MadSci Network: Physics
Query:

Re: How much energy does a squash ball have when hit?

Date: Tue Apr 3 13:31:14 2001
Posted By: Tom Cull, Staff, Clinical Sciences MR Division, Marconi Medical Systems
Area of science: Physics
ID: 984947403.Ph
Message:

A very nice previous answer describes some of the effects of squash ball deformation and elasticity:

A very nice previous answer describes some of the effects of squash ball deformation and elasticity:

 

Re: How does the temperature of a squash ball affect the height of bounce?

 

This question has more background and great explanation of squash balls and empirical models.

 

Conservation of momentum and energy is necessary for the collision of the squash ball with the racket or the wall.  There are few MadSci answers available MadSci Search dealing with collisions and conservation of energy and momentum, use the keywords: momentum collision.  There are plenty of responses about other sports collisions (golf, baseball, soccer).

 

The two things to remember: conservation of momentum and conservation of energy always hold true.   It just may be difficult to apply them with things you can measure.    I would break down the energy into the following components:

 

Ball

 

Object (either the wall or the racket)

 

 

Conservation of momentum:

 

Massball * velocityballbefore + Massobject * velocityobjectbefore =

 

Massball * velocityballafter + Massobject * velocityobjectafter

 

Conservation of Energy:

 

   ½ Massball * (velocityballbefore)2 + Energy of Deformationbefore

+ ½ Massobject * (velocityobjectbefore)2

=

   ½ Massball * (velocityballafter)2 + Energy of Deformationafter

+ ½ Massobject * (velocityobjectafter)2

+ Energy Lost

 

 

So the only real difference in this model of the collision is the Energy of Deformation, otherwise everything is much the same as in collisions you may be familiar with from physics class or textbooks.  To understand this Energy of Deformation better, we need to develop and empirical model for observation and reasonable theory.  This is part of experimental physics and engineering.

 

To model this interaction effectively, one needs to know the coefficient of restitution for the squash ball – object collision as a function of ball speed and deformation.  The deformation properties are going to depend on the material of the ball.  There are a few different types of squash balls available that are ranked on the speed of the ball in play, which is dependent on the energy consumed (lost) during collisions.

 

The energy of deformation is probably a complicated function of the shape of the ball at the time before and after collision.  As stated in the previous answer by Adrian Popa, the ball reaches maximum deformation at impact when changing direction.  If the ball is compressed or deformed when it collides then the shape might not change much during the collision and very little kinetic energy will be lost.   In other words, the squash ball – object collision varies in coefficient of restitution depending on how squashed the squash ball is at time of impact.  This same effect is true with other types of balls (basketball, soccer, baseball, golf), except that other balls restore to their original form much more quickly and strongly because they have a stronger elastic surface force.

 

 

Sincerely,

 

Tom “Squashed” Cull

 

 


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