# Edge Height of Billiard Table for No Reaction to Ball Impact

• ehrenfest
In summary, in order to prevent any reaction between the billiard ball and the table surface, the edge (cushion) of a billiard table should be at a height of 7/10 of the diameter of the ball. This can be achieved by assuming a perfectly elastic collision, no slipping of the ball, and using the equations Fdt=dP and Torque dt=dL to relate the height to the radius of the ball. The assumption of an instantaneous collision is not necessary as long as the force is constant.
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.

## 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?

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.

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).

## 1. What is the edge height of a billiard table?

The edge height of a billiard table is typically between 29 and 31 inches, with 30 inches being the standard height.

## 2. Why is the edge height important for no reaction to ball impact?

The edge height is important because it affects the angle at which the balls will ricochet off the edges of the table. If the edge is too high, the balls may bounce off at a more extreme angle, causing them to react unpredictably.

## 3. What is the recommended edge height for no reaction to ball impact?

The recommended edge height for no reaction to ball impact is 30 inches. This is the standard height used in professional and tournament billiards.

## 4. How does the edge height affect gameplay?

The edge height can greatly affect gameplay as it can influence the angle and speed at which the balls will bounce off the edges of the table. A higher edge height may make the game more challenging, while a lower edge height may make it easier.

## 5. Can the edge height be adjusted?

Yes, the edge height of a billiard table can be adjusted. However, it is important to note that changing the edge height may also affect the overall playing surface and may require adjustments to be made to maintain a level playing field.

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