Calculating Work Done in Stretching (WJEC GCSE Science (Double Award): Physics): Revision Note

Calculating Work Done in Stretching

Higher Tier Only

• When a spring is stretched by a force work is done by the spring

• The work done in stretching a spring is equal to the elastic energy stored in the spring

Work Done in Stretching a Spring

Work is done on a spring when it is stretched

• Work done is calculated using the equation:

$W=\frac{1}{2}Fx$

• Where:

  • W  = work done by the spring or elastic potential energy (J)

  • F = force applied to stretch the spring (N)

  • x = extension of the spring (m)

• This is only valid for springs not stretched beyond their limit of proportionality 

Calculating Work Done from the Force-Extension Graph

• Work done is calculated from the area under a force-extension graph

• The area under the graph forms a triangle shape

  • Where the area of a triangle is $\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$

• So, the work done = area = $\frac{1}{2}\times \mathrm{extension}\times \mathrm{force}$

Area Under a Force-Extension Graph

The area under the force-extension graph is a triangle. Calculating the area of the triangle gives the work done by the spring when stretched