Edge Height of Billiard Table for No Reaction to Ball Impact

[ehrenfest]

Homework Statement

Show that the edge (cushion) of a billiard table should be at a height of 7/10 of the diameter of the billiard ball in order that no reaction occurs between the table surface and the ball when the ball strikes the cushion.

Homework Equations

The Attempt at a Solution

I am not entirely sure what this problem is asking me to show. Should I assume the collision is perfectly inelastic? Should I assume that the ball is initially rolling without slipping? Should I assume that the ball rolls without slipping after the collision? Do I assume that the collision is instantaneous?

 

[pam]

1. Collision is perfectly elastic.
2. No slipping.
3. Instantaneous.
Draw an FBD of the ball in contact with the edge and the table.
Use Fdt=dP, and Torque dt =dL to relat H to R.

 

[ehrenfest]

Thanks. I completed the problem and you do not even need to assume that the collision is instantaneous (as long as the force is constant).