A rubber ball and a clay ball of identical mass are thrown at a wall at the same speed. The rubber ball bounces back; the clay ball sticks. Which ball exert...
Question 1 Report
A rubber ball and a clay ball of identical mass are thrown at a wall at the same speed. The rubber ball bounces back; the clay ball sticks. Which ball exerts a greater impulse on the wall?
Answer Details
Impulse (equal to the change in momentum) depends on how much the velocity of an object changes, \(\Delta p = m\Delta v\), not just on whether it stops. Both balls have the same mass and hit the wall at the same speed \(u\), but they behave differently afterwards.
The clay ball sticks to the wall, so its final velocity is zero: its change in momentum has magnitude \(mu\). The rubber ball bounces back at (approximately) the same speed, reversing its direction: its final velocity is \(-u\), so its change in momentum has magnitude \(m(u-(-u)) = 2mu\), twice as large as the clay ball's.
The rubber ball exerts the greater impulse on the wall, because reversing an object's momentum requires twice the impulse needed to simply bring the same momentum to zero. It is a common misconception that the ball which stops (the clay ball) must experience the bigger change, but stopping is only "half" of the momentum reversal that the bouncing ball undergoes.
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