AQA A-Level Physics Paper 1, June 2024: Question 25

1 mark · Medium difficulty · Multiple Choice

Calculate the increase in elastic strain energy stored in a wire when the load is increased from F to 2F.

Practise this question

Question

Multiple choice question 25 asks for the increase in elastic strain energy stored in a uniform wire when the load is increased from F to 2F, given that the wire obeys Hooke's law and initially stores energy E. Four options are provided: A (E), B (2E), C (3E), and D (4E).
Question text

25 A uniform wire is stretched by a load F.

The elastic strain energy stored in the wire is E.

The load is increased from F to 2F.

The wire obeys Hooke’s law.

What is the increase in the elastic strain energy stored in the wire?

[1 mark]

A E

B 2E

C 3E

D 4E

Mark scheme

Show the mark scheme The mark scheme table shows question number 25 has the correct answer C, corresponding to the increase in energy being 3E, assessed under AO2.

25 C 3E AO2

How to answer it

Question 25: Elastic Strain Energy in a Stretched Wire

What this question tests

This question assesses your understanding of Hooke's law, elastic strain energy, and proportional reasoning (AO2). Specifically, it tests whether you can recognise the non-linear (squared) relationship between force/extension and stored energy, rather than assuming a simple linear doubling.

Question Part 25

Multiple Choice Question (1 Mark)

✅ Correct Answer: C (3E)

When the load increases from F to 2F , the final elastic strain energy is 4E . The increase in energy is 4E - E = 3E .

💡 Key Knowledge

  • Hooke's Law: F = kx (Force is directly proportional to extension).
  • Elastic Strain Energy ( E ) is given by the area under a force-extension graph: E = 0.5 × F × x .
  • Substituting x = F / k gives the alternative formula: E = 0.5 × F² / k , showing that E is proportional to F² .

🧠 Exam Technique

Read the question carefully: it asks for the increase in energy ( Final - Initial ), not just the final total energy. Many students spot 4E and immediately select option D without checking what is actually being asked.

❌ Common Errors

  • Option D (4E): Failing to calculate the increase. 4E is the total final energy, not the change in energy.
  • Option B (2E): Treating elastic strain energy as directly proportional to force ( E ∝ F ) instead of proportional to force squared ( E ∝ F² ).

📐 Step-by-Step Calculation Breakdown

  1. Initial State: Initial force = F , Initial energy E₁ = E = 0.5 × F² / k .
  2. Final State: Final force = 2F . Final energy E₂ = 0.5 × (2F)² / k = 0.5 × 4F² / k = 4 × (0.5 × F² / k) = 4E .
  3. Calculate Increase: Increase = E₂ - E₁ = 4E - E = 3E .
Mark Scheme Allocation: Correct option C awarded 1 mark. (AO2 - Application of physics equations and proportional reasoning).

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.