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Two small pucks of masses m1 and m2 are joined by a massless spring and lie on a frictionless horizontal table. They are given initial velocities v1 and v2 that are perpendicular to each other and both lie in the horizontal plane. Determine the total mechanical energy E of the system as measured in the centre-of-mass frame.

1. (1/2)*(m1*m2/(m1+m2))*(v1² + v2²)
2. (1/2)*(m1+m2)*(v1² + v2²)
3. (1/2)*(m1*m2/(m1+m2))*(v1² - v2²)
4. (1/2)*(m1*m2/(m1+m2))*(v1 + v2)²

Correct answer: (1/2)*(m1*m2/(m1+m2))*(v1² + v2²)

Solution

The energy in the C-frame is (1/2)*mu*v_rel² where v_rel is the relative velocity; because v1 and v2 are perpendicular, v_rel² = v1² + v2².

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