Changes in energy: elastic potential energy, E_e, in joules, J

The idea

Elastic potential energy is the energy stored in a stretched or compressed elastic object, such as a spring or elastic band, because work has been done to change its shape. When a force stretches a spring, energy is transferred from the store of the object doing the stretching to the elastic potential energy store of the spring. The amount stored depends on the spring constant and the extension. For a linear spring, E_e = ½ k x², where E_e is in joules, J, k is the spring constant in newtons per metre, N/m, and x is the extension in metres, m. Doubling the extension quadruples the energy because x is squared. When the spring is released, this stored energy is transferred to other stores, for example kinetic energy of a moving object or thermal energy through friction.

What earns the marks

• State that elastic potential energy is energy stored in a stretched or compressed elastic object, measured in joules, J.
• Identify that work done in stretching or compressing an elastic object is transferred to its elastic potential energy store.
• Use the equation E_e = ½ k x², substituting k in N/m and x in m to obtain E_e in J.
• Recognise that extension x must be in metres and that doubling x increases E_e by a factor of four because of the x² term.
• Describe a transfer from the elastic potential energy store to kinetic or thermal energy stores when the object returns to its original shape.

Common mistakes and how to put them right

• Using the extension in centimetres instead of metres.

  Put it right by dividing by 100 before substituting into E_e = ½ k x².

• Forgetting to square the extension.

  Put it right by applying the x² term, so an extension of 0.20 m gives x² = 0.040 m².

• Omitting the factor of ½.

  Put it right by including ½, since the force increases from zero to kx as the spring stretches.

Exam tips

• Write the equation E_e = ½ k x² before substituting values so the examiner can see your method.
• Convert all lengths to metres and check that the final unit is joules, J.
• When a question asks for a comparison, calculate both values and state the ratio, for example four times greater.