Problem of Billiards

ehrenfest

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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?

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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).

"Problem of Billiards"

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