Bounce balls under table

Thanks to Prof. Harry Nelson for requesting this demonstration.

This demonstration consists of a table, about 33 inches wide by 22 inches long and just under 2 feet high, a golf ball, a rubber ball and some water. Bounce the golf ball off the floor so that it hits the underside of the table. It bounces back to the floor, continuing in the same direction, and, depending on the angle at which you bounced it, it either emerges from the other side of the table, or continues bouncing back and forth between the table and the floor until it does. Bounce the rubber ball in the same manner, and when it strikes the underside of the table, it bounces back towards you. Now wet the surface of the rubber ball and try again. This time, it behaves as the golf ball did, bouncing away from you until it emerges from the opposite side of the table. (It may take some practice to get the ball to land in the proper place at the proper angle to bounce to the underside of the table, but it is not difficult.)

Why does this happen?

In a simple collision with the floor, a ball dropped straight down, with no spin, exchanges momentum with the floor so that it ends up with its momentum essentially reversed, and it bounces straight up with almost the same initial speed it had just as it hit the floor. That is, it exchanges essentially twice its momentum with the floor. (The collision can never be perfectly elastic, so there is some loss of energy in the collision, and the rebound speed is somewhat less than the original speed at collision.) In a collision with a surface at any angle that is not perpendicular to the surface, since the ball now has a component of velocity that is parallel to the surface, it rebounds at the same angle at which it struck the surface. So, if we bounce a ball off the floor so that it bounces up and hits the underside of a table, as in this demonstration, we expect it to return to the floor at a point farther underneath the table, then either bounce out from under the table on the other side, or return to the table, taking another bounce, or several bounces, until it emerges at the other side of the table. This is the behavior that we observe when we throw the golf ball under the table.

If, however, there is significant friction between the ball and the surface that it strikes, the friction, in opposing the parallel component of the ball’s velocity, imparts a torque to the ball, so that in the collision, the ball acquires spin. Between the golf ball and the floor or the table, there is very little friction, so the collisions between the golf ball and the floor, and the golf ball and the table, involve simple exchange of momentum, and the path the golf ball takes is what one would expect. There is, however, considerable friction between the surface of the rubber ball and both the floor and the table. Therefore, when the ball bounces off the floor, it picks up top spin, so that when it strikes the table, instead of bouncing forward, it bounces backward. The friction between it and the table not only causes this spin to change the direction of the rebound, but reverses the ball’s spin as well, so that it now has backspin (or at least zero spin or weaker topspin). When it strikes the floor again, it thus bounces back to you, maintaining or acquiring backspin in the collision with the floor. If you wet the rubber ball, there is now very little friction between the ball and the floor or the table, and only simple momentum exchange can occur in the collisions between the ball and the floor or the table. The wet rubber ball thus behaves as the (dry) golf ball does, and bounces through to the opposite side of the table.