AQA AS Level Physics Paper 2, June 2024: Question 10

1 mark · Medium difficulty · Multiple Choice

Identify the correct pair of graphs showing the variation of elastic strain energy with extension and tension for a wire obeying Hooke's law.

Practise this question

Question

Multiple choice question 10 showing four pairs of graphs labeled A, B, C, and D. Each pair displays elastic strain energy Es on the y-axis against extension delta L on the first graph, and Es against tension T on the second graph, with various linear and curved relationships.
Question text

10 A wire obeys Hooke’s law.

When the wire is extended by ΔL, the elastic strain energy is Es and the tension in the wire

is T.

Which pair of graphs shows the variation of Es with ΔL and the variation of Es with T?

[1 mark]

A

B

C

D

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer for question 10 is D, showing two curved exponential-style graphs for both Es versus delta L and Es versus T.

10 D

How to answer it

Elastic Strain Energy and Hooke's Law Graphs

What this question tests

This question assesses your understanding of the mathematical relationships governing elastic deformation, specifically how elastic strain energy ( E_s ) relates to extension ( ΔL ) and tension ( T ) for a wire obeying Hooke's law.

Question 10

Analyzing Graph Variations for Hooke's Law

✅ Correct Answer: D

Both graphs must show a curved, non-linear relationship (specifically a parabola/power-law curve) passing through the origin.

💡 Key Knowledge

  • Hooke's law: T = k ΔL (where k is the spring constant).
  • Elastic strain energy is the area under a force-extension graph: E_s = ½ T ΔL .
  • Substituting T = k ΔL gives E_s = ½ k (ΔL)² .
  • Substituting ΔL = T / k gives E_s = ½ T² / k .

🧠 Exam Technique

Instead of guessing, derive the algebraic equations linking the variables on the axes. Look at the power of the independent variable on the horizontal axis to determine if the graph should be a straight line (power of 1) or a curve (power of 2).

❌ Common Errors

Students frequently fall into the trap of assuming that because tension is directly proportional to extension ( T ∝ ΔL ), energy must also be directly proportional to extension or tension in a linear fashion, leading them to mistakenly choose option A.

📐 Step-by-Step Derivation

  1. Graph 1 ( E_s vs ΔL ): Since E_s = ½ k (ΔL)² , E_s is proportional to (ΔL)² . This represents a square law relationship, which plots as an upward-curving parabola.
  2. Graph 2 ( E_s vs T ): Since E_s = ½ T² / k , E_s is proportional to T² . This also represents a square law relationship, yielding an upward-curving parabola.
  3. Conclusion: Both graphs must be curved, confirming option D as the correct selection.
Mark Scheme Allocation: 1 mark total for selecting option D.

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.