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All equation deep-dives

Elastic potential energy

Energy
AQA 8463
On the equation sheet
ORIGINAL

Ee = 1/2 k e2

e is the EXTENSION, not the length, and it is squared: two separate marks to lose.

Current GCSE 8463 policy: The full AQA GCSE Physics 8463 equation sheet is provided with both papers in 2026; use fluency practice to learn selection and rearrangement, not to memorise the list.

Board and spec code confirmed against AQA 8463 · registry checked 2026-07-17How this checking works

Know the equation

SymbolQuantityUnit
Eeelastic potential energyJ
kspring constantN/m
eextensionm

Rearrangements

  • e = sqrt(2 Ee / k)
  • k = 2 Ee / e2

Apply it — mark your own working

Work each one out on paper first, then reveal the mark scheme and tick the marks you actually earned. That is exactly how you should mark past papers.

Q1

A spring has a natural length of 20 cm and a spring constant of 40 N/m. It is stretched until its length is 35 cm. The limit of proportionality is not exceeded. Calculate the elastic potential energy stored in the spring. Give your answer to 2 significant figures.

[3 marks]

Total for this question: 3

Do the calculation on paper first — then mark it.

Q2

A spring with a spring constant of 400 N/m stores 2.0 J of elastic potential energy. The limit of proportionality is not exceeded. Calculate the extension of the spring. Give your answer to 2 significant figures.

[3 marks]

Total for this question: 3

Do the calculation on paper first — then mark it.

Where the marks get lost

  • Using the stretched length (35 cm) instead of the extension (35 - 20 = 15 cm).
  • Leaving the extension in cm: 15 cm must become 0.15 m before it is squared.
  • Forgetting to square e, or forgetting the square root when rearranging for e.

Exam tip: Work out the extension in metres as a separate first line. The equation only holds while the limit of proportionality is not exceeded, so look for that phrase in the question.

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