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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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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
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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
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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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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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