Question

Block A in Fig. 1 has mass 1.00 kg, and block B has mass 3.00 kg. The blocks are forced together, compressing a spring between them; then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. Block B acquires a speed of 1.20 m/s.
(a) What is the final speed of block A?
(b) How much potential energy was scored in the compressed spring?

Answer 1

Answer on Question #60999-Physics-Mechanics-Relativity

Block A in Fig. 1 has mass $1.00 \, \mathrm{kg}$ , and block B has mass $3.00 \, \mathrm{kg}$ . The blocks are forced together, compressing a spring between them; then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. Block B acquires a speed of $1.20 \, \mathrm{m/s}$ .

(a) What is the final speed of block A?

(b) How much potential energy was scored in the compressed spring?

Solution

(a) Use the law of conservation of momentum:

$$p _ {i} = p _ {f}$$ $$0 = m _ {1} v _ {1 f} - m _ {2} v _ {2 f}$$ $$v _ {1 f} = \frac {m _ {2} v _ {2 f}}{m _ {1}} = - \frac {(3 . 0 0 k g) (1 . 2 0 \frac {m}{s})}{1 . 0 0 k g} = 3. 6 0 \frac {m}{s}$$

(b)

Use the law of conservation of energy:

$$U = K _ {1} + K _ {2} = \frac {m _ {1} v _ {1 f} ^ {2}}{2} + \frac {m _ {2} v _ {2 f} ^ {2}}{2} = \frac {1}{2} \left((1. 0 0 k g) (3. 6 0 \frac {m}{s}) ^ {2} + (3. 0 0 k g) (1. 2 0 \frac {m}{s}) ^ {2}\right) = 8. 6 4 J.$$

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