A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Young Modulus and Stress-Strain Graphs — mark scheme explained
The short answer
The Young modulus is a fundamental concept in mechanics and materials science that describes the stiffness of a material. It is defined as the ratio of tensile stress to tensile strain within the elastic limit of a material. Understanding this concept is crucial for various applications, from engineering design to material selection.
The question
A metal wire with a cross-sectional area of 2 × 10 -6 m 2 and an original length of 2 meters is subjected to a force of 400 N. The wire extends by 5 mm. Calculate the Young modulus of the material. [Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Calculate the tensile stress (σ): σ = F / A = 400 N / (2 × 10 -6 m 2 ) = 2 × 10 8 Pa.
- S2
Calculate the tensile strain (ε): ε = ΔL / L 0 = 5 × 10 -3 m / 2 m = 2.5 × 10 -3 .
- S3
Calculate the Young modulus (E): E = σ / ε = (2 × 10 8 Pa) / (2.5 × 10 -3 ) = 8 × 10 10 Pa.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Calculate the tensile stress (σ): σ = F / A = 400 N / (2 × 10 -6 m 2 ) = 2 × 10 8 Pa.
- S2
Calculate the tensile strain (ε): ε = ΔL / L 0 = 5 × 10 -3 m / 2 m = 2.5 × 10 -3 .
- S3
Calculate the Young modulus (E): E = σ / ε = (2 × 10 8 Pa) / (2.5 × 10 -3 ) = 8 × 10 10 Pa.
Final answer: The Young modulus of the material is 8 × 10 10 Pa.
Common mistakes
- Confusing tensile stress with tensile strain — Review the definitions: Tensile stress (σ) is force per unit area (F / A), and tensile strain (ε) is the fractional change in length (ΔL / L 0 ).
- Using incorrect units for cross-sectional area — Always convert the diameter to the cross-sectional area using the formula A = π(d/2) 2 before calculating stress or strain.
- Forgetting to convert units consistently — Check that all units are consistent throughout the calculation. Convert units as necessary to maintain consistency.
- Misinterpreting the slope of the stress-strain graph — Ensure that you only use the slope of the linear portion of the stress-strain graph to determine the Young modulus.
- Using the wrong formula for calculating the Young modulus — Review and memorize the correct formula for Young modulus: E = (F × L 0 ) / (A × ΔL).
- Not accounting for the original length in strain calculations — Always include the original length (L 0 ) in the strain calculation: ε = ΔL / L 0 .
Where the marks go
- Full worked solution (all marking points)4 marks