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1、CHAPTER8DynamicsII:MotioninaPlaneRecommendedclassdays:3minimum,4preferredBackgroundInformationChapters8isacontinuationofsingle-particledynamics,firsttotwo-dimensionalproblemsinwhichthex-andy-motionsareindependentandthentocircularmotion.Manyofthestudentdifficultieswithforceandmotionth
2、atseemtohavebeenresolvedinChapters5–6resurfacewhenstudentsconsidermotioninaplane.ThefactthattheseissuesreappearineachnewcontextshowshowdifficultitisforstudentstoadoptaNewtonianthoughtpattern.Ontheotherhand,two-dimensionalmotionprovidesanopportunitytospiralbacktomanyearliertopicsforad
3、ditionalpractice.Manystudentideasabouta“forceofmotion”takeonnewlifeintwo-dimensionalsituations.Clement(1982)posedthefollowingproblemtoengineeringstudentsinacalculus-basedphysicscourse:Arocketismovingsidewaysindeepspace,withitsengineoff,fromAtoB.Itisnotnearanystarsorplanetsorotherouts
4、ideforces.ItsengineisfiredatpointBandleftonfor2swhiletherockettravelsfrompointBtosomepointC.DrawintheshapeofthepathfromBtoC.ThenshowthepathfrompointC,aftertheengineisturnedoff.Thisfigureshowsthemostcommonresponse.AnincorrectlineartrajectorybetweenBandCwasdrawnby89%ofstudents.Thisispe
5、rhapsnottoosurprisingbecausefewstudentswouldhaveanyreasontorecognizethatthissituationgivesaparabolic(orevencurved)trajectory.Moreinterestingisthat62%ofstudentspredictedthattherocketwouldreturntoitsoriginaldirectionaftertheengineisshutoffatC.Interviewswithstudentsfoundmanygivingexplan
6、ationssuchas“WhateverwasmakingitgototherightbeforewilltakeoveragainafterpointC.”Thisreflectsacontinuingbeliefina“forceofmotion”towardtheright.Circularmotionrequiresashiftinthinkingfromtheemphasisuntilnowonlinearmotionandmotionthatcanbedecomposedintoindependentlinearmotionsalongtwoaxe
7、s.Not8-1surprisingly,thisevokesnewdifficultiesforstudents.Arons(1990)citesanexperimentinwhichamarbleisrolledaroundtheinsideofanincompletecircularhooplyingflatonatable.Studentsareaskedtopredictthemarble’strajectoryafterpassingpointB.Somepredictitwillcontinuewithperfectcircularmotion,r
8、eenteringthe
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