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AS · Practice questions · Stress, strain and the Young modulus

Strip away the shape.

Six original Cambridge-style questions on spring constants, stress and strain, and the Young modulus.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Spring, then material.

01
Analysis
[2 marks]

State Hooke law and the condition under which it holds.

  • The extension is proportional to the applied load (F = kx) ✓
  • This holds up to the limit of proportionality ✓
02
Analysis
[2 marks]

A spring extends by 25 mm under a load of 5.0 N. Find its spring constant.

  • k = F / x = 5.0 / (25 × 10⁻³) ✓
  • k = 200 N m⁻¹ ✓
03
Analysis
[3 marks]

A wire of diameter 0.50 mm carries a tension of 30 N. Find the tensile stress.

  • Area A = πd²/4 = π × (0.50 × 10⁻³)² / 4 = 1.96 × 10⁻⁷ m² ✓
  • σ = F / A = 30 / (1.96 × 10⁻⁷) ✓
  • σ = 1.5 × 10⁸ Pa ✓
04
Analysis
[2 marks]

A wire of original length 1.6 m stretches by 0.80 mm under load. Find the strain.

  • ε = x / L = (0.80 × 10⁻³) / 1.6 ✓
  • ε = 5.0 × 10⁻⁴ ✓
05
Analysis
[3 marks]

For the wire in questions 3 and 4, the stress is 1.5 × 10⁸ Pa at a strain of 5.0 × 10⁻⁴. Find the Young modulus of the material.

  • E = σ / ε = (1.5 × 10⁸) / (5.0 × 10⁻⁴) ✓
  • E = 3.0 × 10¹¹ Pa ✓
06
Analysis
[2 marks]

Distinguish between the limit of proportionality and the elastic limit.

  • The limit of proportionality is where the load-extension graph stops being a straight line (Hooke law fails) ✓
  • The elastic limit is the point beyond which the material no longer returns to its original length (permanent deformation begins) ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.