C6-college physics-shy.ppt

Lecture7LinearMomentum Collisions Keywords linear momentum动量impulse冲量impulse momentumtheorem动量定理time averageforce平均冲力interaction相互作用airbags气囊particlessystem composedofsomeparticles质点系internalforces amongparticles内力externalforces actedonfromsurroundings外力 Momentum FromNewton slaws forcemustbepresenttochangeanobject svelocity speedand ordirection WishtoconsidereffectsofcollisionsandcorrespondingchangeinvelocityMethodtodescribeistouseconceptoflinearmomentum scalar vector Linearmomentum productofmassvelocity Golfballinitiallyatrest sosomeoftheKEofclubtransferredtoprovidemotionofgolfballanditschangeinvelocity Momentum Vectorquantity thedirectionofthemomentumisthesameasthevelocity sAppliestotwo dimensionalmotionaswell Sizeofmomentum dependsuponmassdependsuponvelocity Impulse Inordertochangethemomentumofanobject say golfball aforcemustbeappliedThetimerateofchangeofmomentumofanobjectisequaltothenetforceactingonitGivesanalternativestatementofNewton ssecondlaw F t isdefinedastheimpulseImpulseisavectorquantity thedirectionisthesameasthedirectionoftheforce ConcepTest Supposeaping pongballandabowlingballarerollingtowardyou Bothhavethesamemomentum andyouexertthesameforcetostopeach Howdothetimeintervalstostopthemcompare 1 Ittakeslesstimetostoptheping pongball 2 Bothtakethesametime 3 Ittakesmoretimetostoptheping pongball Convinceyourneighbor ConcepTest Supposeaping pongballandabowlingballarerollingtowardyou Bothhavethesamemomentum andyouexertthesameforcetostopeach Howdothetimeintervalstostopthemcompare 1 Ittakeslesstimetostoptheping pongball 2 Bothtakethesametime 3 Ittakesmoretimetostoptheping pongball Note Becauseforceequalsthetimerateofchangeofmomentum thetwoballsloosemomentumatthesamerate Ifbothballsinitiallyhadthesamemomenta ittakesthesameamountoftimetostopthem Problem TeeingOff A50 ggolfballatrestishitby BigBertha clubwith500 gmass Afterthecollision golfleaveswithvelocityof50m s FindimpulseimpartedtoballAssumingclubincontactwithballfor0 5ms findaverageforceactingongolfball Problem teeingoff Given mass m 50g 0 050kgvelocity v 50m sFind impulse Faverage 1 Useimpulse momentumrelation 2 Havingfoundimpulse findtheaverageforcefromthedefinitionofimpulse Note accordingtoNewton s3rdlaw thatisalsoareactionforcetoclubhittingtheball ofclub CONSERVATIONOFMOMENTUM ConservationofMomentum Definition anisolatedsystemistheonethathasnoexternalforcesactingonitAcollisionmaybetheresultofphysicalcontactbetweentwoobjects Contact mayalsoarisefromtheelectrostaticinteractionsoftheelectronsinthesurfaceatomsofthebodies Momentuminanisolatedsysteminwhichacollisionoccursisconserved regardlessofthenatureoftheforcesbetweentheobjects ConservationofMomentum Theprincipleofconservationofmomentumstateswhennoexternalforcesactonasystemconsistingoftwoobjectsthatcollidewitheachother thetotalmomentumofthesystembeforethecollisionisequaltothetotalmomentumofthesystemafterthecollision ConservationofMomentum Mathematically MomentumisconservedforthesystemofobjectsThesystemincludesalltheobjectsinteractingwitheachotherAssumesonlyinternalforcesareactingduringthecollisionCanbegeneralizedtoanynumberofobjects Problem TeeingOff cont Let sgobacktoourgolfballandclubproblem factorof10timessmaller ConcepTest SupposeapersonjumpsonthesurfaceofEarth TheEarth1 willnotmoveatall2 willrecoilintheoppositedirectionwithtinyvelocity3 mightrecoil butthereisnotenoughinformationprovidedtoseeifthatcouldhappened ConcepTest SupposeapersonjumpsonthesurfaceofEarth TheEarth1 willnotmoveatall2 willrecoilintheoppositedirectionwithtinyvelocity3 mightrecoil butthereisnotenoughinformationprovidedtoseeifthatcouldhappened Note momentumisconserved Let sestimateEarth svelocityafterajumpbya80 kgperson Supposethatinitialspeedofthejumpis4m s then tinynegligiblevelocity inoppositedirection TypesofCollisions Momentumisconservedinanycollisionwhataboutkineticenergy InelasticcollisionsKineticenergyisnotconservedSomeofthekineticenergyisconvertedintoothertypesofenergysuchasheat sound worktopermanentlydeformanobjectPerfectlyinelasticcollisionsoccurwhentheobjectssticktogetherNotalloftheKEisnecessarilylost PerfectlyInelasticCollisions Whentwoobjectssticktogetherafterthecollision theyhaveundergoneaperfectlyinelasticcollisionSuppose forexample v2i 0 Conservationofmomentumbecomes PerfectlyInelasticCollisions WhatamountofKElostduringcollision lostinheat gluing sound MoreTypesofCollisions ElasticcollisionsbothmomentumandkineticenergyareconservedActualcollisionsMostcollisionsfallbetweenelasticandperfectlyinelasticcollisions MoreAboutElasticCollisions BothmomentumandkineticenergyareconservedTypicallyhavetwounknownsSolvetheequationssimultaneously ProblemSolvingforOne DimensionalCollisions SetupacoordinateaxisanddefinethevelocitieswithrespecttothisaxisItisconvenienttomakeyouraxiscoincidewithoneoftheinitialvelocitiesInyoursketch drawallthevelocityvectorswithlabelsincludingallthegiveninformation SketchesforCollisionProblems Draw before and after sketchesLabeleachobjectincludethedirectionofvelocitykeeptrackofsubscripts SketchesforPerfectlyInelasticCollisions TheobjectssticktogetherIncludeallthevelocitydirectionsThe after collisioncombinesthemasses ProblemSolvingforOne DimensionalCollisions cont WritetheexpressionsforthemomentumofeachobjectbeforeandafterthecollisionRemembertoincludetheappropriatesignsWriteanexpressionforthetotalmomentumbeforeandafterthecollisionRememberthemomentumofthesystemiswhatisconserved ProblemSolvingforOne DimensionalCollisions final Ifthecollisionisinelastic solvethemomentumequationfortheunknownRemember KEisnotconservedIfthecollisioniselastic youcanusetheKEequationtosolvefortwounknowns GlancingCollisions Forageneralcollisionoftwoobjectsinthree dimensionalspace theconservationofmomentumprincipleimpliesthatthetotalmomentumofthesystemineachdirectionisconservedUsesubscriptsforidentifyingtheobject initialandfinal andcomponents GlancingCollisions The after velocitieshavexandycomponentsMomentumisconservedinthexdirectionandintheydirectionApplyseparatelytoeachdirection ProblemSolvingforTwo DimensionalCollisions SetupcoordinateaxesanddefineyourvelocitieswithrespecttotheseaxesItisconvenienttochoosethexaxistocoincidewithoneoftheinitialvelocitiesInyoursketch drawandlabelallthevelocitiesandincludeallthegiveninformation ProblemSolvingforTwo DimensionalCollisions cont WriteexpressionsforthexandycomponentsofthemomentumofeachobjectbeforeandafterthecollisionWriteexpressionsforthetotalmomentumbeforeandafterthecollisioninthex directionRepeatforthey direction ProblemSolvingforTwo DimensionalCollisions final SolvefortheunknownquantitiesIfthecollisionisinelastic additionalinformationisprobablyrequiredIfthecollisionisperfectlyinelastic thefinalvelocitiesofthetwoobjectsisthesameIfthecollisioniselastic usetheKEequationstohelpsolvefortheunknowns Rocketpropulsion Theoperationofarocketdependsuponthelawofconservationoflinearmomentumasappliedtoasystemofparticles wherethesystemistherocketplusitsejectedfuel Becausethegasesaregivenmomentumwhentheyareejectedoutoftheengine therocketreceivesacompensatingmomentumintheoppositedirection Therefore therocketisacceleratedasaresultofthe push orthrust fromtheexhaustgases RocketPropulsion TherocketisacceleratedasaresultofthethrustoftheexhaustgasesThisrepresentstheinverseofaninelasticcollisionMomentumisconservedKineticEnergyisincreased attheexpenseofthestoredenergyoftherocketfuel RocketPropulsion Theoperationofarocketdependsonthelawofconservationofmomentumasappliedtoasystem wherethesystemistherocketplusitsejectedfuelThisisdifferentt