Question

A small ball of mass m is aligned above a larger ball of mass M = 2.1 kg (with a slight separation, as with the baseball and basketball of Figure (a)), and the two are dropped simultaneously from height h = 2.1 m. (Assume the radius of each ball is negligible compared 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 (see Figure (b))?

Answer 1

a) PE = M g h

KE_final = 1/2 M v²

M g h = 1/2 M v²

v = sqrt (2 g h)

from conservation of KE

1/2 m (2 g h) + 1/2 M (2 g h) = 1/2 m v_f²

m (2 g h) + M (2 g h) = m (-sqrt(2 g h) + M/m sqrt(2 g h))²

m + M = m - 2 M + M²/m

m = M / 3

= 2.1 / 3

m = 0.7 kg

b) 1/2 m v_f² = m g H

H = 4 h = 4 * 2.1

H = 8.4 m