# 1.1.5 Elastic Potential Energy

### Elastic Potential Energy

• When a spring is stretched (or compressed), work is done on the spring which results in a transfer of energy to the spring’s elastic store
• Elastic potential energy is defined as:

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

• This means that any object that can change shape by stretching, bending or compressing (eg. springs, rubber bands) can store elastic energy

How to determine the extension, e, of a stretched spring

• The amount of elastic potential energy stored in a stretched 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 above equation assumes that the spring has not been stretched beyond its limit of proportionality

The spring on the right has been stretched beyond the limit of proportionality

#### Worked Example

A mass is attached to the bottom of a hanging spring with a spring constant of 250 N/m. It stretches from 10.0 cm to 11.4 cm.

Calculate the elastic energy stored by the stretched spring.

Step 1: Determine the extension of the spring

Step 2: List the known quantities

• Spring constant, k = 250 N/m
• Extension, e = 1.4 cm = 0.014 m

Step 3: Write out the elastic potential energy equation

Ee = ½ ke2

Step 4: Calculate the elastic potential energy

Ee = ½ × 250 × (0.014)2 = 0.0245 J

Step 5: Round the answer to 2 significant figures

Ee = 0.025 J

#### Exam Tip

Look out for units! If the question gives you units of cm for the length you MUST convert this into metres for the calculation to be correct.

### 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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