# Force on a spring and other simple systems

Forces may change the shape of an object. An elastic object, such as a spring, stores elastic potential energy when stretched or squashed. The extension of an elastic object is directly proportional to the force applied.

## Hooke's Law

When an elastic object, such as a spring, is stretched, the increased length is called its extension. The extension of an elastic object is directly proportional to the force applied to it:

F is the force in newtons (N)

k is the 'spring constant' in newtons per metre (N/m)

x is the extension in metres (m)

This equation works as long as the elastic limit (the limit of proportionality) is not exceeded. If a spring is stretched too much, for example, it will not return to its original length when the load is removed.

### The spring constant

The spring constant, k, is different for different objects and materials. It is found by carrying out an experiment. For example, the unloaded length of a spring is measured. Different numbers of slotted masses are added to the spring and its new length is measured each time. The extension is the new length minus the unloaded length.

Graph showing Hooke's Law, extension is plotted against force

Assuming the limit of proportionality (elastic limit) is not exceeded, a graph of force against extension produces a straight line that passes through the origin. The gradient of the line is the spring constant, k. The greater the value of k, the stiffer the spring.