Momentum-and-Isolated-Systems動量與分離系統(tǒng)教學課件

MomentumandIsolatedSystemsThepreviouspartofLesson2focusedontheLawofConservationofMomentum.Itwasstatedthat...Foracollisionoccurringbetweenobject1andobject2inanisolatedsystem,thetotalmomentumofthetwoobjectsbeforethecollisionisequaltothetotalmomentumofthetwoobjectsafterthecollision.Thatis,themomentumlostbyobject1isequaltothemomentumgainedbyobject2.Totalsystemmomentumisconservedforcollisionsoccurringinisolatedsystems.Butwhatmakesasystemofobjectsanisolatedsystem?Andismomentumconservedifthesystemisnotisolated?Thisisthefocusofthislesson.Asystemisacollectionoftwoormoreobjects.Anisolatedsystemisasystemwhichisfreefromtheinfluenceofanetexternalforce.Therearetwocriteriaforthepresenceofanetexternalforce;itmustbe...aforcewhichoriginatesfromasourceotherthanthetwoobjectsofthesystemaforcethatisnotbalancedbyotherforcesConsiderthecollisionoftwoballsonthebilliardstable.Thecollisionoccursinanisolatedsystemaslongasfrictionissmallenoughthatitsinfluenceuponthemomentumofthebilliardballscanbeneglected.Ifso,thentheonlyunbalancedforcesactinguponthetwoballsarethecontactforceswhichtheyapplytooneanother.Thesetwoforcesareconsideredinternalforcessincetheyresultfromasourcewithinthesystem-thatsourcebeingthecontactofthetwoballs.Forsuchacollision,totalsystemmomentumisconserved.Readthefollowingdescriptionsofacollisionandevaluatewhetherornotthecollisionoccursinanisolatedsystem.Ifitisnotanisolatedsystem,thenidentifythenetexternalforce.Collision

Description

IsolatedSystem?YesorNo

IfNo,thentheexternalforceis...

1Twocarscollideonagravelroadwayonwhichfrictionalforcesarelarge.2HansFullisdoingtheannualvacuuming.HansispushingtheHoovervacuumcleaneracrossthelivingroomcarpet.3Twoairtrackgliderscollideonafriction-freeairtrack.Collision

Description

IsolatedSystem?YesorNo

IfNo,thentheexternalforceis...

1Twocarscollideonagravelroadwayonwhichfrictionalforcesarelarge.NoThefrictionbetweenthecarsandtheroadisanexternalforce2HansFullisdoingtheannualvacuuming.HansispushingtheHoovervacuumcleaneracrossthelivingroomcarpet.NoThefrictionbetweenthecleanerandthefloorandtheappliedforcebyHansareexternalforces3Twoairtrackgliderscollideonafriction-freeairtrack.YesTherearenoexternalforces.ThesystemisisolateIfasystemisnotisolated,thenthetotalsystemmomentumisnotconserved.Tounderstandthisconcept,wewillreturntoouroriginalanalogy.SupposeJackandJill(eachwith$100intheirpockets)undergoafinancialinteractioninwhichJackhandsJill$50forthepurchaseofsomegoods.IfJackandJillwereisolatedfromtheinfluenceoftherestoftheworld,thenJackwouldendupwith$50andJillwouldendupwith$150.Thetotalmoneyinthesystemwouldbe$200bothbeforeandafterthetransaction;totalsystemmoneywouldbeconserved.Ifhowever,athirdinfluenceentersfromoutsideofthesystemtotakeawayor(morefortunately)toaddmoneytothesystem,thentotalsystemmomentumwouldnotbeconserved.Ifathiefinterferedwithhisfilthyhandssoastosteal$20,thenperhapsJackwouldfinishwith$40andJillwouldfinishwith$140.Inthecaseofanon-isolatedsystem,thetotalmomentumisnotconserved.UsingEquationsasa"Recipe"forAlgebraicProblem-SolvingAsdiscussedinapreviouspartofLesson2,totalsystemmomentumisconservedforcollisionsbetweenobjectsinanisolatedsystem.Themomentumlostbyoneobjectisequaltothemomentumgainedbyanotherobject.Forcollisionsoccurringinanisolatedsystems,therearenoexceptionstothislaw.Thislawbecomesapowerfullawinphysicsbecauseitallowsforpredictionsofthebefore-andafter-collisionvelocities(ormass)ofanobject.InthisportionofLesson2,thelawofmomentumconservationwillbeusedtomakesuchpredictions.Thelawofmomentumconservationwillbecombinedwiththeuseofa"momentumtable"andsomealgebraskillstosolveproblemsinvolvingcollisionsoccurringinisolatedsystems.ConceptExampleA15-kgmedicineballisthrownatavelocityof20km/hrtoa60-kgpersonwhoisatrestonice.Thepersoncatchestheballandsubsequentlyslideswiththeballacrosstheice.Determinethevelocityofthepersonandtheballafterthecollision.BeginningtoformasolutionSuchamotioncanbeconsideredasacollisionbetweenapersonandamedicineball.Beforethecollision,theballhasmomentumandthepersondoesnot.Thecollisioncausestheballtolosemomentumandthepersontogainmomentum.Afterthecollision,theballandthepersontravelwiththesamevelocity("v")acrosstheice.Drawadiagram!Ifitcanbeassumedthattheeffectoffrictionbetweenthepersonandtheiceisnegligible,thenthecollisionhasoccurredinanisolatedsystem.Momentumshouldbeconservedandtheproblemcanbesolvedforvbyuseofamomentumtableasshownbelow.BeforeCollision

AfterCollisionPerson

060*vMedicineball

30015*vTotal

300300Observeinthetableabovethattheknowninformationaboutthemassandvelocityofthetwoobjectswasusedtodeterminethebefore-collisionmomentaoftheindividualobjectsandthetotalmomentumofthesystem.Sincemomentumisconserved,thetotalmomentumafterthecollisionisequaltothetotalmomentumbeforethecollision.Finally,theexpression"60*v"and"15*v"wasusedfortheafter-collisionmomentumofthepersonandthemedicineball.Tosolvetheproblemfor"v"(thevelocityofboththeobjectsafterthecollision),setthesumoftheindividualmomentumofthetwoobjectsequaltothetotalmomentum.Thefollowingequationresults:Solution60*v+15*v=300

75*v=300

v=4km/hr

Usingalgebraskills,itcanbeshownthatv=4km/hr.Boththepersonandthemedicineballmoveacrosstheicewithavelocityof4km/hrafterthecollision.(NOTE:Theunitkm/hristheunitontheanswersincetheoriginalvelocityasstatedinthequestionhadunitsofkm/hr.)Granny(m=80kg)whizzesaroundtherinkwithavelocityof6m/s.ShesuddenlycollideswithAmbrose(m=40kg)whoisatrestdirectlyinherpath.Ratherthanknockhimover,shepickshimupandcontinuesinmotionwithout"braking."DeterminethevelocityofGrannyandAmbrose.Assumethatnoexternalforcesactonthesystemsothatitisanisolatedsystem.Beforethecollision,GrannyhasmomentumandAmbrosedoesnot.ThecollisioncausesGrannytolosemomentumandAmbrosetogainmomentum.Afterthecollision,theGrannyandAmbrosemovewiththesamevelocity("v")acrosstherink.SincethecollisionbetweenGrannyandAmbroseoccursinanisolatedsystem,totalsystemmomentumisconserved.Thetotalmomentumbeforethecollision(possessedsolelybyGranny)equalsthetotalmomentumafterthecollision(sharedbetweenGrannyandAmbrose).Thetablebelowdepictsthisprincipleofmomentumconservation.BeforeCollision

AfterCollision

Granny

80*6=48080*vAmbrose

040*vTotal

480480ObserveinthetableabovethattheknowninformationaboutthemassandvelocityofGrannyandAmbrosewasusedtodeterminethebefore-collisionmomentaoftheindividualobjectsandthetotalmomentumofthesystem.Sincemomentumisconserved,thetotalmomentumafterthecollisionisequaltothetotalmomentumbeforethecollision.Finally,theexpression"80*v"and"40*v"wasusedfortheafter-collisionmomentumoftheGrannyandAmbrose.Tosolvetheproblemfor"v"(thevelocityofbothpersonsafterthecollision),setthesumoftheindividualmomentumofthetwoobjectsequaltothetotalmomentum.Thefollowingequationresults:80*v+40*v=480

120*v=480

v=4m/sUsingalgebraskills,itcanbeshownthatv=4m/s.BothGrannyandAmbrosemoveacrosstheicewithavelocityof4m/safterthecollision.(NOTE:Theunitm/sistheunitontheanswersincetheoriginalvelocityasstatedinthequestionhadunitsofm/s.)Thetwocollisionsaboveareexamplesofinelasticcollisions.Technically,aninelasticcollisionisacollisioninwhichthekineticenergyofthesystemofobjectsisnotconserved.Inaninelasticcollision,thekineticenergyofthecollidingobjectsistransformedintoothernon-mechanicalformsofenergysuchasheatenergyandsoundenergy.ThesubjectofenergywillbetreatedinalaterunitofThePhysicsClassroom.Tosimplifymatters,wewillconsideranycollisionsinwhichthetwocollidingobjectssticktogetherandmovewiththesamepost-collisionspeedtobeanextremeexampleofaninelasticcollision.Nowwewillconsidertheanalysisofacollisioninwhichthetwoobjectsdonotsticktogether.Inthiscollision,thetwoobjectswillbounceoffeachother.Whilethisisnottechnicallyanelasticcollision,itismoreelasticthancollisionsinwhichthetwoobjectssticktogether

A3000-kgtruckmovingwithavelocityof10m/shitsa1000-kgparkedcar.Theimpactcausesthe1000-kgcartobesetinmotionat15m/s.Assumingthatmomentumisconservedduringthecollision,determinethevelocityofthetruckafterthecollision.Inthiscollision,thetruckhasaconsiderableamountofmomentumbeforethecollisionandthecarhasnomomentum(itisatrest).Afterthecollision,thetruckslowsdown(losesmomentum)andthecarspeedsup(gainsmomentum).Thecollisioncanbeanalyzedusingamomentumtablesimilartotheabovesituations.BeforeCollision

AfterCollision

Truck

3000*10=300003000*vCar

01000*15=15000Total

3000030000Observeinthetableabovethattheknowninformationaboutthemassandvelocityofthetruckandcarwasusedtodeterminethebefore-collisionmomentaoftheindividualobjectsandthetotalmomentumofthesystem.Sincemomentumisconserved,thetotalmomentumafterthecollisionisequaltothetotalmomentumbeforethecollision.Theafter-collisionvelocityofthecarisused(inconjunctionwithitsmass)todetermineitsmomentumafterthecollision.Finally,theexpression"3000*v"wasusedfortheafter-collisionmomentumofthetruck(visthevelocityofthetruckafterthecollision).Tosolvetheproblemfor"v"(thevelocityofthetruck),setthesumoftheindividualafter-collisionmomentumofthetwoobjectsequaltothetotalmomentum.Thefollowingequationresults:3000*v+15000=30000

3000*v=15000

v=5.0m/s

Usingalgebraskills,itcanbeshownthatv=5.0m/s.Thetruck'svelocityimmediatelyafterthecollisionis5.0m/s.Aspredicted,thetruckhassloweddown(lostmomentum)andthecarhasgainedmomentum.Thethreeproblemsaboveillustratehowthelawofmomentumconservationcanbeusedtosolveproblemsinwhichtheafter-collisionvelocityofanobjectispredictedbasedonmass-velocityinformation.Thereareadditionalpracticeproblems(withaccompanyingsolutions)laterinthislessonwhichareworththepractice.However,becertainthatyoudon'tcometobelievethatphysicsismerelyanappliedmathematicscoursewhichisdevoidofconcepts.Forcertain,mathematicsisappliedinphysics;however,physicsisaboutconceptsandthevarietyofmeansinwhichtheyarerepresented.Mathematicalrepresentationsarejustoneofthemanyrepresentationsofphysicsconcepts.Avoidmerelytreatingthesecollisionproblemsasmeremathematicalexercises.Takethetimetounderstandtheconceptofmomentumconservationwhichprovidesthebasisoftheirsolution.PreviewofWhat’sAhead!Thenextsectionofthislessoninvolvesexamplesofproblemswhichprovidearealtestofyourconceptualunderstandingofmomentumconservationincollisions.Beforeproceedingwiththepracticeproblems,besuretotryafewofthemoreconce