phy1025f practical manual - uct physics department · 2016 phy1025f practical manual 10 v1.1 –...

2016PHY1025FPracticalManual v1.1–January2016

PHY1025F

PRACTICAL

MANUAL


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PHY1025FPracticalManual

TABLEOFCONTENTS

L1–ReactionTime..................................................................................................5

L2–Hooke’sLaw.....................................................................................................7

L3–LinearMotion..................................................................................................9

L4–Flywheel........................................................................................................11

L5–Viscosity.........................................................................................................15

L6–ThinLenses....................................................................................................15

L7–SpeedofaWaveonaString..........................................................................23

L8–ElectricFieldMapping...................................................................................25

L9–ElectricCircuitsWorksheet..................................[HandoutonDayofPractical]

N1–NotesfortheReactionTimePractical...........................................................27

Introduction......................................................................................................27

Planninganexperiment.....................................................................................27

Writingalaboratoryreport...............................................................................28

Graphsandbest-fitline.....................................................................................31

N3–NotesfortheLinearMotionPractical...........................................................32

TheLoggerProandLoggerLiteSoftware...........................................................32

UsingLoggerProandLoggerLite.......................................................................32

N5–NotesfortheViscosityPractical....................................................................34

LINEARFIT..........................................................................................................34

N6–NotesfortheThinLensesPractical................................................................34

TYPEAevaluationofuncertainty.......................................................................35

Comparingresults..............................................................................................36


L1–ReactionTime

Goals

1. Usea1Dkinematicequationtomeasureyourreactiontime2. Investigatehowavarietyofstimulimayimpactreactiontime3. Collectdataandproduceawell-formattedtable

Thedeliverableforthispracticalisanabbreviatedwrite-upincludingthefollowingsections:DATA,ANALYSIS,UNCERTAINTY,andCONCLUSIONS.

ReactionTimeMeasurement

Introduction

Reactiontimeisthetimebetweenastimulusandyourresponse.Thestimulusisprocessedbyyournervoussystembeforeyouareabletoreact,andthetimelagisyourreactiontime.Stimulicouldbevisual(sight),auditory(hearing),tactile(touch),olfactory(smell)orgustatory(taste).

Inthisexperimentyouwillbemeasuringyourreactiontimewhenpresentedwithvisual,auditoryandtactilestimulation. Theonlyequipmentyouwill need is ameter stick. Because thedistanceanobject falls is afunctionoftime,youcanmeasurethedistancethemeterstickdropsandusethistocalculateyourreactiontime.

Theformulaforanobjecttravelingatconstantaccelerationis:

𝑥 = 𝑥! + 𝑣!𝑡 +12𝑎𝑡! (1)

where 𝑥! initialpositionoftheobject 𝑣! initialvelocityoftheobject

𝑎 accelerationoftheobject,inthiscaseaccelerationduetogravity,9.8m/s2 𝑡 elapsedtime

Procedure

Beforeactuallyperformingeachexperiment,discusswithyourlabpartnersthedifferenttypeofstimulation(visual, auditory and tactile) andmakea prediction regarding howeachmight impact your reaction time.Whichtypeofstimuliwillproducethefastestreaction?Whichwillbetheslowest?Why?

Yourpartnershouldholdthemeterstick.Whenyourpartnerdropsthestick,catchitasquicklyasyoucan.Recordthenumberofcentimetersthestickfellbeforeyoucaughtit.Youmaytakethemeasurementatthebottom,middleortopofyourgrasp,butBECONSISTENT.Takeatleastthreemeasurementsforeachtypeofstimulus(themore,thebetter).Makesureyouareisolatingonlyonestimulus,e.g.don’twatchtherulerifyouaretestingforauditoryresponse!Repeattheprocedureforeachpartner.Recordyourowneactiontimesinawell-formattedtable(SeePage29forhelpwithformatting).


Analysis

Onceyouhavecollectedyourdata,convert thedistance fallentotime(willneedtorearrangeEq. (1)andcaptureyourresultsinasecondwell-formattedtable. Includeonlyonesamplecalculation;theotherscanbe done with a calculator. Be careful with your units and be sure to calculate average values for eachstimulus.

Uncertainty

Answerthefollowingquestions:

1. What factors (sources of uncertainty)mayhave produced variation in your reaction time results?Aretheybigorsmall?

2. Howcouldyouminimizethesefactors?

Conclusions

QuestionstoconsiderwhenwritingyourCONCLUSIONS:

1. Forwhichstimuluswasyourreactiontimebest?Why?Diditcoincidewithyourprediction?2. Howdidyourreactiontimedifferfromyourpartners?Wasitasignificantdifference?3. Doyouthinkyoucouldimproveyourreactiontime?Ifso,how?4. Don’tforgettoconsiderthestandarddiscussionpointsforyourconclusion(don’tnecessarilyneed

touseallofthem,seepage30formoreinformation).a. Quotingthefinalresult.b. Comparingthisresultwithothersandmakingcommentsasappropriate.c. Discusstheuncertaintyinthepractical.d. Suggestwaystoimprovetheexperiment.


L2–Hooke’sLaw

Goals

1. Investigatetherelationshipbetweenanextensionofaspringandthemagnitudeoftheappliedforce2. Drawingabest-fitlinetographicaldataanddeterminingtheslopeofthebest-fitline


DeterminingaSpringConstant

Introduction

Ithasbeenobservedthattheapplicationofaforcetoaspiralspringwillcausetheextensionofthatspring.Whatisnotcleariswhethertherelationshipbetweentheappliedforceandextensionofthespringislinear,i.e.,willdoublingtheappliedforcedoubletheextension?

Thisrelationshipmaybedeterminedbyplottingagraphoftheappliedforcevs.springextensionandthen,iftherelationshipislinear,thespringconstantkcanbefoundbyapplyingHooke’sLaw:

𝐹 = 𝑘𝑥 (2)

where𝐹isthemagnitudeoftheappliedforceand𝑥isthemagnitudeofthespringextension.

NotethatwhenHooke’sLawisstatedinvectorform,theequationbecomes

𝐹 = −𝑘𝑥 (3)

where the negative sign indicates the direction of the force exerted by the spring with respect to thedisplacementoftheendofthespring, i.e., thespringreactsbyopposingtheextension𝑥,whilethespringconstant,𝑘,isalwaysapositivenumber.

Procedure

You are supplied with a spiral spring suspended from a retort stand, a small bucket, a number of ballbearingsofgivenmass,andametrestick.

In thisexperimentaknown force is applied to the spiral springbyhangingamass𝑚from theendof thespring.Themagnitudeoftheforceexertedonthespringis𝑚𝑔andtheextensionproducedbytheappliedforceismeasuredwiththeaidofthemetrestick.

Themassofeachballbearingisapproximately13.7grams.Confirmthemassofanyoneoftheballbearingsbyusingatriple-beambalance.

Beginbyattaching thebucket to theendof the springandusing thepointeron theendof the spring torecordtheheightofthebucketabovethetabletop.Nowaddtheballbearingsoneatatime,recordingthenewpositionofthepointeraseachballisadded.Takeasmanyreadingsasyoucan.Tabulatethedatainawell-formedtable.


Analysis

Usingtheattachedinstructions,plotthedataonagraphofforce(y-axis)vs.extension(x-axis).

Drawalineof‘bestfit’byeye.

Note: If you obtain a straight-line graph that passes through the origin, then the extension is directlyproportionaltotheforceexertedonthespring.Ifthegraphisastraightline,butdoesnotpassthroughtheorigin,thenthegraphindicatesthattheextensionislinearlyrelatedtotheappliedforce,butisnotdirectlyproportional.

Ifitisestablishedthatthespringextensionisdirectlyproportionaltotheappliedforce,thentheconstantofthat proportionality can be obtained from the slope𝑚of the straight-line graph since the equation for astraightlineis𝑦 = 𝑚𝑥 + 𝑐.

Whenyoudeterminetheslopeofthebest-fitline,dosobychoosingtwoconvenientpointsthatareasfarapartaspossibleontheline.Whendetermining𝑚,donotusesomearbitrarypairofdatapoints;youneedtodeterminetheslopeofthebestfitline–nottheslopeofalinebetweentwoarbitrarydatapoints.

Fromtheslopeofthegraph,determinethespringconstant.

Uncertainty


1. Whatfactorsmayhaveproducedvariationinyourmeasurements?Aretheybigorsmall?2. Howcouldyouminimizethesefactors?

Conclusions


1. Quote your calculated spring constantwith appropriate units. Does this value seem reasonable?Whyorwhynot?

2. Howdoesyourvaluecomparetoonefromanothergroup?3. Areyouconfidentinyourresult?Howcouldyoubemoreconfidentinyourspringconstantvalue?


L3–LinearMotion

Goal

1. Investigate linear motion, specifically position, velocity and acceleration using Vernier GoMotionsensors.

There is no formalwrite-up required for this practical, but youwill hand in a lab book inwhich you havetabulatedandgrapheddata,andinwhichyouwillhavemadenotesandansweredspecificquestionsaboutthetwoinvestigationsdoneduringthepractical.

Part1–AccelerationofaFreeFallingObject

Aim

The aim of Part 1 is to determine the accelerationwithwhich a free-falling object falls, and to considerwhetherthisagreeswiththegenerallyacceptedvalueofthegravitationalacceleration,g,inCapeTown.

Procedure

Theapparatus isaVernierGoMotionsensorthat isabletorecordthepositionofa free-fallingobject; thecomputationaldevicethatcontrols theGoMotionsensor isabletocalculatetherelevantpositionvs. timeandvelocityvs.timegraphs.(Usethe03LinearMotionPart1LoggerLiteTemplatefoundonVula.)

Pickyourfree-fallingobjectfromtheavailableselection:aplasticcone,anetballandaminisoccerball.

Capture asmany graphs as youneed – at least six (6) – and from these determine the rangeof possiblevaluesoftheaccelerationwithwhichthefree-fallingobjectfell.TherecommendedmethodtodeterminetheaccelerationistousetheLinearFitfunctiononaselectedportionofthevelocityvstimegraph.Notethattheansweryouwillgetwillnotbeaspecificvalue,althoughyouarewelcometodeterminetheaverageofthesevalues,butarangeofvalues,i.e.,theanswerisanintervalofnumbers.

Analysis

Isthegenerallyacceptedvalueofthegravitationalaccelerationofg=(9.79824±0.00044)m/s2withinyourmeasuredinterval?Commenteitherway.

Part2–CartonanInclinedPlane

Aim

TheaimofPart2istoinvestigatetheposition,velocityandaccelerationvs.timegraphsofacartthatgoesupanddownaninclinedplane.

Procedure

Theapparatuscomprisesofacartonaninclinedtrack,andaVernierGoMotionsensorthatisabletorecordthepositionof the cart (with reference to the sensor). At the bottomof the track there is a spring thatallowsthecartto‘bounce’backupthetrack.ThedesktopPCconnectedtotheGoMotionsensorisabletocalculatetherelevantmotiongraphs.(UsethePHY1025FPractical3Part2iconfoundonthedesktop.)


Letthecartgofromthetopofthetrack(startthecartabout30cmfromthefaceofthesensor)andcaptureasetofgraphs–positionvs. time,velocityvs. time&accelerationvs. time–ofthecartas it runsupanddownthetrack.

Onceyouarehappywiththecapturedmotiongraphs,carefullycopythethreegraphs–byhand–ontoasinglepieceofgraphpaperandpastetheseinyourlabbook.

Analysis


1. Is the acceleration always positive when the velocity is positive, and is the acceleration alwaysnegativewhenthevelocityisnegative?Whyorwhynot?

2. Istheaccelerationofthecartupthetrackthesameastheaccelerationofthecartdownthetrack?Whyorwhynot?


L4–Flywheel

Goals

1. Investigatetherelationshipbetweenlinearmotionandangular(rotational)motion;andspecificallyinvestigatethetransferofpotentialenergyintolinearkineticenergy,rotationalkineticenergy,andthermalenergy.

2. Verifytheenergybalanceequationwhichisunderpinnedbythelawofconservationofenergy.


ConservationofEnergy

Introduction

Consider the relationshipbetween theangular velocity𝜔(speedof rotation),of anobject likea flywheel,andtheinstantaneouslinearvelocity𝑣ofapointonthecircumferenceoftherotatingobject.SeeFigure1.Thelinearvelocity𝑣ofapointonthecircumferenceoftheaxlewilldependontheangularvelocity𝜔,andthedistanceofthepointfromthecentreofrotation,i.e.,theradius𝑟oftheaxle.

Figure1:Diagramshowingtherelationshipbetween𝜔and𝑣

Therelationshipbetweentheangularvelocity𝜔andthelinearvelocity𝑣is:

𝑣 = 𝜔𝑟 (4)

where 𝑣 linearvelocityatapointontherotatingobject(inm/s) 𝜔 angularvelocityoftheobject(inrad/s)

𝑟 distanceofthepointfromthecentreofrotation(inm)

NowconsiderthecaseofamassconnectedtotheflywheelasshowninFigure2.


Figure2:Diagramshowinghowthefallingmassacceleratestheflywheel

Themass𝑚has a certain potential energy when it is at heightℎ!, and some of that potential energy isconvertedasthemassmovesdownthroughdistance𝑠toheightℎ!.Thechangeinpotentialenergy,∆𝑈!,isconverted into the kinetic energy of the falling mass,𝐾𝐸!"#$%&, and the rotational kinetic energy of theflywheel,𝐾𝐸!"#$#%"&$',withsomeoftheenergybeingdissipatedthroughfriction,producingthermalenergy,∆𝐸!!!"#$%.Thesystemisdefinedastheflywheelandthefallingmasswiththeassumptionthatallenergyisbeingconserved;anynon-conservative forceswill contribute to the∆𝐸!!!"#$% term. The resultingenergyconservationequationis:

∆𝐸 = 0 → ∆𝑈! + ∆𝐾𝐸!"#$%& + ∆𝐾𝐸!"#$#%"&$' + ∆𝐸!!!"#$% = 0

andaftersomerearrangement(andignoring∆𝐸!!!"#$% fornow)

𝑚𝑔 ℎ! − ℎ! =12𝑚𝑣!! +

12𝐼𝜔!! (5)

where 𝑚 massofthefallingmass 𝑔 gravitationalacceleration ℎ! − ℎ! changeinheightuntildisengagement,i.e.(ℎ! − ℎ!) 𝑣! velocityofmass𝑚atthepointofdisengagement 𝜔! angularvelocityoftheflywheelatdisengagement

𝐼 momentofinertiaoftheflywheel


Themoment of inertia,𝐼, of an object, around some given axis of rotation, is a proportionality constantbetweentheappliedtorque𝜏andtheangularacceleration𝛼oftheobjectaroundthataxis.(Inasenseitistheequivalentofmassm in linearmotion,which isaproportionalityconstantbetweentheapplied force,𝐹andtheacceleration𝑎ofthemass,i.e.,𝐹 = 𝑚𝑎.)So,ingeneral,𝜏 = 𝐼𝛼.

Themomentofinertiaofanobject,aroundsomegivenaxis,dependsonthemassoftheobject,aswellasthewayinwhichthatmassisarrangedaroundtheaxisofrotation;morespecifically,𝐼dependsonthesumofthemassofeachparticleintheobject,multipliedbythesquareoftheradiusofrotationofeachparticlearoundthegivenaxis,i.e.𝐼!"! = 𝑚!𝑟!!

SubstitutingEq.(4)intoEq.(5),weget

𝑚𝑔 ℎ! − ℎ! =12𝑚𝑣! +

12𝐼𝑣𝑟

! (6)

Procedure

TheapparatustobeusedisshowninFigure2.

Mass𝑚isattachedtoalengthofstringandthefreeendofthestringcanbehookedontoapinontheaxleof the flywheel. Theaxlemaybe turnedsoas towind thestringaround thenarrowpartof the flywheel(radius𝑟)anumberoftimesasshown.Themassappliesaconstanttorque𝜏totheaxleandwhenthemassisreleasedfromrest,itacceleratestheflywheel(angularly),foraslongasthestringisconnectedtotheaxle.

• Usingatriple-beambalance,determineandrecordthemass𝑚.• Using theVernier calipers supplied to you, determine the diameter of the axle aroundwhich the

stringhasbeenturned,thencalculateandrecordtheradius𝑟oftheaxle.• Determineandrecordthedistance,𝑠 = (ℎ! − ℎ!),throughwhichthemasswillfallwhilethestring

appliesatorque𝜏totheflywheel.Therearetwopossiblewaystodeterminethedistance.o Usingameterstick,measuretheinitial(hi)andfinalposition(hf)ofthemass.o Usingthepositionvs. timegraphproducedbytheGoMotionsensor, the initialpositionof

themass(hi)willcorrespondtothelowestpointonthegraphandthefinalposition(hf)willcorrespondtothehighestpointonthegraph.

Forsix (6)repeats,andusingtheGoMotionsensorprovided,recordandtabulatethevelocityof themasswhen it reachesheightℎ!, i.e.,when the string is released from theaxle. Note:usea consistent startingpointnocloserthan15cmfromtheGoMotionsensor.

Table1:Positionℎandvelocity𝑣valuesforthefallingmass

Recording# h2(m) h1(m) Velocity@h1(ms-1)1 2 3 4 5 6 Averages:


Analysis

Calculatethemeanvelocity(𝑣)fromthetabulatedreadings.Fromtherangeofvelocityvalues,estimatetheuncertainty𝑢(𝑣)inthemeasurementoftheaveragevelocity(atheightℎ!).

Using𝑔 = 9.8 𝑚𝑠!! and𝐼 = (31.0 ± 1.0)× 10!! 𝑘𝑔𝑚! , calculate∆𝑈! ,∆𝐾𝐸!"#$%& , and∆𝐾𝐸!"#$#%"&$' atthemomentthatthemassreachesheightℎ!.

Calculate a value for∆𝐸!!!"#$% . The energy equation (Eq. (6)) incorporating non-conservative forcesbecomes:

𝑚𝑔 ℎ! − ℎ! =12𝑚𝑣! +

12𝐼𝑣𝑟

!+ ∆𝐸!!!"#$% (7)

Uncertainty


1. Whatfactors(sourcesofuncertainty)mayhaveproducedvariationinyourvelocitymeasurements?Aretheybigorsmall?


Conclusions


1. DotheseenergieslookreasonableanddotheysatisfyEq.(6)(i.e.does∆𝐾𝐸!"#$%& +∆𝐾𝐸!"#$#%"&$' =∆𝑈!)?

2. Whatnon-conservative forces contributed to your value for∆𝐸!!!"#$%? Did your∆𝐸!!!"#$% valuesurpriseyou?

3. Don’tforgettoconsiderthestandarddiscussionpointsforyourconclusiona. Quotingthefinalresult.b. Comparingthisresultwithothersandmakingcommentsasappropriate.c. Discusstheuncertaintyinthepractical.d. Suggestwaystoimprovetheexperiment.


L5–Viscosity

Goals

1. Investigatetheeffectofthevariablesinhydrodynamicflowofaviscousliquid.2. Calculatetheviscosityofwater.3. Performevaluationofuncertaintyandcomparetoknownresults.4. Considerwhethersomesourcesofuncertaintycontributemoretothefinaluncertaintythanothers.

Thedeliverable for thispractical is anabbreviatedwrite-up including the following sections:PRELIMINARYINVESTIGATION,DATA,ANALYSIS,UNCERTAINTY,andCONCLUSIONS.

Aim

Theaimof thisexperiment is to investigate the relationshipbetween the flowofa liquid, thehydrostaticpressure,thelengthofthetubeandtheradiusofthetubethroughwhichtheliquidismoving.

Introduction

It has been observed that a pressure difference is required to enable the flow of a viscous fluid in longcylindricaltubeswithaconstantcross-section.Theresultingflowrate(Q)isproportionaltotheradiusofthetubetothepoweroffour.Thishasimportantimplicationsforairflowinlungalveoliandbloodflowinthearteries, and this practical will help you understand the physics behind administering a saline drip to apatient.

Thevolumetricflowrate,Q,isthevolumeofliquid,ΔV,flowinginatimeinterval,Δt,

𝑄 =∆𝑉∆𝑡

(8)

Theflowrateinapipeofconstantcross-sectionmaybedeterminedbyPoiseuille’sLaw,

𝑄 = 𝜋Δ𝑃 8𝜂𝐿

𝑟! (9)

whereΔP isthepressuredifferencebetweentheendsofthepipe,r istheconstantradiusofthepipe,L isthelengthofthepipeandηistheviscosityofthesolution.

The pressure difference in this example is the hydrostatic pressure due to the depth of fluid Δh (alsocommonlyreferredtoasthepressurehead),andthedensityofthefluid(ρwater=1g/cm3),

Δ𝑃 = 𝜌water𝑔∆ℎ (10)

Apparatus

Youaresuppliedwitha‘header’tank(orabucketfilledwithwater),ametrerule,atubeclamp,ameasuringcylinder, and a stopwatch. You also have four plastic tubes – where each tube has a different internaldiameterof2.5,3.0,4.0,4.3mm. Someofthetubeshaveadaptersontheend,whichyoudon’tneedtoremove.Thereshouldbesometowelsnearbyintheeventofaspill.


Figure3:Experimentalsetupforviscositypractical.

Part1:Preliminaryinvestigation(15minutes)

Answerthefollowingquestionsbriefly inyourownwords inyour labbook. Youcanperformsimpletestswiththeapparatus,butyoudon’tneedtorecordtheactualdatainyourreport.

1. If the valve and clamp are open, explainwhy raising the open end of the tube above the bucketstopstheflowofwater.

2. Whydon’tweneedtoconsideratmosphericpressure,P0,incalculatingthepressuredifference?3. Ifweincreasedtheviscosity,orinternalfrictionη,ofthefluid,whateffectwouldthishaveonQ?

Part2:Measuringtheviscosityofwater

Collectingdata(30minutes)

You are required to tabulate the time taken for a 50 ml set volume of the liquid to run through eachhorizontal pipe to findQ as in Equation (9). You can use the timers or a stopwatch to record the time.Replacethecollectedliquidbacktotheheadertankaftereachrun.Measurethelengthofoneofthepiecesoftubing,L,andthedepthofthewaterinthebucket,Δh,withametreruler.Tochangethetubing:

• Whenthetubevalveisparallelorinlinewiththetubing,itisopenandwaterwillflowthrough.

Figure4:Diagramofanopentubevalve(paralleltoflow)

• Whenthetubevalveisperpendiculartothetubing,itisclosed.Carefullyclosethebluevalvetostopthewaterspillingout.

Figure5:Diagramofaclosedtubevalue(perpendiculartoflow)


• Atanytimeifyouareworriedaboutaleak,bringtheopenendofthepipeupabovetheheightofthebucket,andaskademonstratorforhelpifyouareunsure.

• Inanemergency,youcanalsoapplytheclamparoundtheshortsectionofcleartubingcomingoutofthebuckettopreventyourwaterspillingout.Usetowelstomopupanyspills.

• Afterthevalueisclosed,carefullypullthelongpieceoftubeawayfromthevalve.• Pushthenewtubingintoplacebeforeopeningthevalve.Someofthedifferenttubeshaveadaptersto

makethetubingfitonthevalvemoreeasily.Analysis(45minutes)

CalculateandtabulatevaluesofQusingEquation(8)andr4.TakecaretouseSIunitswheninputtingyourdata.

PlottingQ vs r would give us a 4th order polynomial graph,which is difficult both to draw and interpret.Insteaddrawagraph(byhand)ofQvsr4intheformofyvsx.Trytoplotthevaluesofeachaxisinthesameorderofmagnitude,sothescientificexponentisthesameforallthelabelsonanaxis.Remembertoaddabest-fitline.

AlsoplotthegraphusingtheprogrammeusingLinearFitonthelabPCs–instructionsarefoundintheNotes(page34).Enterthedataforr4(x)incolumn1,andQ(y)incolumn2.Thisprogrammefitsalinearbest-fitlinetothedata,intheformofy=mx+casshowninEquation(12).Recordthevaluesofmandcfromthebest-fitlinetothedata.

𝑄 = 𝜋Δ𝑃 8𝜂𝐿

𝑟! + 0 (11)

𝑦 = 𝑚 𝑥 + 0 (12)

Thisisanexampleof“linearisingequations”tosimplifytheinterpretationandreadingofagraph.Anotheradvantageof linearisingacomplexornon-linearequation is thatwecanuse thegradient,m, tocalculateconstants.Inthiscase,youcancalculateandquotetheviscosityofwaterfromthevalueofthegradient,m.

DiscussionandConclusion(30minutes)

Fromyourgraphsandvalues,summarisethefindingofthisexperimentandstatetheconclusion.

Considerthefollowingquestions:

1. CommentonwhetheryourmeasurementsagreewithPoiseuille’sLaw(inotherwords,wastherelationshipbetweenQandr4linear)?

2. How does your value of the viscosity compare to the standard value of 1.0 mPa·s at roomtemperatureof20°Candatmosphericpressure?

3. Arethereareanyfactorswhichhaveinfluencedtheuncertaintyinyourmeasurement?4. Canyouidentifyanyoneofthesefactorsthatyouthinkcontributedthemosttotheuncertainty?


L6–ThinLenses

Goals

1. Usethreemethodstodeterminethefocallengthofathinconverginglens,andthentocomparetheresultsofeachmethod.

2. Performinformalevaluationsofuncertaintyandtocomparemeasuredresults.


DeterminingtheFocalLength

Introduction

Thin lenses are used extensively in scientific andmedical equipment, such as focusing a laser in an eyecorrectionsurgery.Inordertofindthefocallengthofathinlensthemethodof‘noparallax’isoftenused.

Parallaxinthiscontextisdefinedastheapparentdisplacementofonebodywithrespecttoanotherwhenthepositionof theobserver is changed. To illustrate this idea,hold twopencilsatarm’s lengthwithonepencil a few centimetres behind the other, as shown in Figure 6. Close one eye, andwhile keeping thepencilsstill,moveyourheadfromsidetoside.Notehowthepositionofthepencilsrelativetooneanotherseemstochangeasyoumoveyourhead.

Figure6:Demonstratingparallaxerrorwithtwodisplacedobjects

However,ifyoulinethetwopencilsupasshowninFigure7,thereisn’tarelativeshiftinthepositionsofthepencilsasyoumoveyourheadfromsidetoside. Atthisstage,wesaythereis“noparallax”betweenthepencilsandwecanbeconfidentthattheyarethesamedistancefromtheeye.

Thesametechniquecanbeusedtosettwoimages(whetherrealorvirtual)atthesamedistancefromtheeye,or,forthatmatter,animageandapin,orperhapsanimageandacrosswire.


Figure7:Demonstratingnoparallaxerrorwhentwoobjectsarealigned

Procedure

Threemethodswillbeusedtodeterminethefocallengthoftheconverginglens:

Part1–Distantobjectmethod

Arrangetheopticalbenchsothatlightfromanilluminatedobjectatleast10maway(e.g.thewindowsatthe farsideof the laboratory) fallson the lens. Setupthewhitescreenontheoppositesideof the lens,adjustingitspositionuntiltheimageofthewindowissharplyfocusedonthescreen.

Sincetheraysarrivingatthelensfromthewindowareapproximatelyparallel,theywillformanimageatthelens'focallength.Thedistancebetweenthelensandthescreenisthusthefocallengthofthelensandyoumustrecordthisdistancetothenearestmillimetre.

To evaluate the uncertainty in this measurement, simply look at the scale of the metre stick, and thegeometryof the setup,andestimate theuncertainty. Quote theestimateduncertainty toone significantfigure, e.g., ±2 mm, or ±3 mm, or ±4 mm, etc., and then write the result in the form𝑓!"#$ !"#$%& ± 𝑢(𝑓!"#$ !"#$%&),where 𝑢(𝑓!"#$ !"#$%&)istheuncertainty.

Part2–Parallaxmethod

Withoutmovingthebaseoftheapparatusandthelens,removethescreenandreplaceitwithapin.Whilelooking from thepin side, andmoving yourhead fromside to side, adjust thepositionof thepin so thatthereisnoparallaxbetweenthepinandafeatureintheimageofthewindow,suchastheedgeoftheframeorabeam.

Thepinnowmarksthepositionoftheimage,andthedistancefromthelenstothepinisthefocallength.

Aswiththedistantobjectmethod,determine𝑓!"#"$$"% ± 𝑢(𝑓!"#"$$"%),onceagain,estimatetheuncertaintyandwritetheanswertoonesignificantfigure.


Part3–Methodofconjugatefoci

Thismethodmakesuseofthelensequation:

1𝑓=

1𝑑!"#$%&

+1

𝑑!"!!" (13)

where 𝑓 focallengthofthelens 𝑑!"#$%& object-to-lensdistance 𝑑!"#$% image-to-lensdistance

Placethelensatthecentremarkoftheopticalbenchandtheobject-pinapproximately35cmfromthelens.Lookingfromtheimagesideofthelens-andusingthemethodofnoparallax–movetheimagepintowardsandawayfromthelensuntiltheimagepinisatthesamepositionastheimageitself.Adjusttheheightofthepinsandthelenstoseeboththeobjectpinandtheimagepininvertedatthesametime,similartoasshowninFigures1and2.

Recordthedistances𝑑!"#$%&and𝑑!"#$%.Itisnotnecessarytoestimatetheuncertainties.

Keeping the position of the lens fixed,move the object pin 3 cm further away from the lens. As before,locate the position of the image using themethod of no parallax andmeasure the distances𝑑!"#$%&and𝑑!"#$% onceagain.

Repeat theprocedurebymoving theobject pinover a rangeof positions (closer to and further from thelens)until youhave six setsofmeasurements for eachpositionof theobjectpin. Avoidobjectdistancesshorterthanthefocallengthofthelens,asfoundinMethod1.

Foreachpositionoftheobjectpin,calculate𝑓! for i=1,2,3,4,5,6;andtabulatethecalculatedresultsasfollows:

Table2:Calculatedresultsof𝑓! todetermine𝑓 ± 𝑢(𝑓)ofaconverginglenswiththeconjugatefocimethod

Calculation# 𝑑!"#$%&(mm) 𝑑!"#$% (mm) fivalue(mm)1 2 3 4 5 6

Table2shouldshowsixdifferentlengths–anditmaybeassumedthatthesearedistributednormallyaboutthemean – so use procedure outlined in the notes (page 35) to calculate themean𝑓, and the standarddeviation𝜎.


Todeterminethestandarduncertainty,𝑢(𝑓),inameasurementofthistype,youmustdividethestandarddeviationbythesquarerootofthenumberofreadingsused(sixinthiscase):

𝑢(𝑓) =𝜎6 (14)

When reporting this result,quote theuncertaintyof thismeasurement to twosignificant figures,e.g.,1.4mm,or2.3mm,etc.,andthenwritetheresultintheform:𝑓 ± 𝑢(𝑓).

Note: When you quote this result, write the mean𝑓 , to the same number of decimal places as theuncertainty:

Forexample:𝑓 ± 𝑢 𝑓 →154.6±3.8mm.

Analysis

Be careful with your units. Compare the results obtained for the focal length from the threemethods,consultingtheadditionalnotes(page36)forguidanceonhowtodothis.

Drawaraydiagramforeachpart,labellingtheobject,imageandfocallength.

Discusswhichoftheresultsyoubelievetobethemostcorrectandstatewhyyouthinkso.

Uncertainty


1. Whatfactors(sourcesofuncertainty)mayhaveproducedvariationinyourmeasurements?Aretheybigorsmall?


Conclusions


1. Don’tforgettoconsiderthestandarddiscussionpointsforyourconclusion(don’tnecessarilyneedtouseallofthem)

a. Quotingthefinalresult.b. Comparingthisresultwithothersandmakingcommentsasappropriate.c. Discusstheuncertaintyinthepractical.d. Suggestwaystoimprovetheexperiment.


L7–SpeedofaWaveonaString

Goals

1. Usetwomethodstomeasurethespeed𝑣withwhichawavemovesalongastretchedstring,andtocomparetheresultsofthetwomethods.


Part1–VibratingString

Introduction

Inthismethodstandingwavesaregeneratedinastringbyavibratorfedfromapowerfunctiongenerator,asshowninFigure8.

Figure8:Apparatususedtogeneratestandingwaves.

Thefrequencyandwavelengthofawave(𝑓and𝜆respectively)arerelatedtothespeed,𝑣,ofthewavebytheequation:

𝑣 = 𝑓𝜆 (15)

Thestringiseffectivelyfixedatthe“pulleyend”andsothewavesthatareintroducedontothestringbythevibratorarereflectedatthepulley.Thesereflectedwavesinterferewiththewavesthataremovingtowardsthepulley.Atcertainfrequenciesstandingwavesareproducedandseveralnodeswillbeclearlyvisibleonthe string. Since the distance between adjacent nodes is half a wavelength (i.e.𝜆 2), it is possible todeterminethewavelengthofthewavesundertheseconditions. Aplotof𝑓vs1 𝜆shouldyieldastraight-linegraph,andfromtheslope𝑚ofthelineitispossibletodeterminethespeed𝑣ofawaveonthestring.

Procedure

ConnecttheapparatusasinFigure8andadjustthepowerfunctiongeneratortofindfrequenciesatwhichtherearestandingwavesonthestring.Forexample,itisusualtofindastandingwavewithonenodeatthecentreofthestringatafrequencybetween8Hzand11Hz.Otherstandingwavescanbefoundatintegermultiplesofthatfrequency.


Note:

a) The amplitude adjustment should be as small as possible. If the vibratormakes a harshbrrrr…sound,youareoverdrivingit.

b) Sincethevibratorthatgeneratesthewavesonthestringismovingupanddown,thepointatwhichthestringisattachedtothevibratorisnotanode.

Togetthebestresults,measurethedistancebetweentheextremeleftandright-handnodesasshowninFigure8,andthencalculatethewavelengthλofasinglewave.

Recordthefrequency𝑓andwavelength𝜆foratleast6standingwaves.

PlotagraphBYHANDof𝑓vs1 𝜆.

Now determine the slope𝑚 ± 𝑢(𝑚) of the fitted line using LinearFit on the computers in the lab –instructions are found in the Notes (page 34). Note that𝑢(𝑚)is the uncertainty associated with thismeasurement.

Theslope𝑚 ± 𝑢(𝑚)representsthespeedofthewave,𝑣 ± 𝑢(𝑣)onthestring.

Part2–Mass/TensionCalculation

Introduction

Thespeedofawaveonastringisdependentuponthetension𝑇inthestringaswellasthemassperunitlength𝜇ofthestring:

𝑣 = 𝑇 𝜇 (16)

Bymeasuringthetension𝑇inthestringandthestring’smassperunitlength𝜇,itispossibletocalculatethespeed𝑣ofawaveonthestring.

Procedure

Useatriple-beambalancetomeasurethemassofthe‘masspiece’usedtostretchthestringandcalculatethetension𝑇inthestring;assuming𝑔=(9.80±0.02)ms-2.

Sinceonlyonekindofstringisusedinthisexperiment,usethetriplebeambalancetomeasurethemassofthegivenlengthofstring,andusethemetresticktomeasurethelengthofthatpieceofstring. Calculatethestring’smassperunitlength𝜇.

Finally, use equation (16) to calculate the predicted speed𝑣of awave on the string. Estimatewhat youbelievetheuncertaintyinthisresultmaybe,e.g.,2%,4%,6%,etc.

ComparisonofResults,Uncertainty&Conclusion

IncludethestandarddiscussionpointsforyourUNCERTAINTYandCONCLUSION,suchascomparetheresultsofthetwomethods,commentonthetworesultsandwhichyouconsidertobemorecorrect,compareyourresultswithothergroups,discussanypossiblesourcesofdiscrepanciesandhowyouwouldminimizethem.


L8–ElectricFieldMapping

Goals

1. Investigatethenatureofatwo-dimensional,staticelectricfieldby:a. Determiningtheelectricpotentialatvariouspointsinthefield.b. Plottingtheequipotentiallinesinthefield.c. Consideringthegradients(‘downhill’slopes)betweentheequipotentiallines.d. Calculatingtheelectricfieldatvariouspoints.


PlottingtheElectricPotential

Introduction

The concepts of an electric field𝑬and an electric potential𝑉in a region in space are not two different‘things’,theyaresimplytwointer-relatedmathematicalrepresentationsofthesamephenomenon. Inthestaticfieldsthatwillbeconsideredinthispractical,thesetworepresentationsarerelatedbytheequation:

∆𝑉 = −𝑬∆𝒔 (17)

where (consider𝑦 = 𝑚𝑥 + 𝑐), you can see that if you know how the electric potential,∆𝑉, changes in aregion in space,∆s, then you can determine the electric field,𝑬, which is represented by the ‘downhill’gradientofthechangeinpotential.

AscanbeseenintheexampleinFigure9,oncetheequipotentiallineshavebeenplottedinaregion–hereprojectedontoatwo-dimensionalplanewith(𝑥, 𝑦)co-ordinates– the fieldcanbevisualisedbyarrows, with the base of the arrows on theequipotential line,andthedirectionofthearrowsbeing orthogonal (at right angles) to theequipotentiallineatthatpoint.

The arrow points ‘downhill’ (or from a highpotentialtoalowpotential),andthelengthofthearrow depends on the ‘steepness’ of the field atthatpoint.Whentheequipotentiallinesareclosetogether, the gradient is steep, and when theequipotential lines are further apart, the gradientis‘notsosteep’.

Figure9:Exampleofplottedequipotentiallinesusedtovisualisethefield


The apparatus consists of a signal generator, a digitalmulti-meter (DMM), twometal shapes and a clearPerspex tray in which there is a layer of water (3 mm to 4 mm deep). The signal generator, set to afrequencyofapproximately100Hzandanoutputvoltageof5VRMS,isconnectedtothemetalshapesasshown. The digitalmulti-meter is used to read the potential at various points in thewater; and the co-ordinates of each point is determined from a sheet of graph paperwhich is placed under the tray. TheselectedmetalshapesareplacedinthewaterasshowninFigure10.

Figure10:Apparatususedtoreadelectricpotentials

Note: Itwill be easier to track an individual electric potential value if you set theDMM to readonly onedecimalplace.UsetheRANGEbuttontocontrolthenumberofdecimalplaces.

Procedure

Foroneof the twoconfigurations shown inFigure11 takevoltage readingsatanumberofpointson theplane,sufficienttoplottheequipotentiallinesonasheetofgraphpaper.

After completing the equipotential lines, draw the electric field lines (as described in the introduction),sufficienttoinformthereaderthatyouhaveacleargraspofwhatthe𝑬fieldlookslike.

For a selected configuration, calculate the value of the𝑬field at 3differentlocationsbymeasuring∆𝑉and∆𝑠andusingEquation(17).

Uncertainty&Conclusion

Include the standard discussion points for your UNCERTAINTY andCONCLUSION, such as discuss any possible sources of discrepanciesandhowyouwouldminimizethem,commentonyourE-fieldresults,discuss the relationship between the electric field and potential,commentonthedifferentconfigurations,etc…

Figure11:ConfigurationstodeterminetheE-field.


N1–NotesfortheReactionTimePractical

Introduction

ThepurposeofthePHY1025FpracticalsistodevelopskillsinaPhysicscontextthatwillberelevantforyourfutureinthemedicalprofession.Thesepracticalsaredesignedtoworkonthefollowingskills:Discovery(exploringconcepts),Measurement(takingdata),Graphs(displayingdata),Identifyingrelationships(manipulatingdataandvariables),Uncertainty(measurementsarenotexact,identifyingandpropagatinguncertainty)andDrawingConclusions(summarizingaresultbasedsolelyonwhatisobserved).

YourgradeforthePHY1025Fpracticalswillbebasedonyourlabreport.Eachweek,youwillbegivenan8-pagelabbookwhereyouwillcompleteyourwrite-upandthenhanditinattheendofeachpracticalsession.Duetotimeconstraints,youwillnotalwaysbeexpectedtocompleteafulllabreport,butyouwillalwayshavethefollowingsections:DATA,ANALYSIS,UNCERTAINTY,andCONCLUSIONS.Yourlabbookshouldcontainanymeasureddatainawell-formattedtablewithlabels,anexampleofanycalculationsperformed,copiesofanycompletedgraphs,adiscussionoftheuncertaintyinthepractical,andaclearandconcisesummaryofthepracticaldrawndirectlyfromyourobservations.Allworkshouldbecompletedinthelabbook;anyroughworkwillbeignoredwhilemarkingaslongasitisclearlyindicated.

Planninganexperiment

Thereisnofixed‘recipe’bywhichexperimentsinphysicsareperformedbutpleasenotethefollowing:

DO:

Discusswhatyouneedtodowithyourpartners.

Getafeelforhowtheapparatusworks;ifyouareuncertain,callademonstrator.

SetapageortwoasideinyourlabbookforROUGHNOTESandmakelotsofnotesthatcanbeusedinyourreport.

Drawupatableinwhichtorecordthereadingsyouwilltake;thistablewillprovideafocusforthework.Takethenecessaryreadingsandchecktoseeifthedatayouhavegatheredwillbeadequatetomeetthegoalsoftheexperiment.

Important:ALLrelevantinformationmustbecapturedINYOURLABBOOK…,notonscrapsofpaperornotepads.Youwillnotbeawardedmarks–neitherwillyoulosemarks–forneatness.

DONOT:

Wastetimecopyingtheinstructionsthatareinthemanual…;youwillnotgetmarksforreproducingtheinformationyouhavebeengiven.

StartwritingthereportbeforeyouhavecollectedtherelevantdataANDyouhaveconfirmedthatthecollecteddataareadequateforthetaskathand.


Writingalaboratoryreport

Thepurposeofalaboratoryreportistocommunicatetheaim,theprocessandtheresultofanexperimenttoanoutsideaudience.

There aremany acceptableways to structure a laboratory report andwhile each component of a reportdescribedbelowneednothaveitsownheading–somecomponentscanbecombinedwithothers–allofthecomponentsreferredtoshouldbeaddressedinafulllabreport.

Titleofthereport:Thetitleshouldbeshortanddescriptive.Includethedateaswellasthenamesofthosewhoworkedwithyou.

Aim: State clearly and concisely what value was to be determined, or what phenomenon was to beinvestigated.

IntroductionandTheory:Thereportshouldgivethereaderthetheoreticalunderpinningoftheexperiment.Anyrelevantequationsshouldbeincludedinthissection.

The theorygivenhere lays the foundation for the later interpretation,analysis anddiscussionof thedatacollectedduringtheexperiment.

Apparatus: Show the apparatus used in simple labelled diagrams, sketches and/or circuits. Label thediagrams/sketches/circuitsasFigure1,orFigure2,etc.,asthecasemaybe.

Note:

• itisnotnecessarytomakedetaileddrawingsofminordetailslikeknobsoninstrumentsandtheshapesofboxesandwidgetsonstands;

• itisnotnecessarytodrawanexplodedviewoftheapparatus,and• itisnotnecessarytoprovidea‘partslist’.

Method: Themethod describes, in your ownwords, the procedures that were followedwhen doing theexperiment.Thesearetheproceduresusedtoobtaindataaswellasthoseusedtoanalysethatdata.

DO:Writeparagraphsinthepasttense,usinganimpersonalstyle.Forexample:

TheapparatususedisshowninFigure2…Fivereadingsweretakenandthesewererecordedin Table 1… The linearised data are shown in Table 2… A graph to show the relationshipbetweenAandBisshowninFigure3…Andsoon…

DONOT:Writeinpoint-for-pointform(yes,weknowwhatyouweretaughtatschool).

Donotpresentthemethodasthoughyouareprovidingarecipe.Forexample,donotwrite:• Fetchateabag,• Putitintoacup,• Addhotwater…


Readings (Data): The readings taken (data) are usually presentedwithout comment or analysis in tables.Herearekeypointstoconsiderwhendoingso:

(i) Thetablemusthaveatitle(e.g.,Table1:Measurementsofthewidthofthecylinder).Ifyouusemorethanonetableinyourreport,numbertheminsequence,e.g.,Table1,Table2,etc.

(ii) Eachcolumninthetablemusthaveaheadingandappropriateunits.(iii) Recordthereadingscarefully.Remember,forexample,that36.0cmisnotthesameas36cm.In

thefirstcaseyouarereadingtothenearestmillimetre,whileinthesecondcaseyouareonlyreadingtothenearestcentimetre.

Forexample:

Table3:Readingstakentodeterminethespringconstant

AppliedforceF

(N)

Readingonmetrestick

(mm)

Extensionx

(mm)

Springconstantk=F/x

(Nm−1)

0.000 122 0 n/a

0.100 163 41 2.44

0.201 204 82 2.45

0.298 250 128 2.33

0.400 283 161 2.48

Analysisandcalculations:Showalltherelevantcalculationsandmakesurethatthepurposeandmethodofeverycalculationiscleartothereader.Ifthereisalotofrepetitionthenshowthemethodonceandpresenttheresultsinatable.

Whendoingcalculations,quoteunitsandwritetheanswerstoanappropriatenumberofsignificantfigures.Significantfiguresare:

• Allnon-zerodigits(e.g.,54hastwosignificantdigitswhile456.78hasfivesignificantdigits).• Allzerosappearinganywherebetweentwonon-zerodigits(e.g.,302.05hasfivesignificantdigits).• Alltrailingzeros,wherethenumberhasadecimalpoint(e.g.,36.65000hassevensignificantdigits).• Leadingzerosarenotsignificant(e.g.,0.0003hasonlyonesignificantfigure).

Donotconfusesignificantfigureswithdecimalplaces.Thenumberofdecimalplacesreferstothenumberof figures after thedecimalpoint, e.g., 46.320has five significant figures, but threedecimalplaces;while0.0040hastwosignificantfigures,butfourdecimalplaces.

Evaluationofuncertainty: Theevaluationofuncertainty is a key aspectof all experimental sciences. Theconceptofuncertaintywillslowlybedevelopedduringthesemester,butsomequestionswillalwaysbethesame.YoushouldaddressthefollowingquestionsforeverypracticalintheUNCERTAINTYsection:1.Whatfactors(sourcesofuncertainty)mayhaveproducedvariationinyourmeasurements?Aretheybigorsmall?2. How could you minimize these factors? The answers to these questions should help formulate yourCONCLUSIONS.


Interpretation,DiscussionandConclusion

Inthefinalcomponentsofthereportyouareexpectedtosummarisetheworkby:

• Quotingthefinalresult.• Comparingthisresultwithothersandmakingcommentsasappropriate.• Discusstheuncertaintyinthepractical.• Suggestwaystoimprovetheexperiment.

Forexample,ifyouraimwastomeasuregyoushould,inasentence,statethemethodthatwasusedandgivetheresult.Forexample,youmaysay:

Asimplependulumwasusedtodeterminethevalueoftheearth’sgravitationalaccelerationinCapeTown.Theresultof theexperimentwasthatgwasdeterminedtobe(9.790±0.052)ms−2,withacoverageprobabilityof68%.ThisresultagreeswithinexperimentaluncertaintywiththegivenvalueforginCapeTownwhichis(9.79824±0.00044)ms-2.

Be careful not to mix facts with opinions and avoid meaningless phrases such as “this was a successfulexperiment.” Finally, the explanation that some or other result was influenced by “human error” isdiscouraged; if a human error has been made you are expected to correct that error by repeating theexperiment.


Graphsandbest-fitline

Graphsareessential for thesuccessfulcommunicationofexperiments, sodrawthemas largeaspossible.Everygraphhastohaveatitledescribingthepurposeforwhichithasbeenpresented(e.g.,Figure3:Plottodeterminetheviscosityofthesampleofoil),andifthereismorethanonegraph,numberthemsequentially,e.g.,Figure1,Figure2,etc.

Thegeneralrulesforplottinggraphsare:

• WhenaskedtoplotthegraphofsayPvs.Q,itmeansthatPmustbeontheverticalaxis(y-axis)andQmustbeonthehorizontalaxis(x-axis).

• Eachaxisshouldbelabelledwiththenameofthevariableandtheunits.• Axesshouldbemarkedinscalingfactorsof1,2,5,orthesetopowersoften.Scalingfactorssuchas

3or4usuallymakethescalesdifficulttoreadandshouldbeavoided.• Usea¤or×toshowthedatapoints…,notal(blob).

Forexample:

Inalotofexperimentalworkyouwillneedtodrawalineofbestfitbyeye.

Pleasenote:

• thebestfitlinedoesnotsimplyjointhedatapoints;• thebestfitlinehastomodelthetrendinthedata;and• itispossiblethatthebestfitlinemaynotevengothroughanyofthedatapointsasshowninthe

exampleabove.


N3–NotesfortheLinearMotionPractical

TheLoggerProandLoggerLiteSoftware

VernierSoftwaredevelopseducationaldata-collectinginterfacesandthecorrespondingsoftware.TherearetwolevelsofthesoftwarethatinterfaceswiththeGo!Motionsensor:LoggerPro(forpurchase)andLoggerLite(freelyavailable).Forthelinearmotionpractical,wewillbeusingbothversionsofthesoftware(LoggerLiteforPart1andLoggerProforPart2).

ForthesetwopartsoftheLinearMotionpractical,templateshavebeenalreadycreatedinordertominimizethesetupofthesoftware.ThePart1template(entitled:03LinearMotionPart1LoggerLiteTemplate)isavailableonVulafordownload.ThePart2template(entitled:PHY1025FPractical3Part2)willbeavailableonthedesktopPCinPHYLAB1.ThereisalsoaLoggerLiteversion(entitled:03LinearMotionPart2LoggerLiteTemplate)availableonVulaifyouwouldprefertouseyourlaptopforPart2.

Inorder touseLoggerLiteonyour laptop (PCorMac),youwillneed todownload thesoftware fromtheVernier website (http://www.vernier.com/products/software/logger-lite/) and then install it on yourcomputer.[ItwillalsobeavailableonthecourseVulasite.]Hopefullyyouhavedonethisbeforearrivingtothelab.

UsingLoggerProandLoggerLite

The Logger Pro and Logger Lite software is fairly straight-forward to use, but here are a list of usefulcommandsandfeatures.

Fromthetoolbar:

…tostartcollectingdata

…tostopdatacollection(templateswillautomaticallystopreadingafteranallottedtime)

…toscaleyourgraphautomatically

…forthecursor

…tosavedatainLoggerLiteFormat


Fromthemenu(morecommon):

File … Save …tosavedatainLoggerLiteformat

Data … Clear All Data …tocleardata

Analyze … Autoscale …toscaleyourgraphautomatically

Analyze … Examine …foracursor

Analyze … Linear Fit …tofitalinetotheselecteddata(selectdatausingcursor)

Fromthemenu(lesscommon):

File … Export As …tosaveasCSVortextfile(forlateranalysisinExcel,etc)

Insert … Graph …toaddavelocityoraccelerationgraph

Page … Auto Arrange …toautomaticallyarrangegraphsonthepage

Experiment … Data Collection …toadjustdatacollectionparameters(pre-setifusingtemplates)


N5–NotesfortheViscosityPractical

LINEARFIT

LinearFitcanbeusedtocalculatetheslope𝑚 ± 𝑢(𝑚)andtheintercept𝑐 ± 𝑢(𝑐)ofthebestfitstraightline.

Tostarttheprogram,clickontheLinearFitshortcutonthedesktop,asyoudowithanyprogramrunningonWindows.(Ifyouneedtolog-intothePC,thelog-inis“phylab”withnopassword.)TheprogramwillopenandpresentthepageasshowninFigure12.

Type the𝑥and𝑦values into the appropriate columns and LinearFitwill automatically calculate𝑚 ± 𝑢(𝑚)and𝑐 ± 𝑢(𝑐).

Figure12:DatainputandfittingscreenofLinearFit


N6–NotesfortheThinLensesPractical

TYPEAevaluationofuncertainty

InaTYPEAevaluationoftheuncertainty,astatisticalmethodisusedto inferthevalueoftheuncertaintyassociatedwithameasurementbyquantifyingthe“scatter”,orthe“spread”inthevaluesofasetofdata.

Thecasewherethedataareasetofreadingsoftheform:x1,x2,x3,…

Ahistogramofthereadingsshowsadistributionaroundsomemeanvalue𝑥thatcanberepresentedbyasymmetricalbell-shapedcurve(referredtoasa“Gaussian”)where:

Figure13:Normalor'Gaussian'distributionfunction

When the relevant set of readings, x1, x2, x3,…, xn, for n readings, are plotted as a histogram, and thehistogramallowsonetofitacurvesimilarinshapetoanormaldistribution,thenthebestapproximationof𝑥is𝑥, and the standard uncertainty𝑢(𝑥)is the experimental standard deviation of the mean, !

!of the

fittedcurve.

FormulaeforaTYPEAevaluationofuncertaintywherethedistributionisGaussian

Consideranexperimentinwhichasetofreadings,x1,x2,x3,….xn,wherenisthenumberofreadingsandxiistheithreading,hasbeentaken.Ifthereisascatterinthevaluesofthesereadings,thenitcanbereasonablyassumedthatthedistributionofthereadings‘fits’aGaussianprobabilitydensityfunction.

Usingthisassumption*,therearethreevaluesrequiredtocalculatetheuncertaintyinthemeasurement:• themean𝑥(sometimesthesymbol𝜇isalsousedforthemean)• thestandarddeviation𝜎,and• theexperimentalstandarddeviationofthemeanwhich,whenthedistributionofthevaluesofthe

meanofthereadingsisnormal,isthestandarduncertainty𝑢(𝑥).

Thefollowingequationsareusedtocalculatetheparametersusedtodeterminetheuncertaintyassociatedwiththemeasurement:

Meanofthedata: 𝑥 =1𝑛

𝑥!

!

!!!

(18)

Standarddeviation: 𝜎 =1

𝑛 − 1𝑥! − 𝑥 !

!

!!!

(19)

,

�̅�isthemean,and

𝜎isthestandarddeviation.


Standarduncertainty:ortheexperimentalstandarddeviationofthemean

𝑢(𝑥) =𝜎𝑛 (20)

Note:1) *Theassumptionthatthedistributionofthevaluesofthereadingsisnormalvalidatesthestatement

that“theexperimentalstandarddeviationofthemeanisthestandarduncertaintyu(x)”forthemajorityofcases.However,itisimportanttorealisethatadifferentapproachmayberequiredwherethedistributionofvaluesisnot‘normal’.

2) BecauseaGaussiandistributionwasassumed,theprobabilitythatthemeasurandlieswithinonestandarduncertaintyofthebestapproximation,is68%.

Comparingresults

Tosay that tworesultsare“close”or“nearly thesame” ismeaningless in thecontextof laboratorywork.Theresultsofanytwoexperimentscanonlybemeaningfullycomparediftheintervalsassociatedwitheachoftheresultsareknown.

Morespecifically:• Iftheintervalsthatrepresenttheresultsoftwomeasurementsoverlap,thenwesaythesetwo

results“agreewithinexperimentaluncertainty.”• Iftheintervalsthatrepresenttheresultsoftwomeasurementsdonotoverlap,thenwesaythese

results“donotagreewithinexperimentaluncertainty.”

For example, say three studentsmeasure the periodTof a pendulum and they each quote the result asfollows:

T1=(5.73±0.41)s

T2=(5.62±0.10)s T3=(6.28±0.25)s

Thethreemeasurementsmaybepresentedintheformofintervalsonanumberline:

• NotethattheintervalsassociatedwithT1andT2overlap,andtherefore“thesetworesultsagreewithinexperimentaluncertainty”.

• TheintervalsassociatedwithT1andT3alsooverlapso“thesetworesultsagreewithinexperimentaluncertainty”.

• However,theintervalassociatedwithT3doesnotoverlapwiththeintervalassociatedwithT2andtherefore“thesetworesultsdonotagreewithinexperimentaluncertainty.”

5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 T(s) ||||||||||||||

T1 X T2 X T3 X

Figure14:Comparisonofresults

phy1025f practical manual - uct physics department · 2016 phy1025f practical manual 10 v1.1 –...

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