# 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.** 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, 376 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. **0.3 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 192.4 N at 60° with the horizontal

b. \(\mu_{s}\) = 0.577

**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

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).