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Elastic Potential Energy (Oxford AQA IGCSE Combined Science Double Award)

Revision Note

Leander Oates
Oxford AQA Combined Science Double Award: PhysicsOxford AQA Physics

Elastic Potential Energy

Extension Tier only

What is elastic potential energy?

  • 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 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

The extension of a spring when a force is applied

Stretching a spring, for IGCSE & GCSE Physics revision notes
When a force is applied to either end of a spring, it stretches. Work is done on the spring as it extends, therefore energy is transferred

How to calculate elastic potential energy

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

A spring stretched beyond its elastic limit

Elastic limit of a spring, for IGCSE & GCSE Physics revision notes
When a spring is stretched beyond its elastic limit it will no longer return to its original length

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 energy in the elastic potential store of the stretched spring.

Step 1: Determine the extension of the spring

  • The extension of the spring is its extended length minus its original length

e space equals space 11.4 space minus space 10.0

e space equals space 1.4 space cm space

  • Convert cm to m

e space equals space fraction numerator 1.4 over denominator 100 end fraction

e space equals space 0.014 space straight m

Step 2: List the known quantities

  • Spring constant, k space space equals space 250 space straight N divided by straight m

  • Extension, e space equals space 0.014 space straight m

Step 3: Write out the elastic potential energy equation

E subscript e space equals space 1 half space cross times space k space cross times space e squared

Step 4: Calculate the elastic potential energy

E subscript e space equals space 1 half space cross times space 250 space cross times space open parentheses 0.014 close parentheses squared

E subscript e space equals space 0.0245 space straight J

Step 5: Round the answer to 2 significant figures

E subscript e space equals space 0.025 space straight J

Examiner 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.

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    Leander Oates

    Author: Leander Oates

    Expertise: Physics

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.