AQA A-Level Physics Paper 1, June 2023: Question 26

1 mark · Medium difficulty · Multiple Choice

Identify which graph shows the variation of tensile stress with distance along a heavy cable supporting a load at its lower end.

Practise this question

Question

A diagram shows a heavy vertical cable attached to a fixed support at J and carrying a load at its lower end K. Four graphs labeled A, B, C, and D show the variation of tensile stress sigma with distance d from J to K. Graph A shows a linear decrease to zero at K. Graph B shows a linear increase from J to K. Graph C shows a constant stress from J to K. Graph D shows a linear decrease from a positive value at J to a lower positive value at K.
Question text

26 A heavy cable is attached to a fixed support and carries a load at its lower end.

The weight of the cable is not negligible.

The cable has constant cross-sectional area and density.

Which graph shows the variation of tensile stress σ in the cable with

distance d from J to K?

[1 mark]

A B

C D

A

B

C

D

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer is D.

26 D

How to answer it

Tensile Stress in a Heavy Cable

What this question tests

This question assesses your understanding of tensile stress, the effect of non-negligible object weights under gravity, and how forces vary continuously throughout an extended structure. You must apply the definition of stress ( σ = F / A ) while accounting for the changing internal tensile force from the fixed support (J) down to the loaded end (K).

Question 26

Analysis & Solution

✅ Correct Answer: D

Graph D is correct. The tensile stress starts at a higher value at the fixed support J (due to supporting both the hanging load and the entire weight of the cable) and decreases linearly with distance d to a lower, non-zero value at K (supporting only the hanging load).

💡 Key Physics Knowledge

  • Definition of Stress: Tensile stress σ = F / A , where F is the tensile force and A is the cross-sectional area.
  • Internal Force Profile: At any point distance d from J, the cable must support the hanging load W plus the weight of the cable segment hanging below that point.
  • Linear Variation: Since the cable has constant density and cross-sectional area, its weight is directly proportional to its length. Therefore, the force decreases linearly as you move from J to K.

🧠 Exam Technique

  • Boundary Value Check: Test the extremes! At d = J (top), the force is maximum because it supports Weight of Load + Weight of Cable . At d = K (bottom), the force is minimum because it only supports the Weight of Load (which is > 0 ).
  • Eliminate graphs where stress drops to zero at K (like Graph A) because the load at the bottom still exerts a downward force.

❌ Common Student Errors

  • Choosing A: Assuming stress drops to zero at the bottom (K) because students forget the hanging load or assume no force acts at the free end.
  • Choosing B: Incorrectly thinking stress increases downwards, confusing tension with depth-based pressure in fluids ( p = ρgh ).
  • Choosing C: Assuming uniform stress throughout the cable, ignoring the cable's own substantial weight.
Mark Allocation: This is a 1-mark multiple-choice question. Full mark is awarded solely for selecting option D.

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.