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Work is done when a spring is extended or compressed. Elastic potential energy is stored in the spring. Provided plastic deformation has not happened, the work done is equal to the elastic potential energy stored.

The elastic potential energy (energy transferred in stretching) stored can be calculated using the equation:

energy transferred in stretching = 0.5 × spring constant × (extension)²

This is when:

• energy transferred in stretching is measured in joules (J)
• spring constant is measured in newtons per metre (N/m)
• extension is measured in metres (m)

This equation also works for the reduction in length when a spring is compressed.

Example

A spring has a spring constant of 3 N/m. It is stretched until it is extended by 50 cm. Calculate the energy transferred during the stretching, assuming it is not stretched beyond the elastic limit.

First, convert centimetres to metres:

50 cm = 50 ÷ 100 = 0.5 m

Then calculate using the values in the question:

energy transferred = 0.5 × spring constant × (extension)²