SOLUTIONS MANUAL FOR Engineering Mechanics Statics SI Units (Global Edition) 15th Edition. Russell

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Chapter 1

1

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2

2

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3

kN/μs,

Mg/mN,

MN/(kg∙ms).

3

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*1-4.

4

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5

5

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6

6

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7

7

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*1-8.

8

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Chapter 2

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2

q = 78.6°

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Ans: FR = 8.67 kN, f = 3.05º

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Ans: FR = 10.5 kN, f = 17.5°

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Ans: T = 6.57 kN, q = 30.6°

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50 N

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F3

30i N

2

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Express F1, F2, and F3 as Cartesian vectors.

y

F2

40

26 kN 5

F1

15 kN

13 12

SOLUTION

x

30

F1 = {15 sin 40°i + 15 cos 40°j} kN = { 9.64i + 11.5j} kN

Ans.

F3

36 kN

F2 = - 26(12>13)i + 26(5>13)j = {−24.0i + 10.0j } kN

Ans.

F3 = 36 cos 30°i - 36 sin 30°j = {31.2i − 18.0j } kN

Ans.

Ans: F1 = {9.64i + 11.5j} kN F2 = {−24.0i + 10.0j } kN F3 = {31.2i − 18.0j} kN

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Fz

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g2 > 90°, thus, g2 = cos−1(−0.5) = 120°(Ans.). By resolving F1 and F2 into their x,y, and

g = 120°

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z

The pipe is subjected to the force F, which has components acting along the x, y, z axes. If the magnitude of F is 12 kN, and a = 120° and g = 45°, determine the magnitudes of its three components.

Fz F Fx

x

SOLUTION

y

cos2 a + cos2 b + cos2 g = 1 cos2 120° + cos2 b + cos2 45° = 1 cos b = + 0.5

Fy

cos b = {0.5

b = 60°

Fx = F cos a = |12 cos 120°| = 6 kN

Ans.

Fy = F cos b = |12 cos 60°| = 6 kN

Ans.

Fz = F cos g = |12 cos 45°| = 8.49 kN

Ans.

Ans: Fx = 6 kN Fy = 6 kN Fz = 8.49 kN

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© 2023 by R. C. Hibbeler. Published by Pearson Education, Ltd., Inc., Hoboken, Hoboken, NJ. NJ. All All rights rights reserved. reserved. This This material material is is protected protected under under all all copyright copyright laws laws as they currently exist. exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

The pipe is subjected to the force F, which has components Fx = 1.5 kN and Fz = 1.25 kN. If b = 75°, determine the magnitude of F and Fy.

z

Fz F Fx

SOLUTION Fx = F cos a = 1.5

[1]

Fz = F cos g = 1.25

[2]

x

Fy y

Squaring Eqs.[1] and [2] and rearranging yields: 2.25 F2 1.5625 cos2 g = F2 cos2 a =

[3] [4]

cos2 a + cos2 b + cos2 g = 1 2.25 1.5625 + cos275° + = 1 F2 F2 F = 2.021 kN = 2.02 kN

Ans.

Fy = F cos b = 2.021 cos 75° = 0.523 kN

Ans.

Ans: F = 2.02 kN Fy = 0.523 kN

© 2023 by R. C. Hibbeler. Published by Pearson Education, Ltd., Inc., Hoboken, Hoboken, NJ. NJ. All All rights rights reserved. reserved. This This material material is is protected protected under under all all copyright copyright laws laws as they currently exist. exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

N

N

Vectors: N

N N N 700 N

N 600 N

N

kN

800 N

45° 60°

kN

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N

N

N

N N N 700 N N 600 N N

kN

800 N

kN

© 2023 by R. C. Hibbeler. Published by Pearson Education, Ltd., Inc., Hoboken, Hoboken, NJ. NJ. All All rights rights reserved. reserved. This This material material is is protected protected under under all all copyright copyright laws laws as they currently exist. exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

N

N

N

N

N N

700 N

600 N

800 N 1 186 000 , 546 000 ,

N N

N kN

N N

N kN

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© 2023 by R. C. Hibbeler. Published by Pearson Education, Ltd., Inc., Hoboken, Hoboken, NJ. NJ. All All rights rights reserved. reserved. This This material material is is protected protected under under all all copyright copyright laws laws as they currently exist. exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

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y

y

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F∙uOA

F|| = 4.07 N

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F1

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uAB·uAC

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rCA

FCA

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uBC

uBA·uBC

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FBC =

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