Question

Identical balls are dropped from the same initial height and bounce back to half the initial height. In Case 1 the ball bounces off a cement floor and in case 2 the ball bounces off a piece of stretchy rubber. 1) In which case is the change in momentum of the ball between the instant just before the ball collides with the floor or rubber and the instant just after the ball leaves the floor or rubber the biggest?

A. Case 1
B. Case 2
C. Same in both

Answer 1

C. Same in both

Step-by-step explanation:

Change in momentum is given by:

`\Delta p=p_f-p_i\\\Delta p=mv_f-mv_i`

The speed with which both balls impact their respective contact surface is the same, since the initial height is the same. The speed of both balls when bouncing against their respective contact surface is the same, since both balls reach the same height after the collision. So, we have:

`v_(i1)=v_(i2)(1)\\v_(f1)=v_(f2)(2)\\\Delta p_1=mv_(f1)-mv_(i1)(3)\\\Delta p_2=mv_(f2)-mv_(i2)(4)`

Recall that are identical balls so their mass is the same, replacing (1) and (2) in (3):

`\Delta p_1=mv_(f2)-mv_(i2)`

Equialing with (4):

`\Delta p_1=\Delta p_2`

The change in momentum is the same in both cases.