A small ball of mass m is aligned above a larger ball of mass M = 0.76 kg (with

Question

A small ball of mass m is aligned above a larger ball of mass M = 0.76 kg (with a slight separation, as with the baseball and basketball of fig (a)), and the two are dropped simultaneously from height h = 3.0 m. (Assume the radius of each ball is negligible relative to h.)

(a) If the larger ball rebounds elastically from the floor and then the small ball rebounds elastically from the larger ball, what value of m results in the larger ball stopping when it collides with the small ball?

(b) What height does the small ball then reach (Figure (b))?

Explanation / Answer

kin energy of M-ball is the same as its pot energy, that is
0.5*M*V^2 = Mgh, hence V^2=2gh;
since V is not dependent of mass the speed of m-ball is also V;
now all this bound-rebound stuff is just lyrics to muddle our brain; and we can re-word the problem like this;
“M-ball and m-ball collide head-to-head, both having speed V;
what is mass m if M-ball stops after collision?

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