Elastic Potential Energy (1.1.5) | AQA GCSE Physics Revision Notes 2018 (2023)

• Energy in the elastic potential store of an object 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)
  • When a spring is stretched (or compressed), work is done on the spring which results in energy being transferred to the elastic potential store of the spring
  • When the spring is released, energy is transferred away from its elastic potential store

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:

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 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

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

E_e = ½ ke²

Step 4: Calculate the elastic potential energy

E_e = ½ × 250 × (0.014)² = 0.0245 J

Step 5: Round the answer to 2 significant figures

E_e = 0.025 J

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.