Ball hitting wall

[newarch]

The textbook I am working from says that v = eu, where u is the speed going on to the wall, e is the coefficient of restitution, and v is the speed coming off the wall. But there is no mention of the momentum equation, which has been used in all previous questions. Does the wall gain any momentum?

[sddsddean]

If I remember correctly, in these sorts of textbook questions everything is a perfect world, so, No, the wall can't gain any momentum...it can't move! Therefore, momentum is preserved and you can assume that the only loss of velocity is due to the coefficient of restitution. (I stand to be corrected...it was 30 odd years ago I did this!)

[newarch]

Thanks sddsddean. I'm still a bit puzzled, though, because if the total momentum is preserved, and the ball's momentum changes (which it must if its velocity changes), where does the difference go?

[dundurn]

Did it make a sound as it hit the wall? There's a little bit of energy. Dit the ball deform and then recover its original shape so that its component atoms were forced to move against each other and did they get hotter in doing so? There's a bit more. Basically the coefficient of restitution measures the energy loss in the collision. Billiard balls and shove ha'penny coins have high coefficients. Bubble gum (unchewed) has a lower one and bubble gum (chewed) can be have a coefficient as low as zero.

[Teddio]

Momentum is conserved in any collision.
An elastic collision conserves kinetic energy but an inelastic collision does not.

[newarch]

Thanks for those answers. Dundurn has explained why there is a loss of energy, and I can understand that. But if, as Teddio says, momentum is always conserved, and the ball loses some, what gains the momentum that the ball has lost? I can't quite get this right in my mind yet.

[vascop]

The point here is that the collision with the wall provides an EXTERNAL impulsive force. In this case momentum is NOT generally conserved.
The system in your example is just the one ball moving and it has a certain momentum. Suddenly it hits the wall (external force) and so its momentum CHANGES.
if you think of two balls on a billiard table (both stopped) then the total momentum is zero and will remain so forever. However if one ball is hit by a cue its momentum suddenly increases and now the system of 2 balls has a certain momentum. if the ball which was hit by the cue now collides with the other ball then the conservation of momentum applies between the 2 balls. However if the moving ball misses the other ball and hits a cushion then momentum is not conserved unless the cushion is perfectly elastic (e=1) because this is an external force on the system of 2 balls.