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

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    1 1–1. Evaluate each of the following and express with an appropriate prefix: (a) (430 kg) 2 , (b) (0.002 mg) 2 , and (c) (230 m) 3 . Solution a) (430 kg) 2 = 0.185(10 6 ) kg 2 = 0.185 Mg 2 Ans. b) (0.002 mg) 2 = [2(10 - 6 ) g] 2 = 4 m g 2 Ans. c) (230 m) 3 = [0.23(10 ) m] 3 3 = 0.0122 km 3 Ans. Ans: 0.185 Mg 2 4 m g 2 0.0122 km 3

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    2 1–2. Represent each of the following combinations of units in the correct SI form: (a) Mg > ms, (b) N > mm, (c) mN > (kg # m s). Solution (a) Mg ms = 10 3 kg 10 - 3 s = 10 6 kg > s = Gg > s Ans. (b) N mm = 1 N 10 - 3 m = 10 3 N > m = kN > m Ans. (c) mN (kg # m s) = 10 - 3 N 10 - 6 kg # s = kN > (kg # s) Ans. Ans: Gg > s kN > m kN > (kg # s)

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    3 1–3. What is the weight in newtons of an object that has a mass of (a) 8 kg, (b) 0.04 kg, and (c) 760 Mg? Solution (a) W = 9.81(8) = 78.5 N Ans. (b) W = 9.81(0.04)(10 - 3 ) = 3.92(10 - 4 ) N = 0.392 mN Ans. (c) W = 9.81(760)(10 3 ) = 7.46(10 6 ) N = 7.46 MN Ans. Ans: W = 78.5 N W = 0.392 mN W = 7.46 MN

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    4 Represent each of the following combinations of units in the correct SI form: (a) > m s, (b) > mN, and (c) MN > (kg # ms). Solution (a) kN > m s = 10 3 N > (10 - 6 ) s = GN > s Ans. (b) Mg > mN = 10 g 6 > - 3 = Gg > N Ans. (c) MN > (kg # ms) = 10 6 N > kg(10 - 3 = GN > (kg s) # Ans. *1–4. (10 )N )s KN Mg Ans: GN > s Gg > N GN > (kg # s)

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    5 1–5. Represent each of the following quantities in the correct SI form using an appropriate prefix: (a) 0.000 431 kg, (b) , and (c) 0.005 32 km. 35.3(10 3 ) N SOLUTION a) Ans. b) Ans. c) Ans. 0.005 32 km = 0.005 32 A 10 3 B m = 5.32 m 35.3 A 10 3 B N = 35.3 kN 0.000 431 kg = 0.000 431 A 10 3 B g = 0.431 g Ans: 0.431 g 35.3 kN 5.32 m

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    6 1–6. SOLUTION a) Ans. b) Ans. c) Ans. d) km Ans. # m N = 10 3 m 10 - 6 N = 10 - 3 m = mm ks > mg = 1 10 2 3 s 1 10 2 - 6 kg = 1 10 2 9 s kg = Gs > kg m km = 1 10 2 - 6 1 10 2 3 m = 1 10 2 - 3 m = mm m > ms = ¢ m 1 10 2 - 3 s ≤ = ¢ 1 10 2 3 m s ≤ = km > s Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) (b) (c) ks and (d) km # m N. m km, # N # N > mg, m > ms, Ans: km > s mm Gs > kg mm # N

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    7 1–7. Represent each of the following as a number between 0.1 and 1000 using an appropriate prefix: (a) 45 320 kN, (b) 568(10 5 ) mm, and (c) 0.00563 mg. Solution (a) 45 320 kN = 45.3 MN Ans. (b) 568(10 5 ) mm = 56.8 km Ans. (c) 0.00563 mg = 5.63 m g Ans. Ans: 45.3 MN 56.8 km 5.63 m g

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    8 Represent each of the following combinations of units in the correct SI form: (a) GN # m m, (b) kg > m m, (c) N > ks , and 2 (d) KN > m s. Solution (a) GN # m m = 10 9 (10 - 6 ) N # m = kN # m Ans. (b) kg > m m = 10 3 g > 10 - 6 m = Gg > m Ans. (c) N > ks 2 = N > 10 6 s 2 = 10 - 6 N > s 2 = m N > s 2 Ans. (d) kN > m s = 10 3 N > 10 - 6 s = 10 9 N > s = GN > s Ans. *1–8. Ans: kN # m Gg > m m N > s 2 GN > s

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    9 1–9. SOLUTION a) Ans. b) Ans. c) Ans. = mm # kg m m Mg # = C 10 - 6 m D # C 10 3 kg D = (10) - 3 m # kg mN > m s = 10 - 3 N 10 - 6 s = 10 3 N s = kN > s Mg > mm = 10 3 kg 10 - 3 m = 10 6 kg m = Gg > m Represent eac h of t h e fo ll ow i ng com bi nat i ons of un i ts i n the correct SI form using an appropriate prefix: (a) Mg/mm, (b) (c) m m # Mg. mN > m s, Ans: Gg > m kN > s mm # kg

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    10 1–10. Represent eac h of t h e fo ll ow i ng w i t h SI un i ts h av i ng an appropriate prefix: (a) 8653 ms, (b) 8368 N, (c) 0.893 kg. SOLUTION a) Ans. b) Ans. c) Ans. 0.893 kg = 893(10 - 3 )(10 3 ) g = 893 g 8368 N = 8.368 kN 8653 ms = 8.653(10) 3 (10 - 3 ) s = 8.653 s Ans: 8.653 s 8.368 kN 893 g

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    11 1–11. Using the SI system of units, show that Eq. 1–2 is a dimensionally homogeneous equation which gives F in newtons. Determine to three significant figures the gravitational force acting between two spheres that are touching each other. The mass of each sphere is 200 kg and the radius is 300 mm. Ans: 7.41 m N SOLUTION Using Eq. 1–2, Ans. = 7.41 A 10 - 6 B N = 7.41 m N = 66.73 A 10 - 12 B c 200(200) 0.6 2 d F = G m 1 m 2 r 2 N = a m 3 kg # s 2 b a kg # kg m 2 b = kg # m s 2 ( Q . E . D . ) F = G m 1 m 2 r 2

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    12 Round off the following numbers to three significant figures: (a) 58 342 m, (b) 68.534 s, (c) 2553 N, and (d) 7555 kg. SOLUTION a) 58.3 km b) 68.5 s c) 2.55 kN d) Ans. 7.56 Mg *1–12. Ans: 58.3 km 68.5 s 2.55 kN 7.56 Mg

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    13 1–13. 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 the rocket is on the moon, where the acceleration due to gravity is g m = 1.61 m/s 2 ,determine to three significant figures (c) its weight in SI units and (d) its mass in SI units. Solution a) 3.529(10 6 ) kg = 3.53 Gg Ans. b) W e = mg = 3 3.529 1 10 6 2 kg 4 1 9.81 m > s 2 2 = 34.619 1 10 6 2 kg # m > s 2 = 34.6 MN Ans. c) W m = mg m = 3 3.529 1 10 6 2 kg 4 1 1.61 m > s 2 2 = 5.682 1 10 6 2 N = 5.68 MN Ans. Or W m = W e a g m g b = (34.619 MN) a 1.61 m > s 2 9.81 m > s 2 b = 5.68 MN d) Since the mass is independent of tis location, then m m = m e = 3.53 Gg Ans. Ans: 3.53 Gg 34.6 MN 5.68 MN m m = m e = 3.53 Gg 6

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    14 1–14. and (c) 435 MN 23.2 mm. > (a) 354 mg(45 km) (0.0356 kN), (b) (0.004 53 Mg) (201 ms), > SOLUTION a) Ans. b) Ans. c) Ans. 435 MN > 23.2 mm = 435 A 10 6 B N 23.2 A 10 - 3 B m = 18.75 A 10 9 B N m = 18.8 GN > m = 0.911 kg # s (0.00453 Mg)(201 ms) = C 4.53 A 10 - 3 B A 10 3 B kg D C 201 A 10 - 3 B s D = 0.447 kg # m > N = 0.447 A 10 3 B g # m N (354 mg)(45 km) > (0.0356 kN) = C 354 A 10 - 3 B g D C 45 A 10 3 B m D 0.0356 A 10 3 B N Evaluate each of the following to three significant figures and express each answer in Sl units using an appropriate prefix: Ans: 0.447 kg # m > N 0.911 kg # s 18.8 GN > m

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    15 1–15. Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) (212 mN) , (b) 2 (52 800 Solution (a) (212 mN) 2 = 3 212(10) - 3 N 4 2 = 0.0449 N 2 = 44.9(10) - 3 N 2 Ans. (b) (52 800 ms) 2 = 3 52 800(10) - 3 4 2 s 2 = 2788 s 2 = 2.79(10 3 ) s 2 Ans. (c) 3 548(10) 6 4 1 2 ms = (23 409)(10) - 3 s = 23.4(10) 3 (10) - 3 s = 23.4 s Ans. Ans: 44.9(10) - 3 N 2 2.79(10 3 ) s 2 23.4 s ms) , and (c) 2 [548(10 )] 6 1 > 2 ms.

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