The questions are on the Young modulus test. Take it under real conditions before reading the mark scheme.
Quick answer: Hooke's law says extension is proportional to force (F = kx) up to the limit of proportionality. This mark scheme gives the model answers and the marks for the 8 questions of the Physics 11-12 test on Young modulus, from stress and strain to area under a graph, with the equivalent answers to accept.
Model answers with a marking guide. Award method marks for correct use of formulas even if a later number is wrong, and check powers of ten when areas are converted from millimetres.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: A Level 3.4.2
Question 1 Stress and strain (3 marks)
- A = π(0.6 × 10⁻³)² = 0.000 m².
- σ = 90 ÷ 0.000 = 79577471.546 Pa.
- ε = σ/E = 79577471.546 ÷ 2.0 × 10¹¹ = 0.000398.
Marking: 1 mark for each part.
Question 2 Spring energy (3 marks)
- k = 25 ÷ 0.080 = 312.5 N/m.
- E = ½Fx = ½ × 25 × 0.080 = 1 J.
Marking: (a) 1; (b) 1 for formula, 1 for answer.
Question 3 Reading a stress–strain graph (3 marks)
- E = σ/ε = 280 × 10⁶ ÷ 1.4 × 10⁻³ = 200000000000.000 Pa (200 GPa).
- The ultimate tensile stress (the greatest stress the wire withstands, 450 MPa).
Marking: (a) 1 for substitution, 1 for answer; (b) 1.
Question 4 Aluminium wire (3 marks)
- A = π(0.5 × 10⁻³)² = 0.000 m². σ = 40 ÷ 0.000 = 50929581.789 Pa.
- ε = 50929581.789 ÷ 7.0 × 10¹⁰ = 0.000728.
- x = εL = 0.000728 × 3.00 = 2.18 mm.
Marking: 1 mark for each part.
Question 5 Elastic and plastic (2 marks)
The wire does not return to its original length, because beyond the elastic limit the atomic layers have slipped and the deformation is plastic. A permanent extension remains.
Marking: 1 for permanent extension; 1 for explanation of plastic deformation.
Question 6 Brittle fracture (2 marks)
The graph is a steep straight line that ends suddenly at fracture. Glass has no plastic region: it obeys Hooke’s law up to the point at which it breaks, so it is brittle, and it fractures with very little strain.
Marking: 1 for straight line with no plastic region; 1 for breaks suddenly.
Question 7 Extra energy (2 marks)
E = ½k(x₂² − x₁²) = ½ × 400 × (0.050² − 0.020²) = ½ × 400 × 0.0021 = 0.42 J.
Marking: 1 for the difference of energies; 1 for the answer.
Question 8 Area under a graph (2 marks)
The area represents the work done in stretching, which is the energy stored. Within the elastic limit all of it can be recovered, but beyond that, plastic deformation converts some of it to thermal energy, so it cannot be recovered.
Marking: 1 for work done or energy stored; 1 for explanation of loss beyond elastic limit.
