# Average force on the walls

1. May 9, 2013

### Saitama

1. The problem statement, all variables and given/known data
A ball of mass m bounces between two parallel walls, such that its velocity v is perpendicular to the walls.The collisions with the walls are totally elastic. What is the average force exerted by the ball on the walls, if the distance between the walls is d?

2. Relevant equations

3. The attempt at a solution
When the ball collides with one of the walls and bounces back, the total change in momentum is $2mv$. The average force can be calculated by
$$F_{avg}=\frac{2mv}{\Delta t}$$
What can I substitute for $\Delta t$ here?

Thanks!

2. May 9, 2013

### Staff: Mentor

What's the time between collisions?

3. May 9, 2013

### Saitama

2l/v? But why do I need the time between collisions? $\Delta t$ is the time of contact between the wall and the ball during the collision.

4. May 9, 2013

### Staff: Mentor

I think they mean overall average, not average just during each collision.

5. May 9, 2013

### Saitama

In my previous post, I meant to say l/v. Is that correct?

6. May 9, 2013

### Staff: Mentor

What is l? If you mean d, then no.

7. May 9, 2013

### Saitama

Yes, I mean d. Sorry.

Why is it wrong? Do you mean the time taken between the collisions on the same wall?

8. May 9, 2013

### Staff: Mentor

Yes, exactly.

9. May 9, 2013

### Saitama

Its 2d/v then. Hence the average force is mv^2/d. Thank you Doc Al!

10. May 9, 2013

Good!