# Calculating the energy of springs (E = 1/2 kx²)

I can calculate the energy a spring has because it is stretched.

# Calculating the energy of springs (E = 1/2 kx²)

I can calculate the energy a spring has because it is stretched.

## Lesson details

### Key learning points

- Doubling the stiffness of a spring doubles the energy it has because it is stretched.
- The spring constant is measured in newtons per metre (N/m).
- Doubling the extension of a spring increases the energy it has, because it is stretched, by four times.
- The energy a spring has because it is stretched equals 1/2 × spring constant × (extension)².

### Common misconception

When calculating energy in the elastic store, pupils often work out (½ times spring constant tmes extension) and then square everything, rather than just the extension.

Scaffold calculations to show how elastic energy is calculated, taking pupils through how to do this on their calculators without making a mistake.

### Keywords

Elastic store - If an elastic object is stretched, compressed or bent out of shape, there is energy in the elastic store.

Compress - To make something smaller using forces, e.g. a spring gets shorter when it is compressed.

Extension - The increase in length from the original length of a spring when it is stretched.

Spring constant - A measure of how stiff a spring is and how hard it is to stretch or compress.

### Equipment

Mini-whiteboards.

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Video

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