Particle changing direction after bounce off a moving wall

Question

I am working in a group project on how to model ball/racket interaction in the game of Pong. In our model, we consider the ball as a particle unable to spin and are interested in how the friction between the particle and the moving racket can make the ball change direction in the direction tangential to the movement of the racket. I have found some useful insights but we noticed a weird thing. Consider a ball and a racket in a fixed frame independent of the ball and racket. Define tangential direction as being parallel to the trajectory of the racket. Assume that the ball hits the racket and that their relative speeds are such that the ball bounces off with opposite tangential speed. In other words, the ball hits the racket with an incidence angle alpha and bounces off following its trajectory backwards with the same reversed speed.

If we formulate the law of kinetic energy on the ball, we find that the work on the ball is zero, since the squared speeds before and after are the same. But how does it makes sense that the ball changed direction without any work on it?

EDIT More specifically, if I consider the ball in positions 1 and 2, respectively before and after the bounce, and write the total work on the ball accordingly to the law of kinetic energy, I get: $U_{1-2} = \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2 = 0$, under the assumption that $v_2 = - v_1$. Where did all the work go? How can the total work sum to zero and the ball change its course?

score 0 · Answer 1 · answered May 17 '21 at 00:48

0

You have to consider the whole system including the recoil of the racket. Consider the ball hitting a fixed racket. The ball does work on the racket in stretching its strings. The ball gives up all its kinetic energy in doing so as it comes to rest with respect to the racket. The racket strings then do work on the ball as they convert their potential energy of stretched strings to kinetic energy of the ball.

There is plenty of work being done, although in pieces.

answered May 17 '21 at 00:48

Bill Watts

1,436

Yes, I understand that a lot of energy is dissipated into the racket. I edited my question for clarification. – lukas gamard May 17 '21 at 09:35
If the collision is elastic, the energy is not dissipated; it is temporarily stored. – R.W. Bird May 17 '21 at 15:25

score 0 · Accepted Answer · answered May 17 '21 at 10:19

Net work is not required to modify the direction of an object. It does require force, but no energy is necessary.

As you note in your question, the energy at the start and end is identical, so there is no work that has anywhere to go.

If the object were to change speed, then there would have to be net work done on the object, and we would be able to point to where it came from or went to.

Particle changing direction after bounce off a moving wall

2 Answers2