Height of edge of billiard table

SlowerPhoton
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Homework Statement


Consider a billiard table with balls of radius r. How high should be the edge of the table to not allow undesirable pressures (and thus slips of the ball)? I.e. if there was no gravity, the billiard ball would still bounce off parallelly to the table plane.

However I do not even understand what exactly it says. Please be easy on me, the last I've taken a class on physics was on high school.

The Attempt at a Solution


My answer would be r because otherwise I can see forces that push the ball off the table (in the upward direction). But that seems like a too easy answer for a calculus class.
 
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You are correct that the height must be r or higher or the balls would fly off the table all the time. And you should have it a little higher to be on the safe side. Here is a reference that shows the height of initial contact to be between 61% and 64% of the height of the ball ( between .61*2*r and .64*2*r ) https://www.pooltablefeltcloth.com/cushion-height-guide-for-k-66-k-55.html
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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