M03_KNIG7655_03_ITG_CH03

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1、CHAPTER3VectorsandCoordinateSystemsRecommendedclassdays:2BackgroundInformationSurveys(Knight,1995)havefoundthatonlyaboutone-thirdofstudentsinatypicalintroductoryphysicsclassareknowledgeableenoughaboutvectorstobeginthestudyofNewtonianmechanics.Anotherone-thi

2、rdhavepartialknowledgeofvectors(e.g.,astudentwhocanaddvectorsgraphicallybutisn’tfamiliarwithvectorcomponents),whilethefinalone-thirdhaveessentiallynousefulknowledgeofvectors.Surveyedstudentswhowererepeatingthecoursegenerallydisplayedmajorgapsintheirknowledg

3、eofvectors,andthiswaslikelyacontributingfactortotheirpreviousfailureofthecourse.Studentswhocansuccessfullyaddandsubtractvectorsarestilloftenconfusedastojustwhatavectoris.Whenposedtheopen-endedquestion“Whatisavector?”theymayrespondwith“Avectorisaforce”orsome

4、similaranswer.Thesestudentsmayhavedifficultyrecognizingvelocityoraccelerationasvectorquantities.AlthoughstudentshaveusedCartesiancoordinatesystemsthroughouthighschool,manyhaveahardtimeinterpretingastatementsuchas“Avectorpointsinthenegativex-direction.”These

5、studentsareespeciallypronetomakingsignerrorswhendecomposingvectorsintocomponents.StudentLearningObjectives•Tounderstandthebasicpropertiesofvectors.•Toaddandsubtractvectorsbothgraphicallyandusingcomponents.•Tobeabletodecomposeavectorintoitscomponentsandtorea

6、ssemblevectorcomponentsintoamagnitudeandadirection.3-1•Torecognizeandusethebasicunitvectors.•Toworkwithtiltedcoordinatesystems.PedagogicalApproachThisisastraightforwardchapterthatintroducesjustenoughaboutvectorsforstudentstogetthroughNewton’slaws.Thedotandc

7、rossproductsaredelayeduntilneeded.Anexplicitvectordnotationwitharrows(e.g.,F)isusedthroughoutthetext,ratherthanthemoretraditionalboldfacenotion(e.g.,F).Studentspaylittleattentiontotheboldfacetype,andI’vefoundthattheyhandlevectorsbetterwhenthetextusesthesame

8、notationthattheinstructorandstudentsuseinhandwrittenwork.Whencomponentsarenotrequired,vectorsareoftenwrittenas(magnitude,ddirection)—forexample,F=(50N,30°northofeast).Studentsfindthisalogicalandusefuln