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Stretching things and Hooke’s law

If you get hold of a rubber band and pull it you are using a force on it. That force makes the rubber band get longer – it stretches. The greater the pull the longer it gets. In other words a bigger force makes the rubber band stretch more.

The bigger the force the bigger the extension

Instead of a rubber band we could use a spring like the one in the picture. We can put a force on the spring by hanging a weight from the end of the spring.

The picture shows how the length of a steel spring will change when the load on it is steadily increased. Each part of the drawing shows what happens when an extra 50g is added to the spring. The spring is getting longer and longer.

We call the difference in length between the new length and the length without any weight on the spring the extension of the spring.


If we measured the length of the spring after each new weight had been added we would get a table like the one drawn below although our numbers would probably be different. We can use it to work out the extension of the spring for each weight.

Length (cm) Extension (cm) Mass (g)
15 0 0
18 3 50
21 6 100
24 9 150
27 12 200
30 15 250

We could use a rubber band instead and hang weights on it in just the same way as on the spring.

Hooke's Law

In 1676 a scientist called Robert Hooke used results like ours and realised that the more force that is put on to a piece of elastic or a spring the more it will stretch. Not only that – he realised that the length increased by the same amount every time the force was increased by a fixed amount. This is called Hooke’s law. You can see a graph showing Hooke’s law in the diagram.

When you take the force away the rubber band or spring should go back to its original size. However if you stretch it too much it will not do this size and if it is stretched even more it will break.

We have used grams in the table although forces are measured in Newtons – 1 Newton is the pull of the Earth on about 100 g.

© Keith Gibbs 2020