Forces - Forces and Elasticity

Elastic potential energy is the energy stored in an elastic object which will restore the object to its original shape - the force it creates is called the restoring force.

You can think of elastic potential energy as being similar to gravitational potential energy but it depends on the nature of the substance rather than on gravity. It's not just stretching that generates elastic potential energy, compression does too. When an elastic ball like a squash ball, football or basketball hits the ground, it is compressed and contains more elastic potential energy than before the impact. Work is done to generate the stored energy, so the ball becomes hotter. This is most noticeable with a squash ball - squash players always warm the ball thoroughly before starting the game to ensure that it becomes even more elastic and bounces better. They do this either by hitting it around the court a lot or sometimes, when the weather and the court is particularly cold, putting it in hot water for a few minutes!

When a force is applied to an elastic object, it stretches. When the force is doubled, the amount stretched is doubled and so on. We say that the stretch is directly proportional to the force applied. This was discovered by scientist Robert Hooke in the seventeenth century. We now know that this law is only an approximation and as the elastic limit is approached, Hooke's law ceases to work but it is good enough to be applied in many everyday situations. Mathematically, Hooke's law can be written as F = k e where F is the force (in newtons) required to extend a spring by a distance e which is small compared to the total possible stretch of the spring (in meters) and k is the spring constant (in newtons per meter) for that particular spring. This equation is also used to work out the restoring force.

You may have carried out some experiments using springs in which you have loaded a spring with masses and measured the extension. When you plot a graph from the readings, at first the graph is a straight line whose gradient is the spring constant. At the limit of proportionality, the gradient suddenly changes and becomes much steeper.