Elastic Potential Energy and Energy Transfers

In this lesson you will learn how to calculate elastic potential energy stored in a stretched or compressed spring, understand Hooke's law, and describe energy transfers involving elastic objects. This is part of AQA GCSE Combined Science Trilogy (8464), Section 6.1.

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Hooke's Law

When a spring is stretched or compressed by a force, it extends or compresses. Hooke's law states:

$F = k \, e$F=ke

Where:

• $F$F = force applied in newtons (N)
• $k$k = spring constant in newtons per metre (N/m)
• $e$e = extension (or compression) in metres (m)

This relationship is linear up to the limit of proportionality. Beyond this point, the spring no longer obeys Hooke's law.

Exam Tip: The limit of proportionality is the point where the force–extension graph stops being a straight line. Beyond this point, the spring may also pass its elastic limit — the point after which it will not return to its original length.

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Elastic Potential Energy

When a spring is stretched or compressed within its limit of proportionality, it stores elastic potential energy.

The Equation

$E_e = \frac{1}{2} k \, e^2$Ee​=21​ke2