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Conservation of momentum and kinetic energy: Superball and elastic collisions

A superball has collisions that are nearly perfectly elastic. A superball of mass M is dropped from rest from a height h (where h >> the size of the superball) together with a smaller marble, of mass m; the marble is initially just a little above the top of the superball and remains right over it throughout the fall. The superball hits the floor first and immediatly rebounds elastically, colliding with the marble.

(a) What is the speed of the superball and the marble just before the super ball hits the floor?
(b) What is the speed of the superball just after it rebounds from the floor but before it hits the marble?
(c) What is the velocity of the marble after the superball hits it in the head-on collision?
(d) How high does the marble go after its collision, assuming the marble has stayed in line with the superball, so that all the motion is vertical?
(e) What is the answer to part (d) in the limit M>>m?

Solution Summary

With detailed explanations and calculations, the problems are solved.