Solution Manual for Engineering Mechanics Statics in SI Units, 14th Edition

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11–1.Evaluate each of the following and express with anappropriate prefix: (a) (430 kg)2, (b) (0.002 mg)2, and(c) (230 m)3.Solutiona)(430 kg)2=0.185(106) kg2=0.185 Mg2Ans.b)(0.002 mg)2=[2(10-6) g]2=4mg2Ans.c)(230 m)3=[0.23(10 ) m]33=0.0122 km3Ans.Ans:0.185 Mg24mg20.0122 km3

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21–2.Represent each of the following combinations of units in thecorrect SI form: (a) Mg>ms, (b) N>mm, (c) mN>(kg#ms).Solution(a)Mgms=103kg10-3s=106kg>s=Gg>sAns.(b)Nmm=1 N10-3m=103N>m=kN>mAns.(c)mN(kg#ms)=10-3N10-6kg#s=kN>(kg#s)Ans.Ans:Gg>skN>mkN>(kg#s)

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31–3.What is the weight in newtons of an object that has a massof (a) 8 kg, (b) 0.04 kg, and (c) 760 Mg?Solution(a)W=9.81(8)=78.5 NAns.(b)W=9.81(0.04)(10-3)=3.92(10-4) N=0.392 mNAns.(c)W=9.81(760)(103)=7.46(106) N=7.46 MNAns.Ans:W=78.5 NW=0.392 mNW=7.46 MN

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4Represent each of the following combinations of units inthecorrectSIform:(a)>ms,(b)>mN,and(c)MN>(kg#ms).Solution(a)kN>ms=103N>(10-6)s=GN>sAns.(b)Mg>mN=10 g6>-3=Gg>NAns.(c)MN>(kg#ms)=106N>kg(10-3=GN>(kgs)#Ans.*1–4.(10)N)sKNMgAns:GN>sGg>NGN>(kg#s)

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51–5.Represent each of the following quantities in the correctSI form using an appropriate prefix: (a) 0.000 431 kg,(b), and (c) 0.005 32 km.35.3(103) NSOLUTIONa)Ans.b)Ans.c)Ans.0.005 32 km=0.005 32A103Bm=5.32 m35.3A103BN=35.3 kN0.000 431 kg=0.000 431A103Bg=0.431 gAns:0.431g35.3kN5.32m

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61–6.SOLUTIONa)Ans.b)Ans.c)Ans.d) kmAns.#mN=103m10-6N=10-3m=mmks>mg=11023s1102-6kg=11029skg=Gs>kgmkm=1102-611023m=1102-3m=mmm>ms=¢m1102-3s≤=¢11023ms≤=km>sRepresent each of the following combinations of units inthe correct SI form using an appropriate prefix: (a)(b)(c) ksand (d) km#mN.mkm,#N#N>mg,m>ms,Ans:km>smmGs>kgmm#N

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71–7.Represent each of the following as a number between 0.1and1000usinganappropriateprefix:(a)45 320kN,(b)568(105) mm, and (c)0.00563 mg.Solution(a)45 320 kN=45.3 MNAns.(b)568(105) mm=56.8 kmAns.(c)0.00563 mg=5.63mgAns.Ans:45.3 MN56.8 km5.63mg

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8Represent each of the following combinations of units in thecorrect SI form: (a)GN#mm,(b)kg>mm,(c)N>ks , and2(d)KN>ms.Solution(a)GN#mm=109(10-6) N#m=kN#mAns.(b)kg>mm=103g>10-6m=Gg>mAns.(c)N>ks2=N>106s2=10-6N>s2=mN>s2Ans.(d)kN>ms=103N>10-6s=109N>s=GN>sAns.*1–8.Ans:kN#mGg>mmN>s2GN>s

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91–9.SOLUTIONa)Ans.b)Ans.c)Ans.=mm#kgmmMg#=C10-6mD#C103kgD=(10)-3m#kgmN>ms=10-3N10-6s=103Ns=kN>sMg>mm=103kg10-3m=106kgm=Gg>mRepresent eachof the following combinations of unitsinthe correct SI form using an appropriate prefix: (a) Mg/mm,(b)(c)mm#Mg.mN>ms,Ans:Gg>mkN>smm#kg

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101–10.Represent eachof the following withSI unitshaving anappropriate prefix: (a) 8653 ms, (b) 8368 N, (c) 0.893 kg.SOLUTIONa)Ans.b)Ans.c)Ans.0.893 kg=893(10-3)(103) g=893 g8368 N=8.368 kN8653 ms=8.653(10)3(10-3) s=8.653 sAns:8.653 s8.368kN893g

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111–11.Using the SI system of units, show that Eq. 1–2 is adimensionally homogeneous equation which givesFinnewtons.Determinetothreesignificantfiguresthegravitational force acting between two spheres that aretouching each other. The mass of each sphere is 200 kg andthe radius is 300 mm.Ans:7.41mNSOLUTIONUsing Eq. 1–2,Ans.=7.41A10-6BN=7.41mN=66.73A10-12B c200(200)0.62dF=G m1m2r2N=am3kg#s2b akg#kgm2b=kg#ms2(Q.E.D.)F=G m1m2r2

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12Roundoffthefollowingnumberstothreesignificantfigures: (a) 58 342 m, (b) 68.534 s, (c) 2553 N, and(d) 7555 kg.SOLUTIONa)58.3 kmb)68.5 sc)2.55 kNd)Ans.7.56 Mg*1–12.Ans:58.3km68.5s2.55kN7.56Mg

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131–13.A rocket has a mass of 3.529(10 ) kg on earth. Specify(a) its mass in SI units and (b) its weight in SI units. If therocket is on the moon, where the acceleration due to gravityisgm=1.61 m/s2,determine to three significant figures(c) its weight in SI units and (d) its mass in SI units.Solutiona)3.529(106) kg=3.53 GgAns.b)We=mg=33.52911062kg4 19.81 m>s22=34.61911062kg#m>s2=34.6 MNAns.c)Wm=mgm=33.52911062kg4 11.61 m>s22=5.68211062N=5.68 MNAns.OrWm=Weagmgb=(34.619 MN)a1.61 m>s29.81 m>s2b=5.68 MNd) Since the mass is independent of tis location, thenmm=me=3.53 GgAns.Ans:3.53 Gg34.6 MN5.68 MNmm=me=3.53 Gg6

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141–14.and (c) 435 MN 23.2 mm.>(a) 354 mg(45 km)(0.0356 kN), (b) (0.004 53 Mg) (201 ms),>SOLUTIONa)Ans.b)Ans.c)Ans.435 MN>23.2 mm=435A106BN23.2A10-3Bm=18.75A109BNm=18.8 GN>m=0.911 kg#s(0.00453 Mg)(201 ms)=C4.53A10-3B A103BkgD C201A10-3BsD=0.447 kg#m>N=0.447A103Bg#mN(354 mg)(45 km)>(0.0356 kN)=C354A10-3BgD C45A103BmD0.0356A103BNEvaluate each of the following to three significant figures andexpress each answer in Sl units using an appropriate prefix:Ans:0.447 kg#m>N0.911 kg#s18.8 GN>m

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151–15.Evaluate each of the following to three significant figures andexpress each answer in SI units using an appropriate prefix:(a)(212 mN) , (b)2(52 800Solution(a)(212 mN)2=3212(10)-3N42=0.0449 N2=44.9(10)-3N2Ans.(b)(52 800 ms)2=352 800(10)-342s2=2788 s2=2.79(103) s2Ans.(c)3548(10)6412ms=(23 409)(10)-3s=23.4(10)3(10)-3s=23.4 sAns.Ans:44.9(10)-3N22.79(103) s223.4 sms) , and (c)2[548(10 )]61>2ms.

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