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