrongerthelight,thegreaterthecurrent.Researchersalsofoundthathowmuchofakicktheelectronsgot
(orhowmuchkineticenergytheyhad)dependedonthecolorofthe light.Manyscientistsexpectedastronger lightwould
alsoreleaseanelectronwithgreaterenergy. It tookEinstein’sbrilliancetounderstandwhythecolor (or frequency)of the
lightplayedsuchakeyroleindetermininghowmuchenergytheelectronscameawaywith.Theconsequencesofthisinsight,
alongwiththecontributionsofmanyotherscientists,leadtothedevelopmentofquantummechanics,whichisthebasisfor
themodernelectronicworld.
Figure121-1AlbertEinsteinexplainedthephotoelectricbyclaimingthatlighthadaparticle-likenature.
Thisproject introducesyou to the ideaof thephotoelectriceffectandguidesyou to recreate the typeofdataEinstein
interpreted.
WhatYouNeed
Thebasics
pieceofzincmetal
sandpaperorsteelwool
shortjumperwire
sourceofultravioletlight(acarbonarclamporpossiblyastrong“blacklight”)
sourceofvisiblelight(incandescentlamp)
plateofglass
electroscope,eitherpurchasedorbuiltasaproject
Photoelectriceffectapparatus
408
photoelectriceffectapparatus,suchastheDaedelonEP-05(availablefromwww.daedelon.com)
variableDCvoltagesource
voltmeterormultimeterconfiguredasavoltmeter
various light sourcesofknown frequency: this includes laserpointersofknownwavelength, incandescent, carbon
arc,orultravioletlights
colorfilterswithknownwavelengthoftransmittedlight
Method
Thebasics
ThispartintroducesthebasicideaofthephotoelectriceffectandbringsyoutothedilemmaEinsteinaddressed.
1. Rubthepieceofzincwithapieceofsandpaperorsteelwool.Thisremovesoxidestoexposethemetal.
2. Dischargetheelectroscopebytouchingyourfingertotheelectrode.
3. Usingaveryshortjumper,attachthezinctotheelectroscope.
4. Darkentheroom.
5. Shinethelightfromanultravioletsourceontothezinc.
6. Observetheeffectontheelectroscopeleaves.
7. Dischargetheelectroscopeandcomparetheeffectoftheultravioletsourceandthevisiblesource.Alsocompare
theeffectofshiningtheultravioletsourcethroughapaneofglassthattransmitsmostlyvisiblerangelight,buthardly
anyultravioletlight.
8. Chargetheelectroscopepositivelyandobservetheeffectofshiningultravioletlightonthezinc.
9. Chargetheelectroscopenegativelyandobservetheeffectofshiningtheultravioletlightonthezinc.
Photoelectriceffectapparatus
Thisapproachusesametal target inavacuum tube.Because thecurrents thatneed tobemeasuredaresosmall, it is
helpfultohavethedetectorveryclosetothesourceofthecurrent.Thisproceduregoesthroughthegenericstepstomake
this measurement with specific references to the EP-05 operation (more detailed instructions are available with that
apparatus):
1.Setupthefluorescentlamptofocusonthedetector(photodiode).
2.Attachavoltmetertoreadthestoppingvoltage(stoppingpotential)acrossthephotodiode.(Theconnectionsarethe
redandblackbananajacksontheEP-05.)
3.Placethebluefilterovertheopeninggoingintothephotodiode.TheapparatusshouldbesetupasshowninFigure
121-2.
4.Darkentheroom.Ifnecessary,constructalightshieldfromacardboardboxtoprotectthephotodiodefromstraylight.
5.Adjustthestoppingpotential,soalltheelectronsareturnedbackandthereisnophotocurrent.(Thisisaccomplished
byturningthe“voltageknob”tothefullclockwiseposition.)
6.Now,adjustthestoppingpotentialtoitsminimumvalue.(Thiscanbedonebyturningthevoltageknobasfarinthe
counterclockwisepositionaspossible.)
7.Adjusttheradiationintensitybychangingthedistancebetweenthelightsourceandthedetectortoreadabout10on
theintensityscale.Youarenowcalibratedandreadytomakesomemeasurements.
8.Measurethecurrentreadingandwritedownthereadingonthevoltmeter.
9.Inseveralsteps,increasethestoppingpotentialandrecordthecurrentreadingateachstep.Fivereadingsshouldbe
sufficienttodefinealinearrelationship.
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Figure121-2Photoelectriceffectapparatus.
10.ThedatashouldproducealinearrelationshipsimilartotheoneshowninFigure121-2betweenstoppingpotential
andvoltage.
11.Thevoltagerequiredtoproducezerocurrent isakeypointthatdeterminesthevalueoftheworkfunctionforthe
metal(inthephotodiode).
12.Repeatthepreviousstepsusingthegreenfilter.
13.Replacethefluorescentlampwithatungstenincandescentlamp.Installtheredfilterandrepeattheprevioussteps
untilcurrentversusvoltagecurvesfortheredfilter.
14.AlaserorLEDofknownwavelengthcanalsobeusedasasourceofillumination.Adiverginglens(biconcave)may
behelpfulinspreadingthelaserbeamtofilltheopeningareaofthephotodiode.
15.Foreachcolor,plotthecurrentversusvoltageandextrapolatethecurvetofindthethresholdstoppingvoltagethat
resultsinzerocurrent.
16.Plotthestoppingvoltageversusthefrequencyforeachofthefrequencies(colors)forwhichyoutookdata.
ExpectedResults
Ultraviolet light shiningonapieceof zinc results in a charge separation.This chargecauses the leavesof a negatively
chargedelectroscopetoseparatefurtherandcausestheleavesofapositivelychargedelectroscopetocometogether.This
indicatesthechargeisnegativeor,morespecifically,consistingofelectrons.Visiblelightdoesnotresultinthischargebeing
developedinthezinc.
Usingthephotoelectriceffectapparatus,wefindthat:
1. Thegreater the frequency, thegreater thestopping voltage required to limit thecurrent flow.This relationship is
linear.Thismeansthekineticenergyofthefreedelectronsisproportionaltothefrequencyofthelight.
2. Belowacertainthresholdfrequency,nocurrentisgenerated.
3. Increasing the intensity of the light increases the current (for a given stopping potential and light frequency).
However,increasingthelightintensitydoesnothaveanyeffectonthekineticenergyofthefreedelectrons.
4. TheslopeofthestoppingvoltageversusthefrequencygraphrepresentsPlanck’sconstantdividedbythechargeon
oneelectron.Theequationforthisis:
Becausethewavelengthoflightisusuallymorereadilyavailable,thefrequencycanbedeterminedfromtheequation:
frequency=speedoflight/wavelength
5.Fromtheslopeofthevoltageversusfrequencygraph,Planck’sconstantcanbedeterminedfromtheslopemultiplied
bytheelectroniccharge:q=1.6×10−19C.Aslopeof4=10−5givestheexpectedvalueofPlanck’sconstant.
WhyItWorks
Lightcontainsenergybasedonitsfrequency.Thefrequencyofvisiblelightislowerthanthatofultravioletlightanditdoes
nothaveenoughenergy to freeelectrons fromametal,suchaszinc.As the frequencyof the light increases, theenergy
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eachphotoncarriesisraisedabovethethresholdrequiredtofreeelectronsfromthezinc.
Figure121-3Stopping potential for electrons exposed to various frequencies of light. The slope of this line determines
Planck’sconstant.
Theworkfunctionofametalisameasureofhowtightlyelectronsareheldbytheatomsofthemetal.Ifthephotonenergy
isgreaterthantheworkfunctionofthemetal,electronsarereleased. If thefreedelectronsencounterastoppingvoltage
(stoppingpotential),theamountofextraenergyabovetheworkfunctioncanbedetermined.
Thiscanbesummarizedbytheequation:
KE=Ephoton+W
whereKEisthekineticenergyofthefreedelectron(measuredbytheamountofvoltagerequiredtostoptheelectrons).
Ephotonistheenergycarriedbythephoton.
Wistheamountofenergyjusttofreeoneelectronfromthemetalwithnoextraenergytogetitmoving.
Theenergyinaphotonwasgivenby:
Ephoton=hf
wherehisPlanck’sconstantandfisthefrequencyofthelight.
OtherThingstoTry
A good software simulation of the results of this experiment can be found at http://phet-web.colorado.edu/wb-
pages/simulations-base.html.
ThePoint
Thekeyconceptunderlying thisexperiment is that lightenergycomes inspecificamountsorpackagescalledquantaor
photons.Thesephotonscannotbebrokenupintosmallerunits.Thehigherthefrequencyofthelight,thegreatertheamount
of energy contained in one photon. If a photon has enough energy to release an electron, an electric current can flow;
otherwise,belowthatthreshold,noenergywillflow.Themoreenergythephotonhas,themorekineticenergytheelectron
processeswhenitisreleased.
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Project122
Millikanoil-dropexperiment.Mysterymarbles.Understandinghowtheexperimentworked.
TheIdea
RobertMillikandevisedabrilliant technique toexperimentally determine thechargeof theelectron,which resulted in him
beingawarded theNobelPrize forPhysics.Thisproject letsyou replicateMillikan’s famousexperiment.Basically,Millikan
foundawaytoattachelectronstosmalldropletsofoil,andthenmeasuretheirresponsetoanelectricfield.Becausethisis
amorecomplexexperimentthanmostoftheotherexperimentsinthisbook,itmaybeoutofreachformanyreaders.
For this reasonanotheroption toexplore thisdiscovery isgiven.Oneof theproblemsMillikanhad todealwithwashe
neverknewhowmanyelectronswereonanygivendropofoil.Wecanre-createsomeofthelogicalstepsMillikanfollowed
usingpenniestorepresentelectrons.
WhatYouNeed
Simulation
filmcanistersorplasticprescriptioncontainerswithcovers
spraypaint
about150pennies
digitalscaleorspringbalance
ReplicatingtheMillikanoil-dropexperiment
Millikan’soil-dropapparatus,asshowninFigure122-1
Method
Settingupthesimulatedoildrops
1. Spraypaintorotherwiseobscuretheoutsideofabout8–12plasticcontainers,soyoucan’tseeinside.
2. Measurethemassoftheemptycontainers.
3. Distributeadifferent(random)numberofpenniesineachofthecontainers.
4. Theeasyversionofthisincludesatleastonesetofcontainersthatdifferbyonepenny(suchasContainer7with
12penniesandContainer8with11pennies).
5. A slightly more challenging version is to have no container differing by one penny, but (because of the small
statisticalsample)tohaveatleastonesetofsamplesdifferbytwopenniesandanothersetbytwopennies.
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Figure122-1Millikanoildropexperimentapparatus.CourtesyPASCO.
Findingthechargeofasimulated“electron”(massofapenny)
1. Findthemassofeachcontainerwiththepennies.
2. Subtractthemassofthecontainertoobtainthemassofjustthepenniesineachcontainer.
3. Arrangethemassmeasurementsinorder—smallesttolargest.
4. Subtracteachmassmeasurementfromthepreviousmeasurementinthelist.
5. Identifythesmallest(non-zero)massdifferencebetweenanypairofcontainers.
6. Divideeachofthemassdifferencesbythesmallestmassdifferenceinthelist.
7. Ifanyfractionalnumbersareinthelist,multiplyallthenumberbyafactorthatleavesonlyintegersinthelist.(For
instance,ifoneofthenumbersis1.5,multiplythemallby2.)
8. Makeagraphofthemassdifferencesonthey-axisversustheintegersinStep7.
9. Findtheslopeofthisgraph.Thisshouldgiveyouthemassofthepenny,followingasimilarformof logicMillikan
usedtomeasurethechargeoftheelectron.
TheactualMillikanoil-dropmeasurement
1. Determinethemassoftheoildropbymeasuringthevelocityofthedropasitfalls.Becauseairresistanceaffects
largerdropstoagreaterextent,thevelocityservesasaveryaccuratemeasureofthedropletmass.
2. UsingX-raysoranothersourceofionizingradiation,createarandomnumberofchargesontheelectron.
3. Determine the magnitude of the electric field that just balances the gravitational pull on that droplet. The
gravitational force can be found from themass of the droplet determined in Step 1 and the density of oil. The
greaterthecharge,thegreatertheforceneededtobalanceit.
4. At thispoint,weknow thecharge, butwedon’t knowhowmanyelectronsareonanygivendroplet.This is very
similartothesituationwejustaddressedwiththepennies.Althoughwedidnotknowhowmanypennieswereinany
particularcontainer,wewereabletofindthemassofasinglepenny.Usingasimilarlogic,Millikanwasabletofind
themassofanelectron.
ExpectedResults
Followingtheprevioussimulatedprocedureusingpennies, theslopeof the line inFigure122-2 is2.7grams,which is the
massofasinglepenny.Thisisareasonableaverageforpenniesmintedbeforeandafter1982.Amoreprecisevaluecan
413
beestablishedbysortingpenniesintogroupsbeforeandafter1982.
ThechargeofanelectrondeterminedbyMillikanis–1.6×10−19Coulombs.
OtherThingstoTry
MarblescanbeusedtosimulatethelogicalprocesspursuedbyMillkaninasimilarmannerthatwasdonewithpennies.The
marbleshaveagreatermass,whichmaymakeiteasiertodetectdifference.However,findingarelationshipgraphicallymay
bemoredifficultbecauseofthevariationinmassforarandomsetofmarbles.
Figure122-2Usingthemassofapennytosimulatethephotoelectriceffect.
WhyItWorks
Thesizeofanoildropisfoundbyobservingitsfree-fallvelocityinair.Theoildropisthengivenachargebyexposingitto
ionizingradiation.Theelectricfieldthatestablishesequilibriumwithgravityisrelatedtotheforce.Althoughtheexactnumber
ofelectronsonanygiveoildropcannotbedetermineddirectly, thecommonmultiple leadsus to identify thechargeofa
singleelectron.
ThePoint
TheMillikanoil-dropexperimentdeterminesthechargeofanelectronbymeasuringtheresponseofanoildropchargedby
electronsinanelectricfield.
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Project123
Ping-pongballchainreaction.
TheIdea
Thisisafunandsimpledemonstrationthatwillhelpyouunderstandhowanuclearchainreactionoccurs.Itwasusedyears
agoinaWaltDisneyfilmcalledOurFriendtheAtomandappealstoallreadersincludingtheyoungestandtechnicallyleast
sophisticated.
WhatYouNeed
24spring-typemousetraps
49ping-pongballs
enclosurewithatleastonetransparentside(alargefishtankwithglasssidesandaglassbottomcanworkwell)
optional:2mirrorsthesizeof,orlargerthan,thesideoftheenclosure
Method
1.Setthetraps(Figure123-1).
2.Carefullyplacetwoping-pongballsoneachofthemousetraps(wherethecheesewouldhavegone).SeeFigure123-
2.
3.Layoutthemousetrapsinanarraythatwillfit intotheenclosure,suchasa6×4array.Obviously,youneedtobeextremelygentleandavoidsuddenmotionstopreventaprematurereleaseof themousetrap.Anymishapwill likely
takeothermousetrapsoutwithit.
4.Eitherlowertheenclosureoverthemousetrapsordevelopawaytobringthemousetrapsintotheenclosure.Youmay
need toexperimentwithdifferentmethodsof loading themousetraps.Youmayprefer toplace theping-pongballs
after,ratherthanbefore,movingthetraps.Youmaywanttodevelopawoodenorfoamboardtemplatethatprotects
thetrap’striggermechanismwhileyouareplacingtheping-pongballsorgluethetrapstoaboard.
Figure123-1Eachmousetraprepresentsauraniumatom.
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Figure123-2Eachpingpongballrepresentsaneutron.
5.Withtheping-pongballloadedonthemousetrapsintheenclosure,youarereadytoinitiatethechainreaction.Sofar,
you have used 48 ping-pong balls, so one should be left. The remaining ball is the neutron that starts the chain
reaction.
ExpectedResults
As inanuclear-fissionchainreaction,aneutron(thestarterping-pongball)createsthefirstfissionreaction.Thisevent is
simulatedbythemousetrapreleasingtwoadditionalping-pongballs.These,inturn,potentiallyeachreleasetwomoreballs
(neutrons)initiatingadoublingoftheavailableneutronswitheachfission.Asadditionalping-pongballsarereleased,therate
ofthereactionaccelerates.Thischainreactionissimulatedbyrapidlyreleasingpingpongballs,whichinturnreleasesother
ping-pongballstocontinuethereaction.TheaftermathofthisisshowninFigure123-3.
Figure123-3Afterasimulatedchainreaction.
WhyItWorks
Nuclearfissionoccursinnaturewhenanisotopeofanuclearmaterialabsorbsaneutronandbecomeunstable.Thenucleus
splits, forming two lighter “daughter”nucleiandasprayof freeneutrons thatproduces thecascadingeffectknownasa
chainreaction.Therealsoneedstobeacriticalmassforthisprocesstobecomeself-sustaining.
416
OtherThingstoTry
Itwouldbeinterestingtocaptureavideoimageofthissimulatednuclearreactionandviewitinslowmotion.
ThePoint
Nuclear fission is initiatedbya freeneutron thatcausesanucleus (suchasauranium-238nucleus) tosplit and release
additionalneutrons.Thisisthebasisofnuclearpower,whichcurrentlyprovidesaboutone-fifthoftheelectricityintheUnited
States.
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Project124
Thesodiumdoublet.Whydowethinktheelectronhasbothupanddownspins?
TheIdea
Noonehaseverseenanelectronspin. In fact, for thatmatter,noonehaseverevenseenanelectron.Yet,weknowan
electronbehavesasifitwerespinning.Someofthemostrevealingevidenceforthiscomesfromthelightthatcertainatoms
emitwhenthey’reexcited.
Ifsomesodiumchlorideisexposedtoaflame,theflametakesonacharacteristicyellow/orangecolor.Thisisthecolor
observedinthecommonflametestusedinchemistrylabstoidentifythepresenceofsodiuminsodiumvaporstreetlamps.If
youlookatthelightcomingfromanexcitedsodiumatomwithaspectroscopeordiffractiongrating,thefirstthingyounotice
isasingleorange/yellowlinewithawavelengthbetween589and590nanometers.
However,oncloser inspection,younoticenotonebuttwoorange/yellowlines.Thepurposeofthisproject istoobserve
thesetwolines,knownasthesodiumdoublet,and,moreimportantly,tounderstandwhytheyaresplit.
WhatYouNeed
Bunsenburnerorotherflame
concentratedsodiumchloridesolution
cleannichromewireloop(orawoodensplint)
diffractiongratingorspectroscope
sodiumvapordischargetubewithappropriatehigh-voltagepowersupply
Method
1. Useoneofthepreviousmethodstoproducealightsourcegeneratedbyexcitedsodiumatoms.
2. Darkentheroom.
3. Observethelightusingadiffractiongratingoraspectroscope.
4. Lookcarefully until you seea vertical yellow/orange line. Lookclosely until you notice this line is formedby two
separatelines.SeeFigure124-1.
ExpectedResults
Thepointofthisprojectistoobservetwoseparateyellow/orangelinesthatmakeupthesodiumdoublet.
WhyItWorks
When an electron goes fromone energy level to a lower energy level, it gives off light. Each energy level can hold two
electrons:onewithspinupandtheotherwithspindown.Theelectronwiththespinuptakesaslightlygreateramountof
energy togo fromoneenergy level toanother.Asa result, theelectronswithdifferent spinconditionsgiveoffa slightly
differentcolor(wavelength)light.
ContinuingtheNewJerseyTurnpikeanalogy(fromProject120),let’ssayyoutravelacertaindistancegoingfromExit7to
Exit 8. But things are slightly different if you get off at either an eastbound or westbound ramp at the exit. That small
differencecanbethoughttobesomethingliketheeffectcausedbyelectronspin.
418
Figure124-1Electronsinasodiumatomproduceaprimarycharacteristicwavelengthwhenelectronsmovefromoneenergy
leveltoanother.Aslightlydifferentwavelengthisproduceddependingonwhetherthespinoftheelectronis“up”or“down.”
OtherThingstoTry
Ifanexcitedsodiumatomisexposedtoaverypowerfulmagneticfield,thesespectrallinessplitevenfurther.Thisiscalled
theZeemaneffect,which requiresmagnetic fieldson theorderof18Teslas.However, because this is roughly20 times
morepowerful than the very strongmagnetic fieldsused tostudynuclearmagnetic resonance,wewon’t pursueZeeman
splittingexperimentsinthisbook.
ThePoint
Inanatom,electronshaveupordownspin.Whenanelectrongoesfromoneenergyleveltoanother,theenergygivenoffby
eachofthetwospinorientationsisslightlydifferent.Observingthesplit inthefrequencysupportstheconceptofelectron
spin.
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Project125
Buildingacloudchamber.Whymuonsshouldnotbehere.Specialrelativity.
TheIdea
Cosmicrays are subatomic particles that stream through the universe at high speed. As you read this, dozens of these
particlesarepassingthroughyourbodyharmlesslyeverysecond.Inthisproject,youbuildadevicecalledacloudchamber,
whichwillmakesomeof theseparticlesvisible.Thecloudchambercontainsanalcoholvaporcloud thatproducesvapor
trailswhenachargedparticlepassesthroughit.Thistrailrevealsthepathortracktheparticlestakeastheypassthrough
thevaporcloud.Youbegintolearntorecognizethesignatureofsomeofthoseparticles.
Scientistsbelievemostcosmicrayscomefromthesun.Thesecosmicraysconsistoffragmentsofthenucleiofhydrogen
orheliumatoms,resultinginparticlesthatareeithersinglycharged(protons)ordoublycharged(alphaparticles).Whenthese
cosmic rayparticlesstrike theupperatmosphereof theEarth, theycollidewith theairmoleculespresent.This results in
collisionsthatproducenewparticles,calledsecondarycosmicrays.Thesearewhatyouwilldetectinyourcloudchamber.
Themostcommonresultofthecollisionisaparticlecalledamuon.Themuonisanegativelychargedparticle,whichis
bigger thananelectron,butsmaller thanaproton.Themuons thatarecreated in theupperatmospheredecay incredibly
rapidly.Becauseoftheirextremelyshortlife,theyshouldnotbeabletosurvivethetripthroughtheEarth’satmospheretobe
detectedonitssurface.However,themostcommonparticledetectedinthesecondarycosmicraystreamisthemuon.The
onlyway toexplain theabundanceofmuonsyousee inyourcloudchamber isby turning toEinstein’s theoryof relativity,
whichsaysthattimeslowsdownfortheveryhigh-speedmuons.
AlsopresentintheshowerofsecondarycosmicrayshittingtheEarth’ssurfacearepositronsandelectrons.Thepositrons
areaformofantimatterthatcanalsobeseeninyourcloudchamber.
WhatYouNeed
small2.5gallonfishtank
smallStyrofoamcooler
1literofpureisopropylalcohol(not70percentalcohol,asismorereadilyavailable).Puremethylalcoholcanalso
beused.
sheetofblackfelt largeenoughto linethebottomofthetank(note, thefishtankwillbeturnedupsidedown,so
whatwerefertoasthebottomofthefishtankwillbecomethetopofthecloudchamber)
metalplatethesizeofthetopofthefishtank—aluminumispreferablebecauseitconductsheatbetterthansteel
ducttape,siliconerubbersealant,orweatherstrippingtomakethefishtankairtight
black(solventresistant)paint
about1poundofdryicetoencasethebottomofthefishtank
brightlightsource,suchasapowerfulflashlight
strongmagnet
optional: source of low-level radiation, such as a smoke detector,mantle of oldColeman lantern, or certain old
ceramicobjectsthatcontaincobalt
optional:adigitalvideocamera
Method
Buildingthecloudchamber
420
1. Becausethedryicehasalimitedshelflifeand,formostusers,takesaspecialefforttoobtain,agoodideaistodo
adry runandassemble theseparts beforepickingup thedry ice.Also, rememberdry ice isextremely coldand
shouldnotcomeintocontactwitheyesorskin.
2. Attachtheblackfelttothebottomofthefishtank.UseblackelectricaltapeorVelcrounderthefelttosecureit,so
itremainsinplacewhenthefishtankisinverted.Youmaywanttodevisesomeotherwaytosecurethefeltsuchas
smallwoodensupports.Keepinmindthatwhateveryouusetosupportthefeltmustnotbedegradedbythesolvent
vaporthatwillbepresent.AsolventresistantgluesuchasGorillaGlueorGorillatapecanholdthefeltwithoutbeing
attackedbythealcoholvapor.
3. Placethedryiceinthebottomofthecooler.Ifthedryiceisinlargechunks,youwillhavetochopit.Youcanadda
littlealcoholtothemixturetoformaslushtomakebetterthermalcontactwiththemetalplate.Ifyoudon’thavea
coolerthefishtankwillfitin,useaboxandlineitwithinsulatingmaterial.
4. Soaktheblackfeltwithalcohol.Avoiddrippingthatproducespuddlesofalcoholonthemetalplatebynotusingtoo
muchalcohol.
5. Cover thedry icewith themetalplate,with thesidepaintedblackfacingawayfromthedry ice.Themetalplate
shouldbecompletelyincontactwiththedryice.Youcansecuretheplatetothetankfirstifthatworksbetter.
6. Place the tank—alcohol-soaked felt up—with the metal plate over the dry ice. It is important to establish good
thermal contact between the dry ice and themetal plate. People have used solid blocks of dry ice as well as
crushedice.Goodthermalcontactcanbeachievedbycreatingaslurrybymixingsomeisopropylalcoholinwiththe
dryice.Ifyoucrushthedryice,besuretowearprotectiveclassestoavoidextremelycolddryicefragmentsfrom
contactingyoureyes.Thedryicemixedwithalcoholshouldbearound−70degreesCor−94degreesF.7. Sealthechamberabovethemetalplatebywrappingelectricaltapearoundtheedgewherethemetalplatemeets
thefishtank.(Somepeoplehavefoundthatpouringasmallamountofisopropylalcoholinthechannelsurrounding
themetalplatehelpsformanairtightseal.)Ifairisdrawnintothechamber,thevaporcloudmaynotfromproperly.
8. Itmaybenecessarytokeepthetopofthecloudchamber(wherethealcohol-saturatedfeltis)fromgettingtoocold.
The bottom of the chamber should be near −60 degrees C (−76 degrees F) to enable the formation ofsupersaturated vapor. However, the top of the chamber should be maintained close to room temperature (22
degreesCor72degreesF)topromoteevaporationofthealcohol.Toaccomplishthisitmaybenecessarytowarm
the top of the chamber either with your hands or with some other means to maintain the proper temperature
gradient.Itmightbehelpfultomeasurethetemperaturesofbothsurfaces.
9. Shinethelightfromthesideofthetanktowardthemetalplate.
10. Thestackshouldlooklikethis,fromtoptobottom:
–Bottomofthefishtank
–Blackfeltsoakedwithisopropylalcohol
–Fishtank(metalplatecoveringthetopofthetank)
Figure125-1Cloudchamberassembled.
–Metalplate
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–Sheetsofdryice
–BottomoftheStyrofoamcooler
Observingtracks
1. Atfirst,youwillnoticeamistofalcoholdropletsforminginthetank.
2. Afterabout15minutes,youshouldstarttoseethetracksofparticlespassingthroughthevaporafewcentimeters
abovethebaseplate.
3. Itmay be helpful to view the tracks by looking toward the light source at an angle so that the vapor trails are
illuminatedfrombehind.
4. Ifyouhavea low-levelradiationsource(suchasoneoftheeverydayobjectsmentionedintheparts list),placeit
near the edge of the cloud chamber and compare its effects to cosmic rays. (Smoke detectors have low-level
radioactivematerials,suchasamericium,thatarepackagedsafetyforitsintendeduse.Donotattempttodismantle
asmokedetector togetat the radioactive isotope.Themantle forat leastsomeColemangas-camper lanterns
containstracesofradioactiveThorium,whichcanalsobeasafelow-levelsourceofchargedparticlestoview.)
5. Observewhatamagnetdoestothetracks.Noteinparticularhowtheparticleisdivertedinrelationtotheparticle’s
originalvelocityandthenorth-to-southdirectionofthemagneticfield.
6. Onceyougetthisgoing,avideocameracanbeveryhelpfulinrecordingthetracksandprovidinganopportunityto
analyzethetracksindetail.Stillphotographyisverydifficultbecauseoftherandomnessofthewaythetracksare
createdandtherapiditywithwhichtheyfade.Extractingstillimagesfromavideorecordingismorelikelytoproduce
clearimagesoftracks.
ExpectedResults
Afterthemistformsintoasupersaturatedalcoholvapor,youmaystarttonoticetracksthatlooklikespiderwebsalongthe
chamberbottom.Thesearecosmicraysandshouldbenoticeableroughlyseveraltimeseachminute.
Alpha particles, which are two protons and two neutrons bonded together, form sharp, well-defined tracks about 1
centimeterlong.
Betaparticles,whichconsistofelectrons,havethinnerandlongertracks,roughly3to10centimetersinlength.
Someofthetracksmaycomeinstraightandthensharplybreakinadifferentdirection.Anexampleofthis isshownin
Figure125-2,whichshowsamuonbeingdeflectedasitdislodgesanelectronfromanairmolecule.
422
Figure125-2Collisionbetweenamuonandanatom.Themuonisdeflectedandtheelectron isknockedoutoftheatom,
leavingasecond,faintertrack.
Atrackthatstarts inastraight line,butthenbreaksoffatasharpangle,suchasshown inFigure125-3,most likely is
muondecayduringwhichamuonspontaneouslydecaystoformanelectron.Theelectronisvisibleasathinnertrack.The
twoneutrinosdonotformvaportrailsandarenotvisiblebecausetheyarenotcharged.
Figure125-3Muondecay.Amuon spontaneously decays intoanelectronand twoneutrinos.The neutrinos do not leave
tracksinthecloudchamber.
Youmayseeaveryjagged,erraticpathrepresentingalow-energyparticlebeingscatteredmultipletimes.Thisispictured
inFigure125-4.
Ifyouviewthechamberfromthefront,withtheparticlescomingfromtheleft,andthemagnet’snorthpoleatthetopof
thechamber,particlesbendingtowardthebackofthechamberarepositivelychargedparticles(suchasprotons).Particles
bendingtowardthefrontofthechamberarenegativelycharged.
WhyItWorks
Someof the radiation in cosmic raysor isotope sourcesconsistsof chargedparticles.As thesechargedparticlespass
through thesupersaturatedalcohol vapor in thechamber, theparticle ionizes themoleculesof thevapor.Dropletsof the
vaporthencondenseonthepathleftinthewakeoftheparticle’spath,leavingavisibletrail.
Figure125-4Zigzagpathofslowmovinglow-energychargedparticles.
Collisionsoccurthateitherchangethemotionoftheparticleorresultinasubatomicevent,whichresultsinawholenewmix
of particles. The laws of conservation of momentum and mass must be followed, which helps to identify the particles,
includingthosethatarenotvisible.Nonionizedparticles,suchasneutrons,willnotleaveavisibletrack.
Figure125-5showsasamplingofparticlecollisionsinamoreelaboratedetectionsystem,calledabubblechamber.
OtherThingstoTry
Amuon isoneofmanytypesofsubatomicparticlesthatmaybedetectedbyyourcloudchamber.Amuonhasthesame
chargeasanelectron,butitis207timesmoremassive.Muonsarecreatedwhencosmicraysstriketheupperlayersofthe
Earth’satmosphere.Muonsareunstableanddisintegrateintootherparticlesalmostimmediately.
423
After being created at the top of the atmosphere, muons decay within 2.2 microseconds or 0.0000022 second. A
microsecondisone-millionthofasecond.Inthistime,themuonwouldtravelonly659meters(0.659km).Becausetheyare
createdbetween10and15kmabovethesurfaceoftheEarth,mostmuonswoulddecaybeforereachingthesurfaceofthe
Earth.Thetroubleishowisitevenpossiblethatmuonsareabletotravelthedistancefromwheretheyarecreatedatthe
topoftheatmospheretothegroundbeforedecaying?Eventravelingatover99percentofthespeedoflight,themuonsdo
nothaveenoughtimetomakeittotheground.Weshouldnotseeanymuonsatall.
Figure125-5Subatomicparticletracks.CourtesyBrookhavenNationalLabs.
However,becausethemuonsaretravelingsofast—accordingtoEinstein’stheoryofrelativity—timeslowsdownforthem.
ThefactthatwecanobservemuonsatthesurfaceoftheEarthservesasproofofEinstein’stheory,whichstatesthatthe
timeforthemovingparticleis
wheretisthetimethemuontakesasobservedfromtheEarth,to isthetimeitwouldtakeforastationarymuon,v isthe
speed of the particle which, in this case, is 0.99c, and c is the speed of light.When viewed through the perspective of
Einstein’stheory,themuon’slifetimebecomeslarger(35microseconds),whichgivesitenoughtimetomakeitthroughthe
Earth’satmospherebeforedecaying.
Anothertrackyoumayseeisthatofapositron,whichismoredifficulttodistinguishfromotherpositivelychargedparticles.
However,justknowingthatmanyofthecloudchambereventsarepositronsissignificantinitself.Apositronistheantimatter
versionofanelectron.Now,beforeyoudismissthisasafar-fetchedcontributionfromsciencefiction,thepositron isvery
commonly found incollision fragments fromcosmic rays. (By theway, if youareascience-fiction fan,antimatterplaysa
prominentroleinDanBrown’sAngelsandDemons.)Whenapositroncollideswithanelectron,thetwoannihilateeachother
andreleaseenergy.Althoughitmaybedifficulttoidentifythisevent,yourcloudchamberpositron-electronannihilationsare
common. This subatomic particle process has actually been developed into a useful application in the form of the PET
scanners found inmanymedical imaging labs.TheP inPETstands for “positron.”Today, thePETscansenablemedical
researchersanddiagnosticianstoimagefunctions,suchasthemetabolismofmalignanttumorsandtheearlydiagnosisof
Alzheimer’sdisease,andtoidentifyriskfactorsforheartconditions.
Althoughthetechnologicalapplicationsofpositronannihilationarecomplex, theyarethesameeventsyoucanobserve
takingplaceinyourcloudchamber.
(Backgroundonsubatomicparticlesandtheirdetectionwasderivedfromthefollowingsource,whichisrecommendedfor
further informationon this topic: “CloudChambersandCosmicRays,A LessonPlanandLaboratoryActivity for theHigh
School Science Classroom,” Cornell University, Laboratory for Elementary Particle Physics, 2006, available from
424
http://www.lepp.cornell.edu/Education/rsrc/LEPP/Education/TeacherResources/cloudchamber.pdf.)
ThePoint
Cosmicrays,consistingofchargedsubatomicparticles,arecontinuouslystrikingtheEarth’ssurface.Theseparticlescanbe
detectedbyobservingthetrackstheyleaveinasupersaturatedvaporinadevicecalledacloudchamber.
425
AppendixA
WheretoGetStuff
PASCOScientific
10101FoothillsBlvd.
Roseville,CA95747-7100
1-800-772-8700
www.pasco.com
Sargent-Welch
P.O.Box4130
Buffalo,NY14217
1-800-727-4368
www.sergentwelch.com
FlinnScientific,Inc.
P.O.Box219
Batavia,IL60519
1-800-452-1261
www.flinnsci.com
FreyScientific
c/oSchoolSpecialtyScience
80NorthwestBlvd.
Nashua,NH03063
1-800-225-3739
www.freyscientific.com
EdmundScientific
60PearceAve.
Tonawanda,NY14150
1-800-728-6999
www.scientificsonline.com
DaedalonCorporation
P.O.Box727
Waldoboro,Maine04572
1-800-299-5469
www.daedalon.com
RadioShack
www.radioshack.com
426
AppendixB
(MoreThan)EnoughPhysicstoGetBy.(HighlyOptional)
Equations
Project1
v=Δd/Δt
Project2
d=do+vt
Project3
d=do+v(t–to)
Project5
F=ma
Project8
Project9
v=R/t
R=(v2/g)sin2θ
h=(vsinθ)2/2g
Project10
vx=R/t
Project13
427
Project17
Project19
g=2d/t2
a=2d/t2
Project22
Project31
Project51
Project56
Project67
Project68
Project70
f=v/2(L+0.8d)
Project77
v=λf
v=331+0.6T
Project81
428
Project83
Project85
nisin(θi)=nrsin(θr)
Project86
I/Io=cos2θ
Project96
wherekistheCoulombconstant=9.0×109m2/C2
Project100
Ohm’slaw
V=RI
R=VI,and
I=V/R
Rseries=R1+R2
1/Rparallel=1/R1+1/R2+…
Project103
ThecurrentforachargingcapacitorisgivenbyI=Ioe−t/RC
ThevoltageforachargingcapacitorisgivenbyV=Vo(1–e−t/RC)
ThecurrentforadischargingcapacitorisgivenbyI=Ioe−t/RC
ThevoltageforadischargingcapacitorisgivenbyV=Voe−t/RC
Project116
I=IoeqV/kT
Project121
Ephoton=hf
Project125
429
Unitsusedinthisbook
Length
1m=3.28ft
1mile=1.61km
1inch=2.54cm
Time
1day=86,400s
1year(365¼days)=3.16×107s
EnergyandPower
1J=0.738ft-lb=0.239cal
1kW-hr=3.6×106J1W=1J/s
1hp=746J
Force
1N=0.225lb
1lb=4.45N
Weightandmass
A1kgmasshasaweightof9.8N(onEarth)
A1kgmasshasaweightof2.2lbs(onEarth)
Speed/velocity
1m/s=2.24mi/hr
1km/hr=0.621mi/hr
1km/hr=0.278m/s=0.91ft/s
Volume
1cc=1cm3=1mL
1liter(l)=1000cm3
1gal=3.79liters
Pressure
430
1Pa=1N/m2=1.45×10−4lb/in2
1atm=1.01×105Pa=14.7lb/in2(psi)
=760mm-Hg
=760torr
Examplesofprefixes
1km=1000m
1kg=1000g
1m=100cm=1000mm
1liter=1000mL
1μm=1×10−6meter1nm=1×10−9meter1megohm=1×106ohm
431
Index
absolutezero
acceleration
directionof
andforce
gravitationdeterminedbyapendulum
measuredbyGalileo
measurementof
accelerometer
airpressure
airtrack
Aleo,Chris
alligatorclip
alphaparticles
alternatingcurrent(AC)
AmericanWireGauge(AWG)
americium
ammeter
angle
ofreflection
ofrefraction
ofrepose
angularvelocity
antimatter(AngelsandDemonsbyDanBrown)
Archimedes’principle
astronauts
Apolloastronauts
Atwood’smachine
balloon
ballparkestimate
Bardeen,John
basketball
battery
BCStheory
beatfrequency
bedofnails
Beatles,The
Bernoulli,Johann
betaparticles
bigG
birds(andNewton’sthirdlaw)
blowdryer
Bohr,Niels
bottlerocket
bowlingball
Brachistochrone
Bradbury,Ray
breakdownvoltage
432
Brewsterangle
BrookhavenNationalLabs
bulb,light
Christmastree
electroscope
induction
neon
numberofphotons
bullet
buoyantforce
buzzer
calculator
candle
capacitor
Cartesiandiver
Cash,Johnny
cathoderaytube(CRT)
Cavendish,Henry
centerofgravity
centerofmass
ceramic
hotplatetop
radioactive
superconducting
CERN
chainreaction
Charles’law
circuit
cloudchamber
coefficient
offriction
ofvolumeexpansion
collision
elastic
inelasticcollision
productionofcosmicrays
subatomicparticles
compressor,air
computers
conservation
conservation
ofangularmomentum
oflinearmomentum
Cooper,Leon
Copernicus,N.
copper
corkgun
CornellUniversity
cosmicrays
coulomb
433
CRT
CSI
current
cycloid
DaedalonCorporation
DataStudio
DCpowersupply
DeGregorio,Brad
diffraction
diffractiongrating
diode
discovery
displacement
dollar
Dopplereffect
doubleslitexperiment
Dragoiu,T.
drum-gallon
dryice
dumbbells
Earth
atmosphere
magneticfieldof
massof
EasyScreen
eddycurrent
EdmundsScientific
Einstein,Albert
generalrelativity
photoelectriceffect
specialrelativity
Eisenhower,DwightDavid
EleanorRigby,byTheBeatles
electronspin
electroscope
elevator
ElihuThomson,ringtosser
ellipse
energy
equilibrium
ESPN
Excel.
fancar
Faraday,Michael
feather
fishtank
FlinnScientific
force
centrifugal(fictitiousforce)
434
centripetal
electrostatic
friction
gravity
magnetic
free-fall
frequency,
beat
fundamental
natural,resonant
overtone
FreyScientific
friction
GalileoGalilei
galvanometer
Gay-Lussacapparatus
generalrelativity
GorillaGlue,Tape
Grabowski,Stephen
gravity
gravitywell
Greenland
gyroscope
happy/sadballs
heatoffusion,latentheat
Hovercraft
HoverPuck
hydrogen
hydrogentube
ice
implodingcan
impulse,andmomentum
indexcard
index
ofrefraction
ofrefraction,variable
induction
inertia
insulatedwire
interference,
constructiveinterference
destructiveinterference
interferencepattern
iron
Kepler’slaw
kineticenergy
andphotoelectriceffect
laser
435
latex
leafblower
lens
Lenz’slaw
Leydenjar
light
intensity
meter
monochromaticlight
polarized
speedof
totalinternalreflection
lightemittingdiode(LED)
lightning
liquidnitrogen
Lissajouspattern
littleg
logarithmicscale
Maglevtrain
magnet
accelerationfrom
bendingcosmicrays
braking
cosmicraybendingfrom
cube
neodymium
toholdlensonchalkboard
usedinmotor
magneticfield,
ofEarth
onacurrentinawire
onanelectronbeam
induction
levitation
sensor
shapeof
magneticresonanceimaging(MRI)
magnifyingglass
Malus’slaw
marshmallow
mass
Maxwell,JamesClerk
Meissnereffect
MichiganStateUniversity
microphone
microwaveoven
milk
Millikan,Robert.
Mingdynasty
mirror
436
Misniak,Tom
momentofinertia
momentum
monkey(andcoconut)
moon
motionsensor
mousetrap
multimeter
muon
Mythbusters
NASA
neonbulb
neutralbuoyancy
neutron
NewJerseyTurnpike
Newton’scradle
Newton,SirIsaac
firstlaw
secondlaw
thirdlaw
NobelPrize
non-magneticmaterial
NorthPole
Oersted,Hans
Ohm’slaw
oil-dropexperiment.SeeMillikan,Robert
opticalfibers
optics
oscilloscope
OurFriendtheAtom,byWaltDisney
painteronscaffoldproblem
papercup
PASCOScientific
Peltiereffect
pendulum
period
phasechange
photoelectriceffect.SeeEinstien,Albert
photon
ping-pong
Pisa,LeaningTowerof
Planck’sconstant
plasmaglobe(SunderBall)
PlayDough
pokerchips
polarizingfilters
positron
positronemissiontomography(PET)
potentialenergy
437
powersupply.SeeDCpowersupply
pressure
defined
projectile
atanangle
defined
footballas
horizontalprojectile
launcher
monkeyandcoconut
protractor
pulley
Pythagoreanformula
quantummechanics
RadioShack
rectangularprism
reflection
refraction
defined
resistance
copper
iron
measurement
resonance,resonantfrequency
right-handrule
ringtosser
rippletank
rubberrod
safety
sailboat
Sargent-Welch
satellite
Schrieffer,John
SCUBA
SearsTower
Seebeckeffect
semiconductorheating
seriescircuit
shavingcream
Silver,Dan
skydivers
smokedetectors
Snell’slaw
sodiumdoublet
solarcell
solderingiron
sound
meter
speedof
438
SouthPole
spark
specialrelativity
specificheat
spirograph
spreadsheet.SeeExcel
spring
springconstant
Sputnik
standingwave
staticcharge
staticequilibrium
staticfriction
stopwatch
subatomicparticles
suctioncup
Sunderball(PlasmaGlobe)
sunglasses
superposition.Seealsointerference
supersaturatedvapor
cloudchamber
tablecloth
temperaturesensor(thermocouple)
terminalvelocity
teslacoil
Thanksgivingdinner
thermometer
ThomasYoung,doubleslitexperiment
Thomson,Elihu
Thomson,J.J.
thorium
tightropewalkers
tonegenerator
toolbin
torque
Torricellibarometer
transversewave
truck(birdsflyingin)
tugofwar
tuningfork
turntables
UniversityofMaryland
uraniumatom
USBport
vandeGraaffgenerator
Velcro
velocity
average
constant
439
andkineticenergy
measurement
andmomentum
ofoildrop
relationshipwithcentripetalforce
ofsatellite
usedtofindrangeofaprojectile
versustime
ofwave
videocamera
voltage
voltmeter
AC
DC
Voyager
wave
electromagnetic
light
longitudinal
sound
transverse
waveformgenerator
wavelength
weightless
Wimshurstmachine
workfunction
yardsale
YBa2Cu3O7
Young,Thomas
Zeemaneffect
440
TableofContents
Introduction 12
Section1Motion 19
Project1Gettingstarted.Constantvelocity.Runningthegauntlet 19
Project2Picturingmotion.Gettingamoveon 23
Project3Thetortoiseandthehare.Playingcatch-up 27
Project4Howdoesasailboatsailagainstthewind?Componentsofforce 30
Project5Steppingonthegas 35
Project6Rollingdownhill.Measuringacceleration 38
Project7Independenceofhorizontalandverticalmotion.Basketballtossedfromarollingchair 41
Project8Targetpractice.Horizontalprojectile—rollingoffatable 44
Project9Takingaim.Shootingaprojectileatatarget 47
Project10Mondaynightfootball.Trackingthetrajectory 51
Project11Monkeyandcoconut 55
Section2GoingAroundinCircles 60
Project12Whatisthedirectionofasatellite’svelocity? 60
Project13Centripetalforce.Whatisthestringthatkeepstheplanetsinorbit? 62
Project14Agravitywell.Followingacurvedpathinspace 70
Project15Howfastcanyougoaroundacurve?Centripetalforceandfriction 72
Project16Ping-pongballsracinginabeaker.Centripetalforce 74
Project17Swingingapailofwateroveryourhead 77
Section3Gravity 80
Project18Featherandcoin 80
Project19Howfastdothingsfall? 84
Project20Thebuckstopshere(thefallingdollar).Usingametersticktomeasuretime 90
Project21Weightlesswater.Losingweightinanelevator 93
Project22Whatplanetareweon?Usingaswingingobjecttodeterminethegravitational
acceleration97
Section4ForceandNewton’sLaw 100
Project23Newton’sfirstlaw.WhattodoifyouspillgravyonthetableclothatThanksgivingdinner 100
Project24Newton’sfirstlaw.Pokerchips,weightonastring,andafrictionlesspuck 103
Project25Newton’ssecondlaw.Forcinganobjecttoaccelerate 106
Project26Newton’sthirdlaw.Equalandoppositereactions 111
Project27Newton’sthirdlaw.Bottlerockets.Whydotheyneedwater?(SirIsaacNewtoninthe
passenger’sseat.) 114
441
Project28Pushingwater.Birdsflyinginsideatruck 117
Project29Slippingandsliding 119
Project30Springs.Pullingback.Thefurtheryougo,theharderitgets 121
Project31Atwood’smachine.Averticaltugofwar 123
Project32Terminalvelocity.Fallingslowly 126
Project33Balancingact.Painteronascaffold 129
Project34Hangingsign 132
Project35Pressure.Implodingcans 135
Project36Pressure.Supportingwaterinacup 138
Project37Pressure.Sometimesthenewscanbeprettyheavy 140
Project38Archimedes’sprinciple.Whatfloatsyourboat? 143
Project39Cartesiandiver 145
Project40Anair-pressurefountain 147
Project41Blowingupamarshmallow.Lessiss’more.Whyastronautsdonotuseshavingcreamin
space151
Project42Relaxingonabedofnails 153
Project43Blowinghangingcansapart.WhatBernoullihadtosayaboutthis 156
Project44Centerofmass.Howtobalanceabroom 159
Project45Asimplechallenge.Moveyourfingerstothecenterofameterstick 161
Project46Centerofgravity.Howfarcanastackofbooksextendbeyondtheedgeofatable? 164
Project47Centerofmass.Theleaningtowerofpizza 167
Section5Energy/Momentum 172
Project48Thependulumandyourphysicsteacher’sMingdynastyvase 172
Project49Twoslopes.Differentangle,sameheight 174
Project50Racingballs.Thehighroadversusthelowroad.Whichwins? 177
Project51Linearmomentum.Wherecanyoufindaperfect90-degreeangleinnature? 182
Project52Elasticcollisions 186
Project53Inelasticcollision.Stickingtogether 189
Project54Impulseandmomentum.Eggstremephysics 192
Project55Usinggravitytomoveacar 194
Project56HowcanCSImeasuremuzzlevelocity?Theballisticpendulum 196
Project57Angularmomentum.Ridingabike 198
Project58Momentofinertia.Iceskatersanddumbbells 200
Project59WhatcausedVoyagertopointinthewrongdirection? 203
Project60Momentofinertia.Thegreatsoupcanraceorthat’showIroll 206
Project61Makingwaves.IthoughtInodethis 208
442
Project62Rollinguphill 212
Project63Gettingaroundtheloop.Fromhowfarabovethegrounddoestherollercoasterneedto
start?215
Section6SoundandWaves 218
Project64Whatdoessoundlooklike?Oscilloscopewaveforms 218
Project65Rippletank 228
Project66Simpleharmonicmotion.Theswingingpendulum 232
Project67Simpleharmonicmotion.Thespringpendulum 235
Project68Generatingsinewaves 238
Project69Naturalfrequency 241
Project70Bunsenburnerpipeorgan.Resonantfrequency 243
Project71Springsandelectromagnets.Resonance 246
Project72Speedofsound.Timinganechooldschool.WhyGalileocouldn’tdothiswithlight 248
Project73Speedofsound.Resonanceinacylinder 250
Project74Racingagainstsound.Dopplereffect 253
Project75Addingsounds.Beatfrequency 255
Project76Pendulumwaves 258
Project77Usingwavestomeasurethespeedofsound 261
Section7Light 266
Project78Rayoptics.Tracingthepathoflightusingalaser 266
Project79Twocandles,oneflame 274
Project80Laserobstaclecourse 277
Project81Lightintensity.Puttingdistancebetweenyourselfandasourceoflight 280
Project82Howdoweknowthatlightisawave?ThomasYoung’sdoubleslitexperimentwitha
diffractiongrating283
Project83Howtomeasurethesizeofalightwave 285
Project84Thespeedoflightinyourkitchen.Visitingthelocalhotspots 288
Project85Refraction.Howfastdoeslighttravelinairorwater? 291
Project86Polarization.Sunglassesandcalculatordisplays 294
Project87Whatisthewireofafiber-opticnetwork?Totalinternalreflectionusingalaseranda
tankofwater299
Project88Thedisappearingbeaker 303
Section8HotandCold 306
Project89HowmuchheatisneededtomeltGreenland?Heatoffusion 306
Project90Awaterthermometer 309
Project91Whatisthecoldestpossibletemperature?Estimatingabsolutezero 312
443
Project92Liquidnitrogen 316
Project93Boilingwaterinapapercup 320
Project94Boilingwaterwithice 322
Project95Seebeckeffect/Peltiereffect.Semiconductorheating 325
Section9ElectricityandMagnetism 328
Project96Staticcharges 328
Project97Makinglightning.ThevandeGraaffgenerator 333
Project98TheWimshurstmachine.Separatingandstoringcharges 338
Project99Runningintoresistance.Ohm’slaw 341
Project100Circuits:Bulbsandbuzzers 344
Project101Howdoesheataffectresistance? 347
Project102Resistivity.Canironconductelectricitybetterthancopper? 349
Project103Storingcharge.Capacitors 352
Project104Isthemagneticforcemorepowerfulthangravity? 356
Project105Magneticlevitationusinginduction.Electromagneticringtosser 360
Project106Magneticlevitationusingsuperconductivity.TheMeissnereffect 363
Project107Movingelectronsproduceamagneticfield.Oersted’sexperiment.Themagneticfield
ofacurrent-carryingwire367
Project108Faraday’sexperiment.Currentgeneratedbyamagnet 369
Project109Ifcopperisnotmagnetic,howcanitaffectafallingmagnet?Lenz’slaw 371
Project110Effectofamagnetonanelectronbeam.Theright-handruleformagneticforce 375
Project111Whatistheshapeofamagneticfield? 378
Project112Whathappenstoacurrent-carryingwireinamagneticfield? 380
Project113Ano-frillsmotor 382
Project114Magneticaccelerator 385
Project115Alternatingcurrent 387
Project116Thediode.Anelectronicone-wayvalve 391
Section10TheEarth 394
Project117MeasuringtheEarth’smagneticfield 394
Project118WeighingtheEarth 399
Section11TheTwentiethCentury 402
Project119Whatisthesizeofaphoton? 402
Project120HowisahydrogenatomliketheNewJerseyTurnpike?Seeingtheenergylevelsof
theBohratom405
Project121Photoelectriceffect 408
Project122Millikanoil-dropexperiment.Mysterymarbles.Understandinghowtheexperiment412
444