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A block of mass 1 kg rests on a plank of mass 2 kg. A spring is compressed between the block and one end of the plank, with the other spring end attached to the plank. The entire system is initially at rest on a frictionless surface. When the thread holding the spring compressed is cut, the spring releases. At the instant the spring returns to its natural length, the block moves at 6 m/s. What was the elastic potential energy stored in the spring?

1. 18 J
2. 27 J
3. 36 J
4. 45 J

Correct answer: 27 J

Solution

By momentum conservation, if the block moves at 6 m/s, the plank moves at -3 m/s. The total kinetic energy (= spring's PE) is (1/2)(1)(36) + (1/2)(2)(9) = 18 + 9 = 27 J.

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