A.3.11—Elastic potential energy

Elastic store

For a spring within its linear range,

$$E_{p,elastic}=\frac12k(\Delta x)^2$$

where $\Delta x$ is extension or compression from the natural length.

Area under the graph

The elastic potential energy equals the work done in stretching or compressing the spring. On a force–extension graph it is the area under the graph.

Worked example from local Question Bank row 31357

A spring with $k=100\,\mathrm{N\,m^{-1}}$ is compressed by $0.10\,\mathrm{m}$.

$$E_{p,elastic}=\frac12(100)(0.10)^2=0.50\,\mathrm{J}$$

This is the energy available for transfer when the ideal spring is released.

Common trap

Do not use the total spring length as $\Delta x$, and remember that doubling extension quadruples the stored energy in the ideal model.