S O L U T I O N M A N U A L CONTENTS Chapter 12 General Principles 245 Chapter 14 Equilibrium of a Particle 378 Chapter 15 Force System Resultants 475 Review Kinematics and Kinetics of a Particle 630 Chapter 16 Equilibrium of a Rigid Body 680 Chapter 17 Structural Analysis 833 Chapter 18 Internal Forces 953 th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r b) Chapter 13 Force Vectors Chapter 19 Friction 1023 Review Planar Kinematics and Kinetics of a Rigid Body 1080 Chapter 20 Center of Gravity and Centroid 1131 Chapter 21 Moments of Inertia 1190 Chapter 22 Virtual Work 1270 © 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 th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r 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 12–1 A baseball is thrown downward from a 50-ft tower with an initial speed of 18 ft>s Determine the speed at which it hits the ground and the time of travel SOLUTION v22 = v21 + 2ac(s2 - s1) v22 = (18)2 + 2(32.2)(50 - 0) v2 = 59.532 = 59.5 ft>s Ans v2 = v1 + ac t 59.532 = 18 + 32.2(t) Ans th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r b) t = 1.29 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 12–2 When a train is traveling along a straight track at m/s, it begins to accelerate at a = 160 v-42 m>s2, where v is in m/s Determine its velocity v and the position s after the acceleration s v SOLUTION a = dv dt dt = dv a v dt = L0 = dv -4 L2 60v (v5 - 32) 300 v = 3.925 m>s = 3.93 m>s ads = vdv ds = s L0 ds = s = vdv = v dv a 60 60 L2 3.925 v5 dv v6 3.925 a b` 60 = 9.98 m th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r b) 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 12–3 From approximately what floor of a building must a car be dropped from an at-rest position so that it reaches a speed of 80.7 ft>s 155 mi>h2 when it hits the ground? Each floor is 12 ft higher than the one below it (Note: You may want to remember this when traveling 55 mi>h.) SOLUTION (+ T) v = v20 + 2ac(s - s0) 80.72 = + 2(32.2)(s - 0) s = 101.13 ft # of floors = 101.13 = 8.43 12 Ans th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r b) The car must be dropped from the 9th floor © 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 *12–4 Traveling with an initial speed of 70 km>h, a car accelerates at 6000 km>h2 along a straight road How long will it take to reach a speed of 120 km>h? Also, through what distance does the car travel during this time? SOLUTION v = v1 + ac t 120 = 70 + 6000(t) t = 8.33(10 - 3) hr = 30 s Ans v2 = v21 + ac(s - s1) (120)2 = 702 + 2(6000)(s - 0) Ans th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r b) s = 0.792 km = 792 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 12–5 A bus starts from rest with a constant acceleration of m>s2 Determine the time required for it to attain a speed of 25 m>s and the distance traveled SOLUTION Kinematics: v0 = 0, v = 25 m>s, s0 = 0, and ac = m>s2 + B A: v = v0 + act 25 = + (1)t t = 25 s th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r b) + B A: Ans v2 = v02 + 2ac(s - s0) 252 = + 2(1)(s - 0) s = 312.5 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 12–6 A stone A is dropped from rest down a well, and in s another stone B is dropped from rest Determine the distance between the stones another second later SOLUTION + T s = s1 + v1 t + sA = + + a t c (32.2)(2)2 sA = 64.4 ft sA = + + (32.2)(1)2 ¢s = 64.4 - 16.1 = 48.3 ft th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r b) sB = 16.1 ft 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 12–7 A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h Determine his acceleration if it is constant Also, how long does it take to reach the speed of 30 km/h? SOLUTION v2 = 30 km>h = 8.33 m>s v22 = v21 + ac (s2 - s1) (8.33)2 = + ac (20 - 0) ac = 1.74 m>s2 Ans v2 = v1 + ac t 8.33 = + 1.74(t) Ans th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r b) t = 4.80 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 *■12–8 A particle moves along a straight line with an acceleration of a = 5>(3s1>3 + s5>2) m>s2, where s is in meters Determine the particle’s velocity when s = m, if it starts from rest when s = m Use Simpson’s rule to evaluate the integral SOLUTION a = A 3s3 + s2 B a ds = v dv v ds L1 A 3s + s 0.8351 = B = L0 v dv v Ans th an Th sa eir d i is w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta th lud nt f in te e in lea s s c w g r tru o or o ni c p k n ng to yri an th rs gh d e W Dis in t l is t a no orl sem eac ws t p d W in hi er id ati ng m e on itt W o ed e r b) v = 1.29 m>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 ... a straight path a distance of 20 m reaches a speed of 30 km/h Determine his acceleration if it is constant Also, how long does it take to reach the speed of 30 km/h? SOLUTION v2 = 30 km>h = 8.33... thrown downward from a 50-ft tower with an initial speed of 18 ft>s Determine the speed at which it hits the ground and the time of travel SOLUTION v22 = v21 + 2ac(s2 - s1) v22 = (18)2 + 2(32.2)(50... w le co s p or w of a urs rov k is ill de ny es a ided pro st pa nd s te ro rt o c y of as lel ted th t se y e his s fo by s r in te wo ing the Uni gr rk s u te ity ( tu s d of inc de e o Sta