Hooke’s Law

If we take a metal wire or a spring and hang it from the ceiling it will have a natural, unstretched length of l metres. If we then attach masses to the bottom of the wire is will begin to increase in length (stretch). The amount of length it has increased by we will call the extension and represent by e.

If the extension increases proportionally to the force applied it follows Hooke’s Law:

The force needed to stretch a spring is directly proportional to the extension of the spring from its natural length

So it takes twice as much force to extend a spring twice as far and half the force to extend it half as far.

We can write this in equation form:

Here k is the constant that shows us how much extension in length we would get for a given force. It is called…

The Spring Constant

The spring constant gives us an idea of the stiffness (or stretchiness) of the material.

If we rearrange Hooke’s Law we get:

If we record the length of a spring, add masses to the bottom and measure its extension we can plot a graph of force against extension. The gradient of this graph will be equal to the spring constant.

A small force causes a large extension the spring constant will be small – very stretchy

A large force causes a small extension the spring constant will be large – not stretchy

Spring Constant is measured in Newtons per metre, N/m