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Two blocks of masses m1 and m2 are joined by a massless spring of stiffness k and rest on a frictionless horizontal surface, with block 1 touching a wall. Block 2 is pushed a small distance x toward block 1 (compressing the spring) and then let go. Determine the speed of the system's centre of mass after block 1 leaves the wall.

1. 0
2. x*sqrt(k/(m1+m2)) * m2/(m1+m2)
3. x*sqrt(k/m2) * m2/(m1+m2)
4. cannot be determined

Correct answer: x*sqrt(k/m2) * m2/(m1+m2)

Solution

Block 1 stays pinned to the wall until the spring reaches natural length; at that instant block 2 has speed v2 from energy conservation, and the centre-of-mass speed is m2*v2/(m1+m2).

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