Ep 18.RodABis held inplacebythecordAC.Knowingthatthetension inthe cord is1350Nandthatc=360mm,determine themomentaboutB of the force exerted by the cord at pointAby resolving that forceinto horizontal and vertical components applied (a)atpoint A,(b)atpoint C.C240 mm450 mnSOLUTIONFree-BodyDiagramofRodAB:AC(450)2+(600)2=750mm(a)F=1350N450600=0.6=0.8COSα=sinα=750750F=Fcosai+Fsinaj= (1350 N)0.6i+ (1350 N)0.8j=(810N)i+(1080N)jrx=(0.45 m)i(0.24 m)jM,=F×F=(0.45i0.24j)×(810i+1080)=-486k+194.4kM.=292N-m= (291.6 N-m)k(b)F=(810N)i+(1080N)jrea = (0.36 m)jMg=rc/B×F=0.36jx(810i+1080)M.=292N-m=(291.6 N·m)k
Ep 18
Ep 19.Determinethe moment about the origin Oof the forceF=4i-3j+5k that acts at a PointA.Assume thatthepositionvectorofAis(a)r=2i+3j-4k,(b)r=-8i+6j-10k,(c)r=8i-6j+5kSOLUTIONMo=rxFlikjMo=23-4(a)4 35= (1512)i+(1610)j+ (612)kM。=3i-26j-18kikj610(b)Mo=-8435= (3030)i + (40 + 40)j+ (2424)kMo=0ijkMo=8-65(c)435=(30+15)i+(2040)j+(24+24)kM。=-15i-20j
Ep 19
Ep 20.Determine the value of a that minimizes theperpendicular distance from Point C to asection of pipeline that passes through PointsAand B.2 m3m10m24mSOLUTIONAssumingaforceFactsalongAB,Mc/=|ra/c×F|=F(d)whered=perpendicular distance from Cto line ABF=MAFB(24m)i + (24m)j (28m)k7V(24)2+(24)*+(28)mF-(6)i+ (6)j-(7)k11r4ic =(3 m)i-(10 m)j-(a-10 m)ki了kFMc=3-1010a11i766=[10+6a) +(81-6a)+78k]11[Mc/ = raic ×F](rAic ×F|= (dF)2Sinceor1(10 + 6a) + (81 6a)* + (78)2 = d2121Setting (d)=O to find a tominimized:1[2(+ 6)+2(6(81-60)-0Solvingq=5.92mora=5.92m
Ep 20
Ep 21.To loosena frozen valve,a force Fof magnitude 70 Nisapplied to the handle of the valve.Knowing that =25°M,=-7.32N-m,and M,=-5.16Nm,determineandd.11enSOLUTIONWehaveEMo:rAoxF=Mowhererxo = -(4 cm)i + (ll cm)j (d)kF=F(coscos pisinj+cosOsinok)ForF=70N.0=25°F=(70N)[(0.90631cos)i-0.42262j+(0.90631sin)k)ikj411-dMo=(70 N)cm-0.90631cos0.422620.90631sin=(70N)[(9.9694sin -0.42262d)i +(-0.90631d cos+3.6252sin )j+(1.69048-9.9694cos@)k)cmand(1)M,=(70N)(9.9694sin-0.42262d)cm=732N.cm(2) M,=(70N)(-0.90631dcos@+3.6252sin)cm(3)M,=(70N)(1.69048-9.9694cos)cm=-516N·cm(634.33)24.636°Φ=24.60From Equation (3)=cosor(697.86（1022.90）d==34.577cmFrom Equation (1)ord=0.346m29.583
Ep 21
Ep 22.A piece of plywood in which several holes are being drilledsuccessivelyhas been secured to a workbench bymeans of twonails.Knowing that the drill exerts a 12-N-m couple on thepiece of plywood, determine the magnitude of the resultingforces applied to the nails if they are located (a) at A and B,(b)atBandC, (c)atAandC.240mm450mmSOLUTION(a)M-Fd4F12N·m=F(0.45m)BtF=26.7NTA州H0.45m(b)M=FdE1012N-m=F(0.24m)0.24meF=50.0Nd = /(0.45 m)2 + (0.24 m)2M=Fd(c)=0.510m12N·m=F(0.510m)0.510nF=23.5NF
Ep 22