# Impact and the Coefficient of Restitution

In summary, the conversation discusses the use of the coefficient of restitution in calculating the speed of a ball bouncing off a wall. It is determined that the coefficient of restitution applies only to the normal velocity component because the energy loss is due to compression and expansion of the object. If there is no friction between the ball and the wall, the compression will only occur in the horizontal direction. However, if there is friction, the ball may start rotating and rolling resistance must be taken into account. This can be seen in the example of superballs, which could acquire so much spin that they would reverse direction when bouncing off a surface.

Homework Statement
V1=50 ft/m
e = 0,75
Relevant Equations
e=(relative velocity after collision)/(relative velocity before collision)
Last post with picture, after this i will use Latex.

She say that correct answer is 41 ft/m.

Is this correct?

I get answer b). ##41 \ ft/m##

The coefficient of restitution applies only to the normal velocity component.

PS effectively you just multiplied 50 by 0.75.

PeroK said:
The coefficient of restitution applies only to the normal velocity component.
Why only to normal velocity?
And how to calculate x then?

Why only to normal velocity?
Because the energy lost is in the compression and subsequent expansion of the object, and the extent of the compression depends on the velocity component normal to the contact surface.
And how to calculate x then?
Resolve the initial velocity into components.

Normal component is in x direction, and ball bounce of wall just in x direction.That is why we can use coefficient of restitution in that direction?
And speed in y is same because we need to calculate speed right after collision?
Is that correct?

I guess one has to assume that there is no friction between the ball and the wall so that the compression is only in the horizontal direction.

malawi_glenn said:
I guess one has to assume that there is no friction between the ball and the wall so that the compression is only in the horizontal direction.
Yes, and that.

malawi_glenn said:
I guess one has to assume that there is no friction between the ball and the wall so that the compression is only in the horizontal direction.
Oblique bouncing with friction is quite complicated. Assuming no slipping, as the ball compresses, the frictional component of the reaction force exerts a torque about the ball's centre, causing it to start rotating. So now we have rolling resistance as a new part of the ball starts to compress and a corresponding part starts to decompress.
Superballs (https://en.wikipedia.org/wiki/Super_Ball), popular in the late '60s, could acquire so much spin that at the next bounce they would reverse direction, bouncing back and forth between two points on the floor.