SOLUTION MANUAL CONTENTS
Chapter 1 General Principles Chapter 2 Force Vectors
1 22
Chapter 3 Equilibrium of a Particle
1 71
Chapter 4 Force System Resultants
2 48
Chapter 5 Equilibrium of a Rigid Body
4 21
Chapter 6 St Structural Analysis
515
Chapter 7 Internal Forces
64 3
Chapter 8 Friction
78 7
Chapter 9 Center of Gravity and Centroid
931
Chapter 10 Moments of Inertia
10 71
Chapter 11 Virtual Work
1 19 0
© 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.
© 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.
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. 7.56 56 Mg
Ans.
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1–2.
>
Wood has a density of 4.7 4.70 0 slu slug g ft3. What is its density expressed in SI units?
SOLUTION
> b (0.3048 m) (1 slug) 3
(4.70 slug ft )
(1 ft3)(14.59 kg) 3
=
>
2.42 2. 42 Mg m3
Ans.
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1–3.
Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) kN ms , (b) Mg mN, and (c) MN (kg # ms).
>
>
>
SOLUTION a) kN
>s m
>
(103) N =
b) Mg mN
>
(10 6) s
=
-
(109) N s
(106) g =
#
c) MN (kg ms)
=
Ans.
>
Ans.
=
N
(106) N =
>
GN s
(109) g
(10 3) N -
=
kg # (10 3) s -
=
Gg N
(109) N kg # s
=
>
GN (kg # s)
Ans.
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*1–4.
Represent each of the following combinations of units in the correct SI form using using an appropriate prefix: (a) m ms, (b) mkm, (c) ks mg, and (d) km # mN.
>
>
SOLUTION
> ¢ 110m2 s ≤ ¢ 1102s m ≤ b) km 1102 1102 m 1102 m 1102 s 1102 s c) ks> mg kg 1102 kg 3
a) m ms m
=
=
3
-
-
=
6
3
-
=
3
=
d) km # mN
-
=
10
=
=
m
10
-
6
N
=
Ans.
mm
9
6
3
3
>
km s
=
=
10
Ans.
>
Gs kg 3
-
m#N
Ans.
=
mm # N
Ans.
© 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.
1–5.
Represent each of the following quantities in the correct SI for form m using using an approp appropria riate te prefix prefix:: (a) 0.000 0.000 431 431 kg, 3 (b) 35.3(10 ) N, and (c) 0.005 32 km.
SOLUTION a) 0.000 431 kg
=
0.000 431 A 103 B g
b) 35.3 A 103 B N
=
35.3 35 .3 kN
c) 0. 0.00 005 5 32 km
=
0.005 32 103 m
=
0.43 0. 431 1g
Ans. Ans.
=
5.32 5. 32 m
Ans.
© 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.
1–6.
>
If a ca carr is trave avelin ling g at 55 55 mi mi h, dete etermin rmine e its spee eed d in kilo kil omete eterrs per hour ur a and nd mete eterrs per seco second. nd.
SOLUTION f t 0.3 .3048 048 m m 1 km > a 551 hmi b a 5280 b a b a b 1 mi 1 f t 1000 m 88..5 km> h 88 88..5 km 1000 m 88 1h 88..5 km> h a 88 b a b a b 2424..6 m>s 1h 1 km 3600 s 55 mi 55 mi h
=
=
=
=
Ans.
Ans.
© 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.
1–7.
The pascal (Pa) is actually a very small unit of pressure. pressure. To show sho w this this,, co con nvert 1 Pa = 1 N m2 to lb ft2. Atm Atmosp ospher heric ic 2 pressure at sea level is 14.7 lb in . How many pascals is this?
>
>
>
SOLUTION Using Table Table 1–2, we have 1 Pa
=
2
a
2
m b a 0.3048 b 20.9 A 10 B lb>ft 1 ft 14.7 lb 4.448 N 144 in 1 ft a b a b a b 1 lb in 1 ft 0.3048 m 101.3 A 10 B N> m
1N 1 lb 2 m 4.4482 N
=
2
2
1 AT ATM M
=
=
=
2
2
3
101 10 1 kP kPa a
-
3
2
Ans.
2
2
2
2
Ans.
© 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.
*1–8.
>
>
The specific weight (wt. vol.) of brass is 520 lb ft3. Determine its density (mass vol. ol.)) in SI units units.. Use an appropriate prefix.
>
SOLUTION 3
1 kg 1 ft 4.448 N > a 52520ft0 lbb a 0.3048 b a b a b m 1 lb 9.81 N 8.33 8. 33 Mg> m
520 52 0 lb ft3
=
=
3
3
Ans.
© 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.
1–9.
A roc rocket ket has a mas masss of 250(103) slu slugs gs on ear earth. th. Spe Specif cify y (a) its mass in SI units units and (b) its weight weight in SI units. units. If the rocket is on the moon, where the acceleration due to gravity is gm = 5. 5.30 30 ft s2, determ determine ine to three signific significant ant figures (c) its weight in SI units and (d) its mass in SI units. units.
>
SOLUTION Using Table Table 1–2 and applying Eq. 1–3, we have a) 250 A 103 B slugs
b) We
c) Wm
kg a 14.59 b 1 sl slug ugss
=
C 250 A 103 B slugs D
=
3.6475 A 106 B kg
=
3.65 Gg
Ans.
>
9.81 81 m s2 B C 3.6475 A 106 B kg D A 9.
=
mg
=
35.792 A 106 B kg # m s2
=
35.8 35. 8 MN
=
>
Ans.
>
5.30 30 ft s2 B C 250 A 103 B slugs D A5.
=
mgm
=
C 1.325 A 106 B lb D
=
5.894 A 106 B N
=
N a 4.448 b 1 lb
=
5.89 5. 89 MN
Ans.
Or Wm
=
We
a b gm g
=
(35.792 MN)
a 3232.2.2 ft>>s b 5.30 5. 30 ft s2 2
=
5.89 5. 89 MN
d) Since the mass mass is independ independent ent of of its locatio location, n, then mm
=
me
=
3.65 106 kg
=
3.65 3. 65 Gg
Ans.
© 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.
1–10.
Evaluate 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
=
b) (35 mm)2(48 kg)3
A 10 B m 8532 m a 0.631 b (8.60) kg kg 8.53 A 10 B m> kg 8.53 8. 53 km> kg 6
>
a) (0.631 Mm) (8.60 kg)2
=
=
2
3
=
2
2
-
2
=
C 35 A 10 3 B m D 2 (48 kg)3
2
=
135 13 5 m2 # kg3
Ans. Ans.
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1–11.
Evaluate each of the following to three significant figures and express each answer in Sl units using an appropriate prefix: (a)) 354 (a 354 mg(4 mg(455 km km)) > (0 (0.0 .035 3566 kN kN), ), (b (b)) (0.0 (0.004 04 53 53 Mg) Mg) (20 (2011 ms) ms),, and (c) (c) 435 435 MN 23. 23.2 2 mm.
>
SOLUTION
C 354 A 10 3 B g D C45 A 103 B m D 0.0356 A 103 B N -
>
a) (354 mg)(45 km) (0.0356 kN)
=
0.447 A 103 B g # m =
=
b) (0.00453 Mg)(201 ms)
>
c) 43 435 5 MN 23.2 mm
N
Ans.
=
C 4.53 A 10 3 B A103 B kg D C201 A 10 3 B s D
=
0.91 0. 911 1 kg # s
-
-
435 A 106 B N =
>
0.44 0. 447 7 kg # m N
23.2 A 10
-
3
Bm
Ans.
18.75 A 109 B N =
m
=
>
18.8 GN m
Ans.
© 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.
*1–12.
Convert each of the following and express the answer using an appropr appropriate iate prefix: (a) 17 175 5 lb ft3 to kN m3, (b) 6 ft h to mm s, and (c) 83 835 5 lb # ft to kN # m.
>
>
>
>
SOLUTION 1 ft N > ¢ 175ft lb ≤ a 0.0.304 b a 4.448 b 3048 8m 1 lb ¢ 27.51102 N ≤ 27.5 kN>m
a) 175 lb ft3
3
=
3
3
=
=
3
m
3
m 1h > a 61 fth b a 0.3048 b a 363600 b 1 ft 00 s 0.5081102 m> s 0. 0.50 508 8 mm> s 4.448 N 0.304 0. 3048 8m c) 835 lb ft 183 835 5 lb ft 1 lb 1 ft b) 6 ft h
Ans.
=
-
=
#
1.13 10
=
Ans.
#
=
=
3
3
N#m
=
1.13 1. 13 kN # m
Ans.
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1–13.
Convert each of the following to three significant figures: (a) 20 lb # ft to N # m, (b) 45 450 0 lb ft3 to kN m3, and (c)) 15 (c 15 ft ft h to to mm mm s.
>
>
>
>
SOLUTION Using Table Table 1–2, we have a) 20lb # ft
=
(20 lb # ft)
=
27.1 N # m
Ans. 3
8N 1 kN 1 ft > a 4501 ftlb b a 4.4.44448 b a b a b 1 lb 1000 N 0.3048 m 70.7 kN> m 15 ft 30 304. 4.8 8 mm 1h b a b a b 1.27 mm>s 15ft> h a 1h 1 ft 3600 36 00 s
b) 45 450 0 lb ft3
=
=
c)
8 N 0. 0.304 3048 8m a 4.4.44448 b a b 1 lb 1 ft
=
3
3
3
=
3
Ans. Ans.
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1–14.
Evaluate each of the following and express with an approp app ropriat riate e pre prefix: fix: (a) 43 430 0 kg 2, (b) 0. 0.00 002 2 mg 2, and (c) 230 m 3.
1
1
2
2
1
2
SOLUTION
1 2 0.185110 2 kg b) 10. 0.002 002 mg2 32110 2 g4 a) 43 430 0 kg
2
=
2
c) 230m
3
=
=
6
2
6
2
-
0.2 0. 23 103 m
3
=
0.185 Mg2
Ans.
=
4 m g2
Ans.
=
0.0122 km3
Ans.
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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 Applyi ng Eq. Eq. 1–3, we ha have 20 A 10
a) m
=
W g
b) m
=
W g
=
c) m
=
W g
=
=
-
3
>
B kg # m s2
>
9.81 m s
2
>
=
2.04 2. 04 g
Ans.
=
15.3 15. 3 Mg
Ans.
150 A 103 B kg # m s2
>
9.81 9. 81 m s
2
>
60 A 106 B kg # m s2
>
2
9.81 9. 81 m s
=
6.12 6. 12 Gg
Ans.
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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 Express the result result to three significant figures. Use an appropriate prefix.
SOLUTION a) W
=
b) W
=
c) W
=
> 98.1 98 .1 N A 9.81 m> s B (0.5 g)(10 kg> g) 4.90 mN A 9.81 m> s B (4.5 Mg) A 10 kg> Mg B 44.1 kN A 9.81 m s2 B (10 kg) 2 2
=
-
3
=
3
=
Ans. Ans. Ans.
© 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.
1–17.
If an object has a mass of 40 slugs, slugs, determine its mass in kilograms.
SOLUTION
>
40 slugs (14.59 kg slug)
=
584 58 4 kg
Ans.
© 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.
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
m1 m2
F
=
N
=
F
=
G
=
66.73 A 10
=
7.41 10
r2 #
3
a kgm s b a kgm kg b # 2
2
kg # m =
s2
( Q. E ) E . D D. )
m1 m2 r2
-
-
6
12
B
c 200(200) d 0.6
N
2
=
7.41 mN
Ans.
© 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.
1–19.
>
Water has a density of 1.9 1.94 4 slu slug g ft3 . What is the density expressed in SI units? Express the answer to three significant figures.
SOLUTION 3
r w
=
=
kg 1 ft a 1.941 ftslug b a 14.59 b a b 1 sl slug ug 0.3048 m 999.6 kg> m 1.00 Mg> m 3
3
3
=
3
3
Ans.
© 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.
*1–20.
Two particles have a mass of of 8 8 kg an and 12 kg, res esp pect ectiive vely. ly. If they are 800 mm apart, dete etermin rmine e the f orce of grav aviity actin act ing g bet etw wee een n t th hem. Co Comp mpa are thi t hiss res esul ultt wi witth t th he weight of each each particle.
SOLUTION F
=
G
m1 m2 2 r
Where G
F
=
=
66..73 A 10 66
66..73 A 10 66
-
W1
=
8(9.81)
W2
=
12(9.81)
12
=
B
-
12
B R
>( g
3
8(12)
(0.8)2
78..5 N 78
=
B m
118 N
=
k #
s2)
A
10.0 10
-
9
BN
=
10.0 n N
Ans.
Ans. Ans.
© 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.
1–21.
If a man weighs 155 lb on earth, earth, specif specify y (a) his mass in slugs,, (b) his slugs his mass in kilograms kilograms,, and (c) (c) his weight weight in newt ne wton onss. If the the man man is is on th the e moon moon,, wh wher ere e the the acceleration due to gravity is gm = 5. 5.30 30 ft s2, determine (d) his weight in pounds, pounds, and (e) his mass in kilograms.
>
SOLUTION a) m
=
155 32.2
b) m
=
155
c) W
=
d) W
=
e) m
=
=
4.81 4.8 1 slu slug g
Ans.
kg c 14.59 d 7070.2.2 kg 32.2 15514.44822 689 N =
=
155
155
c 5.30 d 32.2
=
25.5 25 .5 lb
.59 9 kg c 1414.532.2 d
=
70.2 70 .2 kg
Ans.
Ans.
Ans.
Ans.
Also,
m
=
25.5
14.59 kg 5.30
=
70.2 70 .2 kg
Ans.
© 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.
