C6-college physics-shyppt课件

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,FromNewtonslaws:forcemustbepresenttochangeanobjectsvelocity(speedand/ordirection)WishtoconsidereffectsofcollisionsandcorrespondingchangeinvelocityMethodtodescribeistouseconceptoflinearmomentum,scalar,vector,Linearmomentum=productofmassvelocity,Golfballinitiallyatrest,sosomeoftheKEofclubtransferredtoprovidemotionofgolfballanditschangeinvelocity,Momentum,Vectorquantity,thedirectionofthemomentumisthesameasthevelocitysAppliestotwo-dimensionalmotionaswell,Sizeofmomentum:dependsuponmassdependsuponvelocity,Impulse,Inordertochangethemomentumofanobject(say,golfball),aforcemustbeappliedThetimerateofchangeofmomentumofanobjectisequaltothenetforceactingonitGivesanalternativestatementofNewtonssecondlaw(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:accordingtoNewtons3rdlaw,thatisalsoareactionforcetoclubhittingtheball:,ofclub,CONSERVATIONOFMOMENTUM,ConservationofMomentum,Definition:anisolatedsystemistheonethathasnoexternalforcesactingonitAcollisionmaybetheresultofphysicalcontactbetweentwoobjects“Contact”mayalsoarisefromtheelectrostaticinteractionsoftheelectronsinthesurfaceatomsofthebodies,Momentuminanisolatedsysteminwhichacollisionoccursisconserved(regardlessofthenatureoftheforcesbetweentheobjects),ConservationofMomentum,Theprincipleofconservationofmomentumstateswhennoexternalforcesactonasystemconsistingoftwoobjectsthatcollidewitheachother,thetotalmomentumofthesystembeforethecollisionisequaltothetotalmomentumofthesystemafterthecollision,ConservationofMomentum,Mathematically:MomentumisconservedforthesystemofobjectsThesystemincludesalltheobjectsinteractingwitheachotherAssumesonlyinternalforcesareactingduringthecollisionCanbegeneralizedtoanynumberofobjects,Problem:TeeingOff(cont.),Letsgobacktoourgolfballandclubproblem:,factorof10timessmaller,ConcepTest,SupposeapersonjumpsonthesurfaceofEarth.TheEarth1.willnotmoveatall2.willrecoilintheoppositedirectionwithtinyvelocity3.mightrecoil,butthereisnotenoughinformationprovidedtoseeifthatcouldhappened,ConcepTest,SupposeapersonjumpsonthesurfaceofEarth.TheEarth1.willnotmoveatall2.willrecoilintheoppositedirectionwithtinyvelocity3.mightrecoil,butthereisnotenoughinformationprovidedtoseeifthatcouldhappened,Note:momentumisconserved.LetsestimateEarthsvelocityafterajumpbya80-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,wherethesystemistherocketplusit