Solution Manual for Engineering Mechanics: Dynamics, 2nd Edition

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Engineering Mechanics: Dynamics 2eGray, Costanzo, PleshaAnswers to Selected Even-Numbered ProblemsPlease note that answers are not provided for the following type of even-numbered problems:Concept Problems.Computer Problems.Design Problems.For Concept and Computer problems, please consult the solutions manual.Chapter 11.2.rB=A/`D3:883ft1.4ErB=AˇˇxysystemD.4:000O{1:000O| /ftErB=AˇˇpqsystemD.3:313Oup2:455Ouq/ftˇˇErB=AˇˇxysystemDˇˇErB=AˇˇpqsystemD4:123ft1.6EvD.79:68O{C7:190O| /ft=s1.8D3:229radD0:087 31rad1.10vrD504:6ft=sandvD 353:3ft=s1.12D101:1ı1.14xP 2D 0:7679ftandyP 2D5:330ft1.16EvAD .20:02O{C12:81O| /ft=sandEaAD.1:414O{C4:243O| /ft=s21.18rD26:36mm1.20ŒIxxçDŒIyyçDŒI´´çDML2Units ofIxx,Iyy, andI´´in theSIsystem: kgm2;Units ofIxx,Iyy, andI´´in theU.S.Customary system: slugft2Dlbs2ft.1.22Concept problem.1.24the units ofEare kg=ms2.Chapter 22.2Concept Problem2.4Concept Problem1Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha2.6Er1D8:747OurmandEr2D13:73OurmEvavg1D5:467Ourm=sandEvavg2D8:579Ourm=s2.8EvD.154:0O{C266:7O| /ft=s2.10EvD.145:4O{C69:81O| /ft=s2.12Ev1D .0:4623O{C0:08155O| /m=sEv2D .0:002550O{C0:0004499O| /m=s2.141D12:21ıand2D 17:30ı1D102:2ıand2D72:70ı2.16.x/Dcos13C4xp10C24xC16x22.18EaavgD.0:04588O{C3:886O| /ft=s2Eaavg Ea.5s/D.0:001154O{0:003175O| /ft=s22.20ErD E0EvavgD E0dD1:394ftvavgD0:3485ft=s2.22Computer Problem2.24vmaxD2v0D58:67ft=sandvminD0ft=syvminD0ftandyvmaxD2RD2:300ftEavminDv20RO|D.748:2ft=s2/O|andEavmaxD v20RO|D.748:2ft=s2/O|2.26RxD8v20a3y2C4a22RyD4v20a2yy2C4a222.28EvD.203:2O{C117:3O| /ft=sEaD.27:53O{C47:69O| /ft=s22.30vmaxD80:82ft=s2.32EvD.51:32O{1:046O| /ft=sEaD .0:3873O{C19:00O| /ft=s22Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha2.34vD!pd2x2s1Ch2xd2x3d42vD0:5236ft=s;vD0:4554ft=s;andvD02.36EvAD .72:00O{C96:00O| /ft=sEaAD.460:8O{345:6O| /ft=s22.38Computer Problem2.40tbrakingD7:854s2.42jajmaxD3:600m=s2tjamaxj1D3:927sandtjamaxj2D11:78ssjamaxj1D12:84mandsjamaxj2D128:5m2.44Largest distance traveled in1s isdD0:2667m, corresponding toaDˇ1pt2.46v.0/D 0:080 00ft=s2.48v0D10:10m=s2.50acD22:36 g2.52tstopD2:880s2.54D98:10s12.56PxD˚7:000sinŒ.1:000rad=s/tçC10:50cosŒ.0:5000rad=s/tç10:50m=sxD˚7:0007:000cosŒ.1:000rad=s/tçC21:00sinŒ.0:5000rad=s/tç.10:50s1/tm=s22.58tstopD0:2233s2.60vtermD4:998m=s2.62jvjmaxD1:128m=ssjvjmaxD0:1250mandsjvjmaxD 0:1250m2.64v.t/DmgCd1eCdt=mvtermDmgCd2.66vfD3:563m=s2.68Computer Problem3Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha2.70swetD26:31m.swetsdry/sdry.100%/D65:21%2.72P./D ˙rP20C2 gLcoscos02.74PminD4:930rad=s2.76PxD ˙sv20C2gCkL0m.xx0/kmx2x202.78txmaxD0:2433s2.80(a)PrD p2G .mACmB/rr0rrr0(b)(i)PrD 5:980105ft=sand(ii)Pr! 12.82Concept Problem2.84dD186:4ft2.86˛sDaprChv2p2 r3˛sˇˇrDr1D1:442rad=s2and˛sˇˇrDr2D3:631rad=s22.88vDv0Cac.tt0/sDs0Cv0.tt0/C12ac.tt0/22.90vminD113:5ft=s2.92tiD3:497sEvBD.33:33O{34:31O| /m=s2.94RD5:047m2.96tflightD6:263sErlandD.281:8O{4:500O| /m2.98dD24:09m2.100(a)RmaxD4radD45ı(b)RmaxD233:5% of the actual maximum range(c)tRmaxD119:5s2.1021D12sin1.gR=v20/and2D90ı12sin1.gR=v20/1D24:86ıand2D65:14ı4Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha2.104.v0/minD50:75ft=s2.106EvinitialD.5:920O{C7:786O| /m=s:dydxˇˇˇˇxDxBD 0:22442.108hmaxDv20sin2ˇ2gcos2.110Computer Problem2.112tfRmaxD5:211sRmaxD437:1ftandRmaxD45:66ı2.114tmaxD3:000sHmaxD49:21mpercent increase in height with no air resistanceD2:363%2.116Computer Problem2.118(a)EaEbD1 6C23C30D0(b)EaEa EbD84O{42O|C0Ok(c)they are the same2.120(a)E!1D104:7Okrad=s;E!2D104:7O{rad=sandE!3D104:7O|rad=s(b)E!`D1003p3O{C O|C Okrad=sD60:46O{C O|C Okrad=s2.122Derivation, so no answer needed.2.124EvAD10:00O|m=s;EvBD10:00O|m=s;EvCD10:00O|m=s;andEvDD10:00O|m=s2.126E!wheelD 65:71Okrad=s2.128jEaPj D19;300ft=s2Orientation ofEaPfromxaxisD110:0ı.ccw/2.130v0D263:7ft=sandrD6875ft2.132PrD 1:204m=sandPD 0:8504rad=s2.134EvD.0:037 70OurC0:5341Ou/m=sEaD1678OurC236:9Oum=s22.136Concept Problem2.138PrˇˇD90ıD8:825ft=sandPˇˇD90ıD 0:7746rad=s5Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha2.140EaPD.252:9OuC399:8OuB/ft=s22.142Concept Problem2.144Concept Problem2.146D49:69ft2.148PvD3:213m=s22.150SüdkurveD50:56mNordkurveD92:54m2.152D327:3ft2.154dD831:0ft2.156EaD E02.158EaD.39:40O{C42:88O| /m=s22.160Concept Problem2.162ˇˇEaˇˇD.33:69103cos/m=s22.164EaD.121:2O{C230:0O| /ft=s22.166EaD 18:96ft=s2OutC69:91ft=s20:2917s2sOun2.168PvD 5:343m=s2andD17:50m2.170D282:2ft2.172minD564:5fttft0D4:742s2.174jEaj D1v02v0 ss4v202Cv02v0 s22.176dD304:4ftandtfD3:106s2.178Concept Problem2.180Concept Problem2.182PrD684:1ft=sandPD 0:011 57rad=sRrD4:944ft=s2andRD0:000 428 1rad=s22.184vD1:816m=sˇˇEaˇˇD4:573m=s26Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha2.186RrD1:599m=s22.1880D0r0D0:014 86m2.190EvD.1:3m=s/OurC0:22s1rOuEaD 0:048 40s2rOur0:5720m=s2Ou2.192EvD.0:1500OurC1:732Ou/ft=sandEaD.0:3638OurC0:1125Ou/ft=s22.194ErD30:20OurftEvD.3OurC7:550Ou/ft=sEaD.1:888OurC1:500Ou/ft=s22.196D5:602 m!D2630rad=sD25;120rpm2.198vD5490ft=sˇˇEaˇˇD1:005106ft=s22.200EvDv0p2C.r0C/2OurCv0.r0C/p2C.r0C/2OuEaD v20.r0C/3r20C2r0C.1C2/22OurCv20˚.r0C/2C22C.r0C/2Œ2C.r0C/22Ou2.202PAD 0:001 157rad=sandPHD 4:287rad=sRAD 1:684104rad=s2andRHD 0:075 47rad=s22.204PEaD«r3rPR3PrP2OurChr«P3C3RrPC3PrRiOu2.206RrD5:781ft=s2RD 1:421rad=s22.208rDqh2C.dC/2PrDv0hph2C.dC/2andPDv0.dC/h2C.dC/2RrD v20.Cd /d2Ch2Cdd2Ch2C2C2d3=2andRDv20hd2Ch22d2Ch2C2C2d22.210EvD1:758O|m=sandEaD136:9gO|2.212vD0:1185ft=sandˇˇEaˇˇD0:086 42ft=s27Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha2.214arDK2ab21r22.216Computer Problem2.218Concept Problem2.220vH=FDh5:6301050:8091cosx2im=saH=FD5:237sinx2m=s22.222vA=BD144:7m=s2.224EvC =AD.6:857O{C30:27O| /m=s:EaC =AD.1:376O{1:000O| /m=s2:2.226.vP/avgD17:30ft=s2.228Computer Problem2.230vpmaxD330:7ft=sD225:4mph2.232EvBD2:928O{ft=s2.234vrainD16:37ft=s2.236EaBDL1RcosL1P2sinCL2RcosL2P2sinO{CL1RsinCL1P2cosCL2RsinCL2P2cosO|2.238D63:57ı2.240D14:90ı2.242EvBD 3:088O|ft=s:EaBD 0:3192O|ft=s2:2.244EvBD 2:000O|m=s:2.246vAyD 4:596ft=s:2.248EaBD 11:10O{m=s2:@tdD0:1644s2.250a0D0:9374ft=s22.252P`Ddv0ph2Cd22.254Component ofEvC =BalongBCD08Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha2.256rDq.dCcos/2C.hCsin/2PDv0.CdcosChsin/.dCcos/2C.hCsin/2andPrDv0.hcosdsin/p.dCcos/2C.hCsin/22.258tD0:1556s2.260RyeD 9:81m=s2RyCˇˇtD0:4391sD 44:51m=s22.262Concept Problem2.264Concept Problem2.266tD83:82s2.268EvCD.6:500OuRC5:520OuC5:300Ou´/ft=sEaCD.0:6624OuR1:560Ou/ft=s22.270rP.rRsinC2PrPsinC2rPPcos/rPsin.rRC2PrPrP2sincos/D0;rPsin.RrrP2rP2sin2/ Pr.rRsinC2PrPsinC2rPPcos/D0;Pr.rRC2PrPrP2sincos/rP.RrrP2rP2sin2/D02.272EvD.0:04869OuRC7:961Ou0:2999Ou´/m=sEaD.79:79OuRC0:9738Ou0:8120Ou´/m=s22.274ˇˇEamaxˇˇD12:36ft=s22.276EvDdfd´P´OurCKf .´/OuC P´Ou´EaDR´C P´2d2fd´2K2f3.´/OuRC R´Ou´2.278arD 0:1598m=s2;aD 0:1884m=s2;andaD0:2232m=s22.280EvP =BD.10:17O{BC10:33O|B/m=sandvP =BDvP =AD14:50m=sEaP =BD.7:822O{B1:258O|B/m=s2andˇˇEaP =BˇˇDˇˇEaP =AˇˇD7:923m=s22.282Concept Problem2.284Computer Problem2.286sDmgC2dCdtCmeCdmt12.288xDL0Cgmk1cosrkm t2.290v0pgR9Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha2.292D240:5ft2.294The car will lose contact with the ground.acD 1:606m=s22.296PrˇˇD180ıD0PˇˇD180ıD 2:941rad=sRrˇˇD180ıD 40:85m=s2andRˇˇD180ıD02.298PD0:053 91rad=sRD 0:2380rad=s22.300vmaxD6:020ft=s2.302hmaxD0:8898ft2.304jEaAj D18:65m=s22.306ˇˇEaˇˇD172;700ft=s22.308ˇˇEaˇˇminD2:534m=s2Chapter 33.2Concept Problem3.4EaAD2:147O|ft=s2:3.6amaxD17:75ft=s23.8aBmaxD0:1650m=s2D0:5417ft=s23.10RxCEAmL xD03.12aBmaxD5:048m=s2D16:57ft=s23.14dD6:630ft3.16dD417:5ftIf an entire train weighing30106lb was skidding to a stop, instead of a locomotive, we would have the samestopping distance because the weight does not appear in our solution.3.18EaDCdm v2gO| :3.20.s/minD0:34363.22viD5:297ft=s10Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha3.24Computer Problem3.26viD32:68106m=s3.28vmaxDgrmk3.30Spring compressionD0:7367ft3.32kD5:084104lb=ft3.34ımaxD0:1675m.Fs/maxD586:1N3.36Computer Problem3.38xstopD0:1597m3.40kD5:930lb=ft3.42kD9034kg=s23.44v.0/Ds2 kmx20C2L0Lqx20CL23.46Concept Problem3.48Concept Problem3.50Concept Problem3.52D1:401104ft3.54No value of!ccan be found that would cause the person to slide up the wall3.56.FOA/before releaseDmgcos ;.FOA/after releaseDmgcos;.% change inFOA/D30ıD 25:00%3.58jEaj D3:620 gjFLj D43;060N3.60RxCkm x1rupx2Cy2!D0;RyCkm y1rupx2Cy2!D03.62RrrP2Ckm .rru/gcosD0andrRC2PrPCgsinD03.64tsD0:7466s3.66yDmCdtan0eCdx=m1m2g2C2dv20cos20eCdx=m1211Last modified: August 16, 2012

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Engineering Mechanics: Dynamics 2eGray, Costanzo, Plesha3.68aD0Da´;aRD g.sCtan/1stanD 120:1ft=s2;FD0;FDsmgcosssinD.83:16ft=s2/ m;NDmgcosssinD.92:40ft=s2/ m;vmaxD pgssCtan1stanD363:4ft=sD247:8mph3.70FD5971lb3.72.!c/maxD2:733rad=s3.74(a)EaD.318:8103OurC603:0Ou/m=s2(b)PD5:898106NandRD11:33103N3.76!D9:939rad=s3.78BD41:81ı3.80Concept Problem3.82RrrP2CG mer2D0andrRC2PrPD03.84ıminDr5mgrkvBDp2gr3.86Computer Problem3.88hmaxD0:3618ft3.90RxL2y2C RyxyCxPx2L2y2C Py2L2x2C2xyPxPyL2x2y2CgxqL2x2y2D0;RyL2x2C RxxyCyPx2L2y2C Py2L2x2C2xyPxPyL2x2y2CgyqL2x2y2D03.92RP2sincosC.g=L/sinD0andRsinC2PPcosD03.94RrrP2D0andrRC2PrPD03.96M´D2m!20rqr2r20jvrj D!0qd2C2dr0vD!0q2d2C4dr0Cr203.98Concept Problem12Last modified: August 16, 2012

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