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Solution Manual for Engineering Mechanics Statics, 13th Edition

Solution Manual for Engineering Mechanics Statics, 13th Edition gives you the answers you need, explained in a simple and clear way.

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    SOLUTION MANUAL CONTENTS Chapter 1 General Principles Chapter 2 Force Vectors Chapter 3 Equilibrium of a Particle Chapter 4 Force System Resultants Chapter 5 Equilibrium of a Rigid Body Chapter 6 Structural Analysis Chapter 7 Internal Forces Chapter 8 Friction Chapter 9 Center of Gravity and Centroid Chapter 10 Moments of Inertia Chapter 11 Virtual Work 1 22 171 248 421 515 643 787 931 1071 1190

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    1 – 1. 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) 7.5 6 Mg An s .

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    1 – 2. Wood has a density of expressed in SI units? SOLUTION 4.70 slug > ft 3 . What is its density (4.70 slug > ft 3 ) b (1 ft 3 )(14.59 kg) 2.4 2 Mg > m 3 An s . (0.3048 m) 3 (1 slug ) r =

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    = = = = = = 1 – 3. Represent each of the following combinations of units in the correct SI form using an appropriate prefix : (a) , (b) Mg > mN , and (c) MN > (kg # ms). SOLUTION a) kN > m s = (10 3 ) N (10 - 6 ) s (10 9 ) N s GN > s An s . b) Mg > mN = (10 6 ) g (10 - 3 ) N (10 9 ) g N Gg > N An s . c) MN > (kg # ms) = (10 6 ) N kg # (10 - 3 ) s (10 9 ) N k g # s GN > (kg # s) An s . kN > m s

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    = = = = = - = = = = - # = - = - # = *1 – 4. Represent each of the following combinations of units in the correct SI form using an appropriate prefix : (a) (b) m km, (c) ks > mg , and (d) km # m N. SOLUTION a) m > ms ¢ 1 1 m 0 2 - 3 s ≤ ¢ 10 2 3 s m ≤ km > s An s . b) m km 10 2 - 6 10 3 m 10 3 m mm An s . c) ks > mg 10 2 3 s 10 9 s Gs > kg An s . d) km m N 10 10 6 3 kg m 10 6 kg N 10 3 m N mm # N An s . m > ms, 1 1 1 2 1 2 1 1 2 1 2

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    A B = = A B = A = B = 1 – 5. Represent each of the following quantities in the correct SI form using an appropriate prefix : (a) 0.000 431 kg, (b) 35.3(10 3 ) N , and (c) 0.005 32 km. SOLUTION a) 0.000 431 kg 0.000 431 10 g 0.431 g An s . b) 35.3 10 N 35. 3 kN An s . c) 0.005 32 km 0.005 32 10 m 5.32 m An s . 3 3 3

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    = 1 – 6. If a car is traveling at , determin e kilometers per hour and meters per second. SOLUTION i ts spee d in 55 mi > h = 1 h b a 88. 5 km > h 5280 ft 1 mi b a 0.3048 m 1 ft b a 1 km 1000 m b An s . 88.5 km > h = a 88.5 km 1000 m 1 km b a 1 h 3600 s b = 24.6 m > s An s . 55 mi > h a 55 mi 1 h b a

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    = A = - B = A B = = 1 – 7. The pascal (Pa) is actually a v ery small unit of pressure . To show this, convert to . Atmospheric pressure at sea level is 14.7 lb > in 2 . How many pascals is this? SOLUTION Using Table 1 – 2 , we hav e 1 Pa 1 N m 2 a 1 lb 4.4482 N b a 0.3048 1 ft 2 m 2 b 20.9 10 3 lb > ft 2 An s . 1 ATM 14.7 lb in a 4.448 N 1 lb b a 144 in 1 ft b a 1 ft 0.3048 m b 101.3 10 N > m 2 101 kPa An s . 1 Pa = 1 N > m 2 lb > ft 2 2 2 2 2 2 2 2 3

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    = = *1 – 8. The specific weight (wt. vol.) of brass is . Determine its density (mass vol.) in SI units. Use an appropriate prefix. SOLUTION 520 lb > ft 3 ft 3 b a 1 ft 0.3048 m b 3 a 4.448 N 1 kg 9.81 N b 8.33 Mg > m 3 An s . > > 520 lb > ft 3 a 520 lb 1 lb b a

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    A B C A = B D A B = = 1 – 9. A rocket has a mass of slugs 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 grav ity is , determine to three significant figures (c) its weight in SI units and (d) its mass in SI units. SOLUTION Using Table 1 – 2 and applying Eq . 1 – 3 , we hav e a) 250 10 slugs 250 10 slugs a 14.59 kg 1 slugs b 3.6475 10 kg 3 . 6 5 G g 250(10 3 ) g m = 5.30 ft > s 2 3 3 6

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    = A = B B = A B # C A = B D A B = = = = = A n s b) W e mg C 3.6475 10 kg D A 9.81 m > s 2 35.792 10 kg m > s 2 = 35.8 MN c) W m = mg m = C 250 A 10 3 B slugs D A 5.30 ft > s 2 B An s . 1.325 10 lb a 4.448 N 1 lb b 5.894 Or 10 N 5.89 MN An s . W W e a g m b ( 3 5 . 7 9 2 M N ) a 5 . 3 0 ft > s 2 b 5 . 8 9 M m g 32.2 ft > s 2 d) Since the mass is independent of its location , then m m = m e = 3.65 A 10 6 B kg = 3.65 Gg An s . 6 6 6 6

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    A B = = A = B = 1 – 10. E v aluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) (0.631 Mm) > (8.60 kg) 2 , (b) (35 mm) 2 (48 kg) 3 . SOLUTION a) (0.631 Mm) > (8.60 kg) 2 a 0.631 10 m b 8532 m (8.60) kg kg 8 . 5 3 10 m > k g 2 8.53 km > k g 2 6 2 2 2 3

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    C A = - B D = # An s . b) (35 mm) 2 (48 kg) 3 35 10 3 m 2 (48 kg) 135 m kg 3 An s . 3 2

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    C A - B A = B D A = B # = # 1 – 11. (a) 35 4 mg(4 5 km) > (0.035 6 kN) , (b) (0.004 53 Mg) (201 ms), SOLUTION a) (354 mg)(45 km) > (0.0356 kN) 354 10 3 g D C 45 A 10 3 m 0.0356 10 N 0.447 10 N g m 0.447 kg m > N E v aluate each of the following to three significant figures and express each answer in Sl units using an appropriate prefix: and (c) 435 MN > 23.2 mm. 3 B 3

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    A = - B A - B D = # B - = An s . b) (0.00453 Mg)(201 ms) C 4.53 10 3 B A 10 kg D C 201 10 3 s 0.911 kg s An s . c) 435 MN > 23.2 mm = 435 23.2 A 6 N m 18.75 A 10 9 B N m = 18.8 GN > m An s . 3 A 10 10 B 3

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    = *1 – 12. Convert each of the following and express the answer using an appropriate prefix : (a) to (b) to mm > s, and (c) 835 l b # ft to k N # m. SOLUTION a) ft 3 ≤ a 1 ft 0.3048 m b 3 a 4.448 N m 3 ≤ = 27.5 kN > m 3 An s . b) 6 ft > h = a 6 ft 0.3048 m 1 ft b a 1 h 360 0 s b = 0.508 1 10 2 - 3 m > s = 0.508 mm > s An s . c) 835 l b # ft = 1 835 l b # ft 4.448 N 1 lb 0.3048 m 1 ft 1.13 10 3 N # m = 1.1 3 kN # m An s . 175 lb > ft 3 kN > m 3 , 6 ft > h 175 lb > ft 3 = ¢ 175 lb 1 lb b = ¢ 27.5 1 10 2 3 N 1 h b a

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    = = = 1 – 13. Convert each of the following to three significant figures: (a) to , (b) to , and (c) 15 ft > h to mm > s. SOLUTION Using Table 1 – 2 , we hav e a) 20 l b # ft = (20 l b # ft) a 4.448 N 27.1 N # m 0.3048 m 1 ft b An s . b) 45 0 lb > ft 3 1 ft 3 b a 4.448 N 1 lb b a 1 kN 1000 N b a 1 ft 3 0.3048 3 m 3 b 70.7 kN > m 3 An s . c) 15 ft > h = a 15 ft An s . 20 lb # ft N # m 45 0 lb > ft 3 kN > m 3 1 lb b a a 450 lb 1 h b a 304.8 mm 1 ft b a 1 h 360 0 s b = 1.27 mm > s

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    = = 1 – 14. Evaluate each of the following and express with an (c) 1 230 m 2 prefix: 3 . (a) 1 43 0 kg 2 2 , (b) 1 0.002 mg 2 2 , and SOLUTION a) b ) 1 0.002 mg 2 2 = 3 2 1 10 - 6 2 g 4 2 0.185 Mg 2 4 m g 2 An s . An s . c) 23 0 m 3 = 0.23 10 3 m 3 = 0.0122 km 3 An s . appropriate 1 430 kg 2 2 = 0.185 1 10 6 2 kg 2

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    A B - # = = = A B # = = = A B # = = = 1 – 15. Determine the mass of an object that has a weight of (a) 20 mN, (b) 150 kN, and (c) 60 MN. Express the answer to three significant figures. SOLUTION Applying Eq . 1 – 3 , we hav e W 20 10 3 kg m > s 2 a) m g 9.81 m > s 2 2.04 g An s . W 150 10 kg m > s 2 b) m g 9.8 1 m > s 2 15.3 Mg An s . W 60 10 kg 2 c) m g 9.81 m > s 2 6.1 2 Gg An s . 3 6 m > s

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    *1 – 16. What is the weight in newtons of an object that has a mass of : (a) 10 kg , (b) 0.5 g , and (c) 4.50 Mg? Express the result to three significant figures . Use an appropriate prefix. W = A 9.81 m > s 2 B (10 kg) = 98.1 N c) W = A 9.81 m > s 2 B (4.5 Mg) A 10 3 kg > Mg B = 44.1 kN An s . An s . An s . SOLUTION a) b) W = A 9.81 m > s 2 B (0.5 g)(10 - 3 kg > g) = 4.90 mN

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    1 – 17. If an object has a mass of 40 slugs, determine its mass in kilograms. SOLUTION 40 slugs (14.59 kg > slug) = 584 kg An s .

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    = = 1 – 18. 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. SOLUTION Using Eq . 1 – 2, G m 1 m 2 F = N = F = G m 1 m 2 r 2 a kg m 3 G m 1 m 2 r 2 k g # kg m 2 b kg # m s 2 ( Q . E . D . ) 66.73 A 10 - 12 B c 200(200) = 7.41 A 10 - 6 B N = 7.41 m N An s . # s 2 b a 0.6 2 d

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    = = = 1 – 19. Water has a density of . What is the density expressed in SI units? Express the answer to three significant figures. SOLUTION r w a 1.94 slug 1 ft b a 14.59 kg 1 slug b a 1 ft 3 0.3048 m b 999.6 kg > m 3 1.00 Mg > m 3 An s . 1.94 slug > ft 3 3 3 3

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    = A = - B # = = *1 – 20. Tw o particles have a mass of 8 kg and 12 k g , respective ly . I f they are 800 mm apart , determine the force of gravit y acting between them. Compare this result with the weigh t of each particle. SOLUTION F G m 1 m r 2 2 Where G 66.7 3 1 0 1 2 m 3 (k g s 2 ) F = 66.73 A 10 - 12 B B ( 8(12 ) - 9 B N = 10.0 n N An s . W 1 8(9.81) = 78.5 N An s . W 2 12(9.81) = 118 N An s . > 0.8) 2 R = 10.0 A 1 0

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    = = = = = = 1 – 21. If a man weighs 155 lb on earth, specify (a) his mass in slugs, (b) his mass in kilograms, and (c) his weight in newtons. If the man is on the moon, where the acceleration due to gravity is determine (d) his weight in pounds, and (e) his mass in kilograms. SOLUTION 155 a) m = 32.2 4.81 slug An s . b) m = 155 c 14.59 kg 70.2 kg An s . c) W = 155 4.4482 689 N An s . d) W = e) m = Also, 155 c 5.30 155 c 14.59 kg 14.59 kg 25.5 lb 70. 2 kg An s . An s . m = 25.5 5.30 70.2 kg An s . g m = 5.30 ft > s 2 , 32.2 d 1 2 32. 2 d 32.2 d

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    2–5. SOLUTION A n s . A n s . F 1 v = 160 N F 1 v sin 30° = 300 sin 110° F 1 u = 205 N F 1 u sin 40° = 300 sin 110° Resolve the force into components acting along the u and v axes and determine the magnitudes of the components. F 1 u v 70 30 45 F 1 300 N F 2 500 N

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    2–6. R eso lv e t h e f o r ce in to co mp o n e n ts act in g a l o n g t h e u a nd v a x es a nd d ete rmin e t h e m ag ni t ud es o f t h e co mp o n e n ts . F 2 SOLUTION A n s . A n s . F 2 v = 482 N F 2 v s in 65 ° = 500 s in 70 ° F 2 u = 3 76 N F 2 u s in 45 ° = 500 s in 70 ° u v 70  3 0  45  F 1  3 00 N F 2  500 N © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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    SOLUTION Parallelogram Law: The parallelo g ram law of addition i s s hown in Fi g . a . Trigonometry: U s in g the law of s ine s (Fi g . b ), we ha v e Ans. Ans. F AC = 366 N F AC s in 45° = 500 s in 75° F AB = 448 N F AB s in 60° = 500 s in 75° 2–7. The v ertical force act s downward at on the two-membered frame. Determine the ma g nitude s of the two component s of directed alon g the a x e s of and . Set . F = 500 N AC AB F A F F C B A 30  45  © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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    *2–8. Sol v e Prob. 2-7 with . F = 350 lb SOLUTION Parallelogram Law: The parallelo g ram law of addition i s s hown in Fi g . a . Trigonometry: U s in g the law of s ine s (Fi g . b ), we ha v e Ans. Ans. F AC = 256 lb F AC s in 45° = 350 s in 75° F AB = 314 lb F AB s in 60° = 350 s in 75° F C B A 30  45  © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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    2–9. Resolve F 1 into components along the u and axes and determine the magnitudes of these components. v SOLUTION S ine law: A n s . A n s . F 1 u sin 45° = 250 sin 105° F 1 u = 183 N F 1 v sin 30° = 250 sin 105° F 1 v = 129 N F 1 250 N F 2 150 N u v 30 30 105 © 2013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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