Work done in stretching a spring

A force-extension graph can be used to calculate the work done in joules when stretching a spring.

Force should be plotted on the vertical (y) axis

Extension should be plotted on the horizontal (x) axis

As long as the limit of proportionality is not exceeded this should produce a straight line graph that passes through the origin as shown below.

Force-extension graph demonstrating Hooke's law. A straight line passes through the origin (0,0).

In a force-extension graph:

  • the gradient is the spring constant
  • the area under the line is the work done in stretching the spring

Example:

Question

Using the graph, calculate the work done to extend the spring from 0 m to 0.10 m.

The area under the line is a triangle:

Areas = \frac{1}{2} × base × height

= \frac{1}{2} × 0.10 × 5 = 0.25 J