Does the temperature of a football (or baseball, soccer ball, etc) affect how far it will travel when kicked/hit?
Temperature can affect a couple of different variables in a ball to alter the distance it will travel from an impact. For inflated balls, the temperature can change the air pressure inside the ball giving an over inflated effect if it was warmed, or and under inflated effect if it was cold. (Have you ever tried dribbling a basketball without enough air in it?) The amount of air pressure then is directly proportional to the temperature of the air inside.
For solid core balls, like baseballs, golf balls etc' temperature has a similar effect on the ball but the mechanics are a bit different. Here the characteristics of the material inside the ball are responsible for the bounciness of the ball.
A ball's bounciness is dependent on the elasticity of its constructed materials. The property of elasticity allows the ball to retain kinetic energy during a collision by having the ability to flex without breaking and then return to its original shape. This measure of a material's elasticity is called its coefficient of restitution.
An object with a low coefficient of restitution will lose a great deal of its kinetic energy in a collision through breaking or deforming, or through the generation of sound or heat. Compare the kinetic energy transmission through steel balls suspended on strings as they bounce back and forth in an example of a high coefficient of restitution. Now consider a lump of clay or a piece of glass in a collision, both materials having very low restitutional values ' they simply do not transfer energy well because they are not as elastic.
How does all this tie back into the temperature of materials? Temperature can also affect elasticity ' the colder a material gets, the less elastic it can be. Under cold conditions, the material can actually become more of an 'energy sink' ' absorbing energy rather than transferring it.
Both inflated and solid core balls rely on the principle of coefficient of restitution. A warmed, (over inflated) ball is more elastic than a cold, (under inflated) ball just as a solid core ball that is warm has more elasticity than an identical ball that is cold.
Stephen Portz, Technology Teacher, Space Coast Middle School, FL
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'