Page 179 - Schaum's Outline of Theory and Problems of Applied Physics

164 ELASTICITY [CHAP. 13

Supplementary Problems

13.1. A cable is shortened to half its original length. (a) How does this affect its elongation under a given load? (b)How
does this affect the maximum load it can support without exceeding its elastic limit?

13.2. A cable is replaced by another one of the same length and material but of twice the diameter. (a) How does this affect
its elongation under a given load? (b) How does this affect the maximum load it can support without exceeding its
elastic limit?

13.3. A wire 5 m long and 4 mm in diameter supports a load of 80 kg. If the wire stretches by 2.6 mm, find the value of
Young’s modulus for its material.

2
7
2
13.4. A steel wire (Y = 2.9 × 10 lb/in. ) 6 ft long and 0.002 in. in cross section supports a load of 15 lb. (a) What is its
elongation? (b) What would its elongation be if the load were doubled to 30 lb?
13.5. A lead cube 20 mm on each edge is held in the jaws of a vise with a force of 3 kN. By how much is the cube
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compressed? Young’s modulus for lead is 1.6 × 10 Pa.
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13.6. The ultimate strength in tension of a certain type of steel is 5 × 10 Pa. What is the maximum tension a rod made
of this steel and 25 mm in diameter can withstand?
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13.7. An elevator cab weighing 3000 lb is designed for a maximum upward acceleration of 12 ft/s . If the stress in its
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cable is not to exceed 6000 lb/in. , what should the cable diameter be?
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13.8. A steel cable of cross-sectional area 2.5 cm supports a 1000-kg elevator. The elastic limit of the cable is 3 × 10 Pa.
If the stress in the cable is not to exceed 20 percent of the elastic limit, find the maximum upward acceleration of
the elevator.
13.9. Two steel beams are riveted together to form a single longer beam. Eight rivets 10 mm in diameter are used. If a
tension force of 55 kN is applied to the new beam, what is the shearing stress on the rivets? How does this compare
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with their shearing strength of 3.5 × 10 Pa?
13.10. Find the force needed to punch a hole 1 in. square in a steel sheet 0.05 in. thick whose shearing strength is 5 × 10 4
2
lb/in. .
13.11. A punch press that exerts a force of 20 kN is used to punch holes 1 cm square in sheet aluminum. If the shear strength
of aluminum is 70 MPa, what is the maximum thickness of aluminum sheet that can be used with the press?
2
13.12. When a pressure of 300 lb/in. is applied to a mercury sample, it contracts by 0.008 percent. Find the bulk modulus
of mercury.

Answers to Multiple-Choice Questions

13.1. (b), (c), (d) 13.6. (a)

13.2. (b) 13.7. (a)

13.3. (d) 13.8. (b)

13.4. (c) 13.9. (b)

13.5. (b) 13.10. (a)