CHAPTER 3 Investigations

Simulating Uniform Circular Motion

Youhavelearnedabouttheprinciplesrelatedtoobjectsinuniformcircularmotion.Inthisinvestigation,youwilluseasimulationprogramtoverifytherelationshipbetweencentripetalforceandvariablessuchasmass,speed,radius,frequency,andperiodforamassattachedtoaropeswinginginacirclewithuniformcircularmotion.

PurposeToverifytherelationshipbetweencentripetalforceandvariablessuchasmass,speed,radius,frequency,andperiodinuniformcircularmotion

equipment and Materials• accesstoacomputerwithanInternetconnection• graphpaperorgraphingsoftware

Procedure 1. GototheNelsonSciencewebsiteandstartthe

simulation.  2. Displaythevectorsforforce,acceleration,and

velocityinyoursimulation.Determinenetforce(centripetalforce)fordifferentvaluesoftheradius,keepingthemassandspeedconstant.Recordallinformationinatable,anduseatleastfivedifferentvaluesoftheradius.

3. Graphthecentripetalforceversustheradiusandthecentripetalforceversus

1radius

separately.

4. RepeatSteps1and2,butchangethemassandkeepthespeedandradiusconstant.Graphthecentripetalforceversusthemass.

5. RepeatSteps1and2,butchangethespeedandkeeptheradiusandmassconstant.Graphthecentripetalforceversusthespeedandthecentripetalforceversusthesquareofthespeed.

6. DeterminetheperiodandfrequencyforeachspeedusedinStep5,andrecordtheresultsinyourtable.

Analyze and evaluate(a) Examineallyourgraphs.Calculatetheslopeofeach

graphthatproducesastraightline.Howistheslopeofeachgraphrelatedtomass,speed,and/orradius?Explainyourreasoning.  K/U T/I C

(b) Whatistheeffectofincreasingthefollowingonthecentripetalforce?Explainyourreasoning.  T/I

(i) radius (ii) mass (iii)speed

(c) Whatwouldagraphofcentripetalforceversusmv 2

r looklike?Whatwouldtheslopeofthisgraphequal?Explainyourreasoning.  K/U T/I C A

(d)Howisthespeedofthemassrelatedtothefrequencyandtheperiod?  T/I

(e) Whathappenstothecentripetalforcewhenthefrequencyincreases?Whentheperiodincreases?  T/I

Apply and extend(f) Howwouldyouusethissimulationtodescribethe

motionofasatelliteinorbit?  T/I C A

SKIllS MeNU

• Questioning• Researching • Hypothesizing• Predicting

• Planning•  Controlling 

Variables• Performing

• Observing • Analyzing• Evaluating• Communicating

Investigation 3.3.1 OBSERVATIONAL STUDY

SKILLSHANDBOOK A2.4

SKILLSHANDBOOK A5.5

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Analyzing Uniform Circular Motion

Youhavelearnedthatwhileanobjectisinuniformcircularmotionataconstantspeed,itsvelocityisalsoconstantlychangingdirection.Th iscausestheobjecttoacceleratetowardthecentreofitscircularpath.Inthisinvestigation,youwillbuildanapparatustoobserveasmallobjectinuniformcircularmotionandcollectdatatodescriberelationshipsbetweentheobject,itsmass,andtheradiusofitspath.

Testable questionHowdothemagnitudeoftheforce,theradiusofacircularpath,andanobject’smassaffectthefrequencyoftherevolutionofanobjectinuniformcircularmotion?

PredictionPredicttherelationshipbetweenthefrequencyofrevolutionandeachvariableintheTestableQuestion.Explainyourreasoning.

variablesReadtheTestableQuestion,ExperimentalDesign,andProcedure,andidentifythedependent,independent,andcontrolledvariables.

experimental DesignFigure 1showsasimplesetupthatcanbeusedtoperformthisinvestigation.Youwillholdahollowtubeverticallyinyourhandwhileyoutwirltherubberstopperaroundinahorizontalcircle.Astringistiedtotherubberstopperandthenpasseddownthroughthehollowtube,whereitistiedtothemass.Th eforceofgravityprovidesthetensionrequiredtomaketherubberstoppermoveinacircle.

hollow tube

paper clip

string

r

rubber stopper

This space should remainconstant while twirling.

FT

Figure 1

equipment and Materials• eyeprotection• electronicbalanceorscale• 3smallrubberstopperswithcentreholes• hollowtube• 50g,100g,200g,250gmasses• metrestick• 1.5mstringorfishingline• paperclipormaskingtape• graphpaperorgraphingsoftware

Procedure 1. Createadatatableforeachofthefollowing

observations:threesetsofvaluesforchangingtheforceoftension,threesetsforchangingtheradius,andthreesetsforchangingthemass.

2. Measureandrecordthemass,inkilograms,ofeachrubberstopper.

3. Tieonerubberstoppertightlytooneendofthestring.

4. Th readthestringthroughthetube,hangthe200gmassontheotherend(Figure1),andputonyoureyeprotection. 

Wear eye protection. Be sure the area around you is clear from material hanging from the ceiling that you may accidentally hit while swinging the stopper. Be careful not to drop the masses on your feet. Do not wear open-toed shoes. Ensure no one can be hit by the stopper.

5. Practiseswingingthestopperaroundyourheadwithaconstantspeedandconstantradius.Makesureyouarecomfortableandproficientwiththisstepbeforeproceedingtothenextstep.

6. Laytheequipmentonthefloor,andmeasurea75cmdistancefromthecentreofthestoppertothetopofthehollowtube.Fixthisradiusbyplacingthepaperclipatthebottomofthetube(Figure1).

7. Swingthestopperataconstantspeedataradiusof75cm.Trytokeepthepaperclipslightlybelowthebottomofthetubetoensurethatitisnotpushingonthetubeandincreasingthetension.

SKIllS MeNU

• Questioning• Researching • Hypothesizing• Predicting

• Planning•  Controlling 

Variables• Performing

• Observing • Analyzing• Evaluating• Communicating

Investigation 3.3.2 CONTROLLED EXPERIMENT

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8. Complete20cycles,andrecordthetimeinyourtable.Toobtainareasonableaveragevalue,youwillneedtorepeatthisstepseveraltimes.

9. Calculatethefrequencyofrevolution,andrecorditinyourtable.

10. RepeatSteps6to9usingadifferenttensionforcebychangingthemassattheendofthestringto150gandthento100g.

11. Measurethetimefor20completecycleswhentheradiusis60cmandwhentheradiusis45cm,withthesamemassofstopperandthetensionforceduetothe100gmass.Calculateallthefrequenciesandrecordtheminyourtable.

12. Addanotherstopperandmeasurethetimefor20completecyclesataconstantradiusof75cmandaconstanttensionforceduetothe100gmass.

13. Repeattheprocesswithathirdstopperandtheothermasses.Calculatethefrequenciesandrecordtheminyourtable.

Analyze and evaluate(a) Whatvariablesweremeasuredand/ormanipulated

inthisinvestigation?Whattypeofrelationshipwasbeingtested?  T/I

(b) Graphtherelationshipsbetweenthefrequencyofrevolutionandeachofthefollowing:• themagnitudeofthetensionforce• theradiusofthecircle• themassoftheobjectinmotion  T/I C

(c) Deriveanequationforthefrequencyintermsofthetension,theradius,andthemassbycombiningyourresultsfrom(b).  T/I

(d) Th eequationFc 5 4p2mrf 2givesthemagnitudeofthenetforcecausingtheaccelerationofanobjectinuniformcircularmotion.  T/I A

(i) Manipulatetheequationtosolveforfrequency.Howdoesthiscomparewithyourresultsfrom(c)?

(ii) Whatarethemostlikelycausesforanydiscrepancies?

(e) Toobtainthebestaccuracy,thetensionforceactingonthestoppershouldbehorizontal.Whathappenstotheaccuracyasthefrequencyofrevolutionofthestopperincreases?  T/I A

(f) Whatsourcesoferrordidyouencounterandhowdidyouminimizethem?  T/I A

Apply and extend(g) Explainhowthisinvestigationillustratesallthreeof

Newton’slawsofmotion.  T/I C

(h) Howmightyouapplyyourfindingstoasportsactivitythatinvolvescircularmotion?  T/I A

(i) Ifyoulookcarefullyattheswingingstopper,youwillnoticethatthestringtiedtothestopperisnotcompletelyhorizontal.  K/U T/I C

(i) Whateffect,ifany,willthishaveontheaccuracyofyourresults?

(ii) Whathappenstotheorientationofthestringasthespeedofthestopperincreases?Explainyourreasoning.

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