4. Two masses of 3 kg and 5 kg collide head-on, the former moving to the right with the speed 5 m/s and the latter moving to the left with the speed 3 m/s.After collision they stick together. What amount of mechanical energy is lost?

5. A cylinder with a uniform density is rolling over a plane. What fraction of its kinetic energy is rotational kinetic energy?

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  1. 4. Their momenta cancel and the stuck-together mass won't move, because
    5x3 - 3x5 = 0.
    All mechanical energy is lost.

    5. Compare (1/2) I w^2 (the rotational KE) with the sum of (1/2) Iw^2 and (1/2) M V^2.
    Note that I = (1/2) M R^2 (for solid cylinders) and
    V = R w (for rolling objects). You should end up with a fraction independent of M, R and w.

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