# To investigate the relationship between the extension of a compact steel spring and the force producing that extension and to determine the elastic limit and force constant of the spring

To investigate the relationship between the extension of a compact steel spring and the force producing that extension and to determine the elastic limit and force constant of the spring

## Stand

Spring

100g weights with hanger

Clamps and Bosses

A 1 meter ruler

Set square

Goggles

## Diagram

Theory

In 1676, Robert Hooke studied the strain on material. He found that the strain on the material is proportional to the stress producing it. This is shown as:

Extension  Stretching force

Strain is the amount of change in size, which could be length, area or volume. The stress is the force divided by the surface area.

When a spring is stretched, the force that is required to stretch it is proportional to the amount of extension. If a selection of springs were taken to stretch one spring twice a far as the other, twice the amount of force is needed. If three times the amount of force was used then it would produce three times the extension etc. If a graph is produced, it will look like this:

It shows a straight line up to the black dot where the extension is plotted against the force. All springs follow this rule up to this point, which represents the elastic limit. After this point, when the mass is removed from the spring, the spring does not return to its original shape. After the elastic limit has been reached, the spring stops obeying Hooke’s law. Point A is an example of where the mass is removed and the extension remains. This is called the yield point. The extension that remains is the measurement OS that is recorded at the base of the graph. The force constant of a spring is the force needed to cause unit extension. If force (F) produces extension (e) then this can be shown as:

## Hypothesis

From the theory I expect to find that I will get a constant extension with every 100g added to the spring. The graph that is shown in the theory states that the yield point comes after the elastic limit. I predict that it will come very close to it, 1N or 2N away. I also expect the extension up to the elastic limit will be equal distance away from each other. I predict that my graph will look like this:

This graph is what the graph is like in the theory, so ...