# 5.3.4 Work Done on a Spring

### Work Done on a Spring

• 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

### Calculating Work Done on a Spring

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

Ee = ½ × k × e2

• Where:
• Ee = 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

#### Worked Example

A mass is attached to the bottom of a hanging spring with a spring constant k and 0.2 J of work is done to stretch it by 4.5 cm.

Calculate the spring constant, k for this spring. #### Exam Tip

Remember: when calculating the work done the extension, e, is squared (e2)! ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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