Work Done on a Spring (AQA GCSE Physics: Combined Science)

• When a spring is stretched or compressed by a force, work is done by the spring
• Work done is the transfer of energy
  • The energy is transferred to its elastic potential energy store

When a spring is stretched or compressed, there is work done and elastic potential energy is stored

• Elastic potential energy is defined as:

The energy stored in an elastic object when work is done on the object

• Provided the spring is not inelastically deformed (i.e has not exceeded its limit of proportionality), the work done on the spring and its elastic potential energy stored are equal

• The work done, or the elastic potential energy stored, while stretching or compressing a spring can be calculated using the equation:

E_e = ½ × k × e²

• Where:
  • E_e = elastic potential energy in joules (J)
  • k = spring constant in newtons per metre (N/m)
  • e = extension in metres (m)

The elastic potential energy in a stretched spring depends on its spring constant and extension

• This equation is only for springs that have not been stretched beyond their limit of proportionality
  • The term e² means that if the extension is doubled then the work done is quadrupled
  • This is because 2² = 4