《大学物理简明教程》 课件 4-2 collisions

Collison–elasticandinelasticInelastic!Elastic!Whathappensinacollision?–suddenchangeofvelocity–verylargeinternalforces–usuallyexternalforcescanbeneglected–veryshorttime–verysmallimpulsesfromexternalforcesDifferencebetweenelasticandinelasticcollisionsElasticInelasticKineticenergy:ConservedNotconservedMomentum:(bothpartiesmovable)ConservedConservedPerfectlyinelasticcollisionsTransferringmomentumandenergyElasticcollisionin1dimensionKineticenergyisconservedMomentumisconservedSpecialcase–twosystemswithsamemassWithdifferentmasses?Twoidenticalobjects(suchasbilliardballs)haveaone-dimensionalelasticcollisioninwhichoneisinitiallymotionless.Showthatafterthecollision,themovingobjectisstationaryandtheothermoveswiththesamespeedastheotheroriginallyhad.momentumbefore:momentumafter:finalvelocityofthesecondballisthesameastheinitialvelocityofthefirstball:

energybefore:energyafter:

MomentumafterthecollisionKineticenergybeforethecollisionKineticenergyafterthecollisionMomentumbeforethecollisionSolvingthisquadraticequationfornocollisionhappened

velocityafterthecollisionFromconservationofmomentumFromconservationofenergycombiningthetwoequations:thenfindm1Collisonwithfixedobjects(ground/wall)

v1

m1v1Inelasticcollisionin1dimensionAninelasticcollisionisoneinwhichthetotalkineticenergychangesPerfectlyinelasticcollision:thetwoobjectssticktogetherAperfectlyinelasticcollisionremovesmorekineticenergythananyothercollisionBUT:momentumisalwaysconserved!GoalkeeperstoppingafootballnofrictioninairbutkineticenergyislostinthefrictionbetweentheballandthegloveButhowmuchenergyislost?Conservationofmomentum

Buthowmuchenergyislost?Initialkineticenergy:Finalkineticenergy:almostalllost!

Wheredoesthelost

energygo?Kineticenergy???energyfrictionacceleratesblock2reactionforcedeceleratesblock1bothblocksmoveatthesamespeedblock2movesrelativetoblock1!block1deceleratesblock2acceleratesWorkonblock2:Workonblock1:action=reactionWorkonblock2:Workonblock1:kineticenergylostbyblock1kineticenergygainedbyblock2-Solvingcollisionproblems

ElasticMomentumKineticenergyFinal=Initial(Equation1)Final=Initial(Equation2)FinalvelocitiesofbothInelasticFinalvelocityofonesystemorotherrestrictionFinalmomentum=InitialmomentumFinalvelocityoftheotheroneEnergylostElasticcollisionsin2dimensionsMomentumisconservedforallthevectorcomponentsWedonotconsiderrotation!assume“point”massesChosecoordinatesystemwithanaxisinthedirectionofthevelocityofthemovingballconservationofmomentuminthex-direction:conservationofmomentuminthey-direction:2equations,4unknowns!:weneedtohavemoreinformation!theangle?thefinalvelocities?WeneedtwomoreequationsConservationofkineticenergyANDOneofv1f,

v2f,θ1andθ2,oranyrelation/restrictionbetweenthemIfknowingmorethanoneofthem,wemayavoiddealingwithkineticenergyWeknowinitialvelocities,oneoffinalvelocities,andthefinaldirectionofm1Whatarev2andθ2?dividethetwoequations:nowfindequationforthemomentuminyTwoelasticballscollideonafrictionlesshorizontaltabletop.Oneballwasoriginallyatrest.Theotherballhasamassof3kg,andan