M08_KNIG7655_03_ITG_CH08

《M08_KNIG7655_03_ITG_CH08》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

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