Solutions Manual - Intro to Mechanics(Kleppner, Kolenkow, 2ed, 2014)

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1、SolutionsManualtoaccompanyANINTRODUCTIONTOMECHANICS2ndeditionVersion1November2013KLEPPNER/KOLENKOWcKleppnerandKolenkow2013CONTENTS1VECTORSANDKINEMATICS12NEWTON’SLAWS213FORCESANDEQUATIONSOFMOTION334MOMENTUM545ENERGY726TOPICSINDYNAMICS897ANGULARMOMENTUMAN

2、DFIXEDAXISROTATION1058RIGIDBODYMOTION1389NONINERTIALSYSTEMSANDFICTITIOUSFORCES14710CENTRALFORCEMOTION15611THEHARMONICOSCILLATOR17112THESPECIALTHEORYOFRELATIVITY18213RELATIVISTICDYNAMICS19614SPACETIMEPHYSICS2061.1Vectoralgebra1A=(2ˆi3ˆj+7kˆ)B=(5ˆi+ˆj+2k

3、ˆ)(a)A+B=(2+5)ˆi+(3+1)ˆj+(7+2)kˆ=7ˆi2ˆj+9kˆ(b)AB=(25)ˆi+(31)ˆj(72)kˆ=3ˆi4ˆj+5kˆ(c)A
B=(2)(5)+(3)(1)+(7)(2)=21ˆiˆjkˆ(d)AB=237512=13ˆi+31ˆj+17kˆ1.2Vectoralgebra2A=(3ˆi2ˆj+5kˆ)B=(6ˆi7ˆj+4kˆ)(a)A2=A
A=32+(2)2+52=38(b)B2=B
B=62+(7)2+42=101(c

4、)(A
B)2=[(3)(6)+(2)(7)+(5)(4)]2=[18+14+20]2=522=27042VECTORSANDKINEMATICS1.3CosineandsinebyvectoralgebraA=(3ˆi+ˆj+kˆ)B=(2ˆi+ˆj+kˆ)(a)A
B=ABcos(A;B)A
Bcos(A;B)=AB(6+1+1)4=pp=pp0:492(9+1+1)4+1+1)116(b)method1:jABj=ABsin(A;B)jABjsin(A;B)=ABˆiˆjkˆA

5、B=311211=(11)ˆi(3+2)ˆj+(3+2)kˆ=5ˆj+5kˆppjABj=52+52=52pjABj52sin(A;B)==pp0:870AB116(c)method2(simpler)–use:22sin+cos=1psin(A;B)=1cos2(A;B)p=1(0:492)2from(a)0:8711.4DirectioncosinesNotethathere;; standfordirectioncosines,notfortheanglesshown

6、inthefigure:=cos1;x=cos1;y=cos1.zcontinuednextpage=)VECTORSANDKINEMATICS3A=Axˆi+Ayˆj+AzkˆAx=A
ˆi=Acos(A;ˆi)A=cos(A;ˆi)=cosx:Similarly,Ay=Acos(A;ˆj)A=cos(A;ˆj)=cosyAz=Acos(A;kˆ)A=cos(A;kˆ)=coszUsingtheseresults,2222A=Ax+Ay+Az2222=A(++)fromwh

7、ichitfollowsthat222++=1Anotherwaytoseethisis2222222222A=+Az=Ax+Ay+Az=A(++)anditfollowsasbeforethat222++=1:1.5PerpendicularvectorsGivenjABj=jA+BjwithAandBnonzero.Evaluatethemagnitudesbysquaring.2222A2A
B+B=A+2A
B+B2A
B=+2A
B:A
B=0anditfollowsthatA?B.

8、4VECTORSANDKINEMATICS1.6DiagonalsofaparallelogramTheparallelogramisequilateral,soA=B.D1=A+BD2=BA22D1
D2=(A+B)
(BA)=AB=0:HenceD1
D2=0anditfollowsthatD1?D2.1.7LawofsinesTheareaAofthetriangleis111A=Ah=ABsin=jABj222Similarly,11A=