In this lab you will begin to use conservation of energy to.docx

In this lab you will begin to use conservation of energy to.docx

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Inthislabyouwillbegintouseconservationofenergyto

LABORATORYIV

CONSERVATIONOFENERGY

Inthislabyouwillbegintousetheprincipleofconservationofenergytodeterminethemotionresultingfrominteractionsthataredifficulttoanalyzeusingforceconceptsalone.Youwillexplorehowconservationofenergyisappliedtorealinteractions.Keepinmindthatenergyisalwaysconserved,butitissometimesdifficulttocalculatethevalueofallenergytermsrelevantforaninteraction.Someenergymaybetransferredintooroutofthesystemofinterest,andsomemaybetransformedtointernalenergyofthesystem.Oneoutcomecanbethatsomefractionofasystem’senergyofmotionbeforeaninteractionisnotvisibleenergyofmotionaftertheinteraction.Sincetheenergyisnolongerobservableinthemacroscopicmotionofobjects,wesometimessaythattheenergyis"dissipated"intheinteraction.

Thefirstfourproblemsinthislaboratoryexploretheapplicationofconservationofenergyusingcarts.Thefifthproblemdealswiththeveryrealcomplicationoffriction.

Objectives:

Successfullycompletingthislaboratoryshouldenableyouto:

•Useconservationofenergytopredicttheoutcomeofinteractionsbetweenobjects.

•Chooseausefulsystemwhenusingconservationofenergy.

•Identifydifferenttypesofenergywhenapplyingenergyconservationtorealsystems.

•Decidewhenconservationofenergyisnotusefultopredicttheoutcomeofinteractionsbetweenobjects.

Preparation:

ReadPaulM.Fishbane:

Chapter6,Chapter7.Youshouldalsobeableto:

•Analyzethemotionofanobjectusingvideoanalysis.

•Calculatethekineticenergyofamovingobject.

•Calculatetheworktransferredtoorfromasystembyanexternalforce.

•Calculatethetotalenergyofasystemofobjects.

•Calculatethegravitationalpotentialenergyofanobjectwithrespecttotheearth.

Problem#1:

kineticenergyandworki

Youareworkingatacompanythatdesignspinballmachinesandhavebeenaskedtodeviseatesttodeterminetheefficiencyofsomenewmagneticbumpers.Youknowthatwhenanormalpinballreboundsofftraditionalbumpers,someoftheinitialenergyofmotionis"dissipated"inthedeformationoftheballandbumper,thusslowingtheballdown.Theleadengineerontheprojectassignsyoutodetermineifthenewmagneticbumpersaremoreefficient.Theengineertellsyouthattheefficiencyofacollisionistheratioofthefinalkineticenergytotheinitialkineticenergyofthesystem.

Tolimitthemotiontoonedimension,youdecidetomodelthesituationusingacartwithamagnetcollidingwithamagneticbumper.Youwillusealeveltrack,anduseavideodataacquisitionsystemtomeasurethecart’svelocitybeforeandafterthecollision.Youbegintogatheryourcameraanddataacquisitionsystemwhenyourcolleaguesuggestsamethodwithsimplerequipment.Yourcolleagueclaimsitwouldbepossibletoreleasethecartfromrestonaninclinedtrackandmakemeasurementswithjustameterstick.Youarenotsureyoubelieveit,soyoudecidetomeasuretheenergyefficiencybothways,anddeterminetheextenttowhichyougetconsistentresults.Forthisproblem,youwillusetheleveltrack.Forproblem#2,youwillworkwiththeinclinedtrack.

Equipment

Youwillusethevideoanalysisequipmenttoanalyzethemotionofacartcollidingwithanendstop（themagneticbumper）onthetrack.Youwillalsohaveameterstick,astopwatchandabalancetomeasurethemassofthecart.

Predictions

Calculatetheenergyefficiencyofthebumperdiscussedintheproblemintermsoftheleastnumberofquantitiesthatyoucaneasilymeasureinthesituationofaleveltrack.Calculatetheenergydissipatedduringtheimpactwiththebumperintermsofthosemeasurablequantities.

Warmup

Read:

FishbaneChapter6,section6.1.

1.Itisusefultohaveanorganizedproblem-solvingstrategy.Thefollowingquestionswillhelpwithyourpredictionandtheanalysisofyourdata.

2.Makeadrawingofthecartontheleveltrackbeforeandaftertheimpactwiththebumper.Defineyoursystem.Labelthevelocityandkineticenergyofallobjectsinyoursystembeforeandaftertheimpact.

3.Writeanexpressionfortheefficiencyofthebumperintermsofthefinalandinitialkineticenergyofthecart.

4.Writeanexpressionfortheenergydissipatedduringtheimpactwiththebumperintermsofthekineticenergybeforetheimpactandthekineticenergyaftertheimpact.

Exploration

Reviewyourexplorationnotesformeasuringavelocityusingvideoanalysis.Practicepushingthecartwithdifferentvelocities,slowlyenoughthatthecartwillnevercontactthebumper（endstop）duringtheimpactwhenyoumakeameasurement.Findarangeofvelocitiesforyourmeasurement.Setupthecameraandtripodtogiveyouausefulvideoofthecollisionimmediatelybeforeandafterthecartcollideswiththebumper.

Althoughtheeffectoffrictionissmallinourlab,youmaywanttoestimateit.Makeascheduletotesttheeffectoffrictionbythedatafromvideo.

Measurement

Takethemeasurementsnecessarytodeterminethekineticenergybeforeandaftertheimpactwiththebumper.Whatisthemostefficientwaytomeasurethevelocitieswiththevideoequipment?

Takedataforseveraldifferentinitialvelocities.

Analysis

Calculatetheefficiencyofthebumperfortheleveltrack.Doesyourresultdependonthevelocityofthecartbeforeithitsthebumper?

Conclusion

Whatistheefficiencyofthemagneticbumpers?

Howmuchenergyisdissipatedinanimpact?

Whatiseffectoffrictioninyourexperiment?

Stateyourresultsinthemostgeneraltermssupportedbyyouranalysis.

Ifavailable,compareyourvalueoftheefficiency（withuncertainty）withthevalueobtainedbythedifferentproceduregiveninthenextproblem.Arethevaluesconsistent?

Whichwaytomeasuretheefficiencyofthemagneticbumperdoyouthinkisbetter?

Why?

problem#2:

kineticenergyandworkii

Youareworkingatacompanythatdesignspinballmachinesandhavebeenaskedtodeviseatesttodeterminetheefficiencyofsomenewmagneticbumpers.Youknowthatwhenanormalpinballreboundsofftraditionalbumpers,someoftheinitialenergyofmotionis"dissipated"inthedeformationoftheballandbumper,thusslowingtheballdown.Theleadengineerontheprojectassignsyoutodetermineifthenewmagneticbumpersaremoreefficient.Theengineertellsyouthattheefficiencyofacollisionistheratioofthefinalkineticenergytotheinitialkineticenergyofthesystem.

Tolimitthemotiontoonedimension,youdecidetomodelthesituationusingacartwithamagnetcollidingwithamagneticbumper.Youwillusealeveltrack,anduseavideodataacquisitionsystemtomeasurethecart’svelocitybeforeandafterthecollision.Youbegintogatheryourcameraanddataacquisitionsystemwhenyourcolleaguesuggestsamethodwithsimplerequipment.Yourcolleagueclaimsitwouldbepossibletoreleasethecartfromrestonaninclinedtrackandmakemeasurementswithjustameterstick.Youarenotsureyoubelieveit,soyoudecidetomeasuretheenergyefficiencybothways,anddeterminetheextenttowhichyougetconsistentresults.Forthisproblem,youwillusetheinclinedtrack.Forproblem#1,youwillworkwiththeleveltrack.

Equipment

Youwillhaveameterstick,astopwatch,cartmassesandawoodenblocktocreatetheincline.Youmayalsousethevideoanalysisequipmenttoestimatetheeffectoffriction.

Predictions

Calculatetheenergyefficiencyofthebumper（withfrictionandwithout）intermsoftheleastnumberofquantitiesthatyoucaneasilymeasureinthesituationofaninclinedtrack.

Warmup

Read:

FishbaneChapter6,sections6.1-6.2.

Thefollowingquestionswillhelpyoutomakeyourpredictionandanalyzeyourdata.

1.Makeadrawingofthecartontheinclinedtrackatitsinitialposition（beforeyoureleasethecart）andjustbeforethecarthitsthebumper.Definethesystem.Labelthekineticenergyofallobjectsinyoursystematthesetwopoints,thedistancethecarttraveled,theangleofincline,andtheinitialheightofthecartabovethebumper.

2.Nowmakeanotherdrawingofthecartontheinclinedtrackjustafterthecollisionwiththebumperandatitsmaximumreboundheight.Labelkineticenergyofthecartatthesetwopoints,thedistancethecarttraveled,theangleoftheramp,andthereboundheightofthecartabovethebumper.

3.Writeanexpressionfortheefficiencyofthebumperintermsofthekineticenergyofthecartjustbeforetheimpactandthekineticenergyofthecartjustaftertheimpact.

4.Drawaforcediagramofthecartasitmovesdownthetrack.Whichforcecomponentdoesworkonthecart（i.e.,causesatransferofenergyintothecartsystem）?

Writeanexpressionfortheworkdoneonthecart.Howistheangleoftheramprelatedtothedistancethecarttraveledandtheinitialheightofthecartabovethebumper?

Howdoesthekineticenergyofthecartjustbeforeimpactcomparewiththeworkdoneonthecart?

5.Drawaforcediagramofthecartasitmovesupthetrack.Whichforcecomponentdoesworkonthecart（i.e.,causesatransferofenergyoutofthecartsystem）?

Writeanexpressionfortheworkdoneonthecart.Howdoesthekineticenergyofthecartjustafterimpactcomparewiththeworkdoneonthecart?

6.Writeanexpressionfortheefficiencyofthebumperintermsofthecart’sinitialheightabovethebumperandthecart’smaximumreboundheightabovethebumper.

7.Writeanexpressionfortheenergydissipatedduringtheimpactwiththebumperintermsofthekineticenerg