S O L U T I O N M A N U A L CONTENTS Chapter General Principles Chapter Force Vectors 22 171 Chapter Force System Resultants 248 Chapter Equilibrium of a Rigid Body 421 T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) Chapter Equilibrium of a Particle Chapter Structural Analysis 515 Chapter Internal Forces 643 Chapter Friction 787 Chapter Center of Gravity and Centroid 931 Chapter 10 Moments of Inertia 1071 Chapter 11 Virtual Work 1190 © 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 T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) © 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 b) 68.5 s c) 2.55 kN d) 7.56 Mg Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) a) 58.3 km © 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 1–2 Wood has a density of 4.70 slug>ft3 What is its density expressed in SI units? SOLUTION (1 ft3)(14.59 kg) (0.3048 m)3(1 slug) r = 2.42 Mg>m3 Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) (4.70 slug>ft3) b © 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 1–3 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>ms = (103) N (10-6) s b) Mg>mN = = (106) g -3 (10 ) N = (109) g = Gg>N N (106) N kg # (10-3) s = (109) N = GN>(kg # s) kg # s Ans Ans Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) c) MN>(kg # ms) = (109) N = GN>s s © 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 *1–4 Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) m>ms, (b) mkm, (c) ks>mg, and (d) km # mN SOLUTION a) m>ms = ¢ 11023 m m = ≤ ¢ ≤ = km>s s 1102-3 s b) mkm = 1102-611023 m = 1102-3 m = mm c) ks>mg = 1102-6 kg 10 m = 10 11029 s kg -6 Ans = Gs>kg N = 10 -3 m # N = mm # N Ans Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) d) km # mN = 11023 s 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 form using an appropriate prefix: (a) 0.000 431 kg, (b) 35.3(103) N, and (c) 0.005 32 km SOLUTION a) 0.000 431 kg = 0.000 431 A 103 B g = 0.431 g b) 35.3 A 103 B N = 35.3 kN Ans Ans Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) c) 0.005 32 km = 0.005 32 A 103 B m = 5.32 m © 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 car is traveling at 55 mi>h, determine its speed in kilometers per hour and meters per second SOLUTION 55 mi>h = a 55 mi 5280 ft 0.3048 m km ba ba ba b 1h mi ft 1000 m = 88.5 km>h 88.5 km 1000 m 1h ba ba b = 24.6 m>s 1h km 3600 s Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) 88.5 km>h = a 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 To show this, convert Pa = N>m2 to lb>ft2 Atmospheric pressure at sea level is 14.7 lb> in2 How many pascals is this? SOLUTION Using Table 1–2, we have Pa = 0.30482 m2 1N lb b a a b = 20.9 A 10 - B lb>ft2 m2 4.4482 N ft2 ATM = Ans 14.7 lb 4.448 N ft2 144 in2 a b a b b a lb in2 ft2 0.30482 m2 = 101.3 A 103 B N>m2 Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) = 101 kPa © 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.) in SI units Use an appropriate prefix SOLUTION 520 lb>ft3 = a kg 520 lb ft 4.448 N b a ba b ba 0.3048 m lb 9.81 N ft Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) = 8.33 Mg>m3 © 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 rocket has a mass of 250(103) 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 gravity is gm = 5.30 ft>s2, 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 have a) 250 A 103 B slugs = C 250 A 103 B slugs D a = 3.6475 A 106 B kg 14.59 kg b slugs = 3.65 Gg Ans b) We = mg = C 3.6475 A 106 B kg D A 9.81 m>s2 B = 35.8 MN T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) = 35.792 A 106 B kg # m>s2 Ans c) Wm = mgm = C 250 A 103 B slugs D A 5.30 ft>s2 B = C 1.325 A 106 B lb D a 4.448 N b lb = 5.894 A 106 B N = 5.89 MN Or Wm = We a Ans 5.30 ft>s2 gm b = (35.792 MN) a b = 5.89 MN g 32.2 ft>s2 d) Since the mass is independent of its location, then mm = me = 3.65 A 106 B kg = 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 a) (0.631 Mm)>(8.60 kg)2 = a 0.631 A 106 B m (8.60)2 kg2 b = 8532 m kg2 = 8.53 A 103 B m>kg2 = 8.53 km>kg2 Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) b) (35 mm)2(48 kg)3 = C 35 A 10 - B m D (48 kg)3 = 135 m2 # kg3 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 1–11 Evaluate each of the following to three significant figures and express each answer in Sl units using an appropriate prefix: (a) 354 mg(45 km) > (0.0356 kN), (b) (0.004 53 Mg) (201 ms), and (c) 435 MN> 23.2 mm SOLUTION a) (354 mg)(45 km)>(0.0356 kN) = = C 354 A 10-3 B g D C 45 A 103 B m D 0.0356 A 103 B N 0.447 A 103 B g # m N = 0.447 kg # m>N Ans b) (0.00453 Mg)(201 ms) = C 4.53 A 10-3 B A 103 B kg D C 201 A 10-3 B s D = 0.911 kg # s 435 A 106 B N 18.75 A 109 B N T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) c) 435 MN>23.2 mm = Ans 23.2 A 10-3 B m = 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 appropriate prefix: (a) 175 lb>ft3 to kN>m3, (b) ft>h to mm>s, and (c) 835 lb # ft to kN # m SOLUTION a) 175 lb>ft3 = ¢ = ¢ b) ft>h = a 175 lb ft 4.448 N b b a a ≤ 0.3048 m lb ft3 27.511023 N m3 ≤ = 27.5 kN>m3 Ans 1h ft 0.3048 m ba ba b 1h ft 3600 s = 0.5081102-3 m>s = 0.508 mm>s = 1.13 10 4.448 N lb 0.3048 m ft T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) c) 835 lb # ft = 1835 lb # ft Ans N # m = 1.13 kN # 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 1–13 Convert each of the following to three significant figures: (a) 20 lb # ft to N # m, (b) 450 lb>ft3 to kN>m3, and (c) 15 ft> h to mm> s SOLUTION Using Table 1–2, we have a) 20 lb # ft = (20 lb # ft)a = 27.1 N # m b) 450 lb>ft3 = a 4.448 N 0.3048 m ba b lb ft Ans kN ft3 450 lb 4.448 N ba ba ba b lb 1000 N 0.30483 m3 ft = 70.7 kN>m3 1h 15 ft 304.8 mm ba ba b = 1.27 mm>s 1h ft 3600 s Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) c) 15 ft>h = a 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 1–14 Evaluate each of the following and express with an appropriate prefix: (a) 1430 kg22, (b) 10.002 mg22, and (c) 1230 m23 SOLUTION a) 1430 kg22 = 0.18511062 kg2 = 0.185 Mg2 Ans b) 10.002 mg22 = 32110-62 g42 = mg2 Ans = 0.23 103 m Ans 3 = 0.0122 km3 T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) c) 230 m © 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 1–15 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 have a) m = b) m = 150 A 103 B kg # m>s2 W = = 15.3 Mg g 9.81 m>s2 60 A 106 B kg # m>s2 W = = 6.12 Gg g 9.81 m>s2 Ans Ans Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) c) m = 20 A 10 - B kg # m>s2 W = = 2.04 g g 9.81 m>s2 © 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 *1–16 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 SOLUTION a) W = A 9.81 m>s2 B (10 kg) = 98.1 N b) W = A 9.81 m>s2 B (0.5 g)(10 - kg>g) = 4.90 mN Ans Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) c) W = A 9.81 m>s2 B (4.5 Mg) A 103 kg>Mg B = 44.1 kN 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, determine its mass in kilograms SOLUTION Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) 40 slugs (14.59 kg>slug) = 584 kg © 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, F = G N = a m m2 r2 kg # kg kg # m m3 ba b = 2 # kg s m s2 F = G (Q.E.D.) m1 m r2 = 66.73 A 10 - 12 B c 200(200) 0.62 d T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) = 7.41 A 10 - B N = 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 1.94 slug>ft3 What is the density expressed in SI units? Express the answer to three significant figures SOLUTION rw = a 1.94 slug ft ba 14.59 kg ft3 ba b slug 0.30483 m3 Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) = 999.6 kg>m3 = 1.00 Mg>m3 © 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 kg and 12 kg, respectively If they are 800 mm apart, determine the force of gravity acting between them Compare this result with the weight of each particle SOLUTION F = G m1 m2 r2 Where G = 66.73 A 10-12 B m3>(kg # s2) F = 66.73 A 10 - 12 B B 8(12) (0.8)2 R = 10.0 A 10 - B N = 10.0 nN Ans Ans W2 = 12(9.81) = 118 N Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) W1 = 8(9.81) = 78.5 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 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 gm = 5.30 ft>s2, determine (d) his weight in pounds, and (e) his mass in kilograms SOLUTION a) m = 155 = 4.81 slug 32.2 b) m = 155 c Ans 14.59 kg d = 70.2 kg 32.2 Ans c) W = 15514.44822 = 689 N Ans d) W = 155 c Ans 14.59 kg d = 70.2 kg 32.2 Also, m = 25.5 T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk ( stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b) e) m = 155 c 5.30 d = 25.5 lb 32.2 14.59 kg 5.30 = 70.2 kg 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 ... 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... 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),... 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),