18.12: Static Equilibrium and Elasticity
Check Your Understanding
12.1 . x = 1.3 m
12.2 . (b), (c)
12.3. 316.7 g; 5.8 N
12.4. T = 1963 N; F = 1732 N
12.5. \(\mu_{s}\) < 0.5 cot \(\beta\)
12.6. \(\vec{F}_{door\; on\; A}\) = 100.0 N \(\hat{i}\) − 200.0 N \(\hat{j}\); \(\vec{F}_{door\; on\; B}\) = −100.0 N \(\hat{i}\) − 200.0 N \(\hat{j}\)
12.7. 711.0 N; 466.0 N
12.8. 1167 N; 980 N directed upward at 18° above the horizontal
12.9. 206.8 kPa; 4.6 x 10 −5
12.10. 5.0 x 10 −4
12.11. 63 mL
12.12. Fluids have different mechanical properties than those of solids; fluids flow.
Conceptual Questions
1. Constant
3. Magnitude and direction of the force, and its lever arm
5. True, as the sum of forces cannot be zero in this case unless the force itself is zero.
7. False, provided forces add to zero as vectors then equilibrium can be achieved.
9. It helps a wire-walker to maintain equilibrium.
11. Proof
13. In contact with the ground, stress in squirrel’s limbs is smaller than stress in human’s limbs.
15. Tightly
17. Compressive; tensile
19. No
23. It acts as “reinforcement,” increasing a range of strain values before the structure reaches its breaking point.
Problems
25. 46.8 N • m
27. 4,472 N, 153.4°
29. 23.3 N
31. 80.0 kg
33. 40 kg
35. Right cable, 444.3 N; left cable, 888.5 N; weight of equipment 156.8 N; 16.0 kg
37. 784 N, 132.8 N
39. a. 539 N
b. 461 N
c. Do not depend on the angle
41. Tension 778 N; at hinge 778 N at 45° above the horizontal; no
43. 1500 N; 1620 N at 30°
45. 1.2 mm
47. 9.0 cm
49. 4.0 x 10 2 N/cm 2
51. 0.149 \(\mu\)m
53. 0.57 mm
55. 8.59 mm
57. 1.35 x 10 9 Pa
59. 259.0 N
61. 0.01%
63. 1.44 cm
65. 0.63 cm
Additional Problems
69. tan −1 \(\left(\dfrac{1}{\mu_{s}}\right)\) = 51.3°
71. a. At corner 66.7 N at 30° with the horizontal; at floor 177 N at 109° with the horizontal
b. \(\mu_{s}\) = 0.346
73. a. 1.10 x 10 9 N/m 2
b. 5.5 x 10 −3
c. 11.0 mm, 31.4 mm
Challenge Problems
75. F = Mg tan \(\theta\); f = 0
77. With the horizontal, \(\theta\) = 42.2°; \(\alpha\) = 17.8° with the steeper side of the wedge
79. W\(\left(\dfrac{l_{1}}{l_{2} − 1}\right)\); \(\frac{Wl_{1}}{l_{2}}\) + mg
81. a. 1.1 mm
b. 6.6 mm to the right
c. 1.11 x 10 5 N
Contributors and Attributions
Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a
Creative Commons Attribution License (by 4.0)
.