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
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For questions involving calculations, ensure that you show all steps clearly. Use correct units throughout your working and provide a final answer with the appropriate unit. For conceptual questions, provide clear and concise explanations, supported by relevant formulas and diagrams where necessary.
What the command words demand
- Calculate
- Perform a numerical calculation to find a specific value.
- Determine
- Find or establish the value of something using given data and formulas.
- Explain
- Provide a clear and detailed account of how or why something happens.
- Describe
- Give a detailed account of the characteristics, appearance, or behavior of something.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 5-7 minutes for each question in this section to ensure you have enough time to show all steps and check your work.
- Calculate the tensile stress (σ): σ = F / A = 400 N / (2 × 10 -6 m 2 ) = 2 × 10 8 Pa.1 mark
- Calculate the tensile strain (ε): ε = ΔL / L 0 = 5 × 10 -3 m / 2 m = 2.5 × 10 -3 .1 mark
- Calculate the Young modulus (E): E = σ / ε = (2 × 10 8 Pa) / (2.5 × 10 -3 ) = 8 × 10 10 Pa.2 marks
Final answer: The Young modulus of the material is 8 × 10 10 Pa.
Work through every step correctly and you earn all 4 marks.
Another worked example
A wire with a diameter of 0.5 mm and an original length of 1 meter is subjected to a force of 20 N, causing it to extend by 2 mm. Calculate the Young modulus of the material.
- Calculate the cross-sectional area (A): A = π(d/2) 2 = π(0.5 × 10 -3 m / 2) 2 ≈ 1.96 × 10 -7 m 2 .1 mark
- Calculate the tensile stress (σ): σ = F / A = 20 N / (1.96 × 10 -7 m 2 ) ≈ 1.02 × 10 8 Pa.1 mark
- Calculate the tensile strain (ε): ε = ΔL / L 0 = 2 × 10 -3 m / 1 m = 2 × 10 -3 .1 mark
- Calculate the Young modulus (E): E = σ / ε = (1.02 × 10 8 Pa) / (2 × 10 -3 ) ≈ 5.1 × 10 10 Pa.1 mark
Final answer: The Young modulus of the material is approximately 5.1 × 10 10 Pa.
Work through every step correctly and you earn all 4 marks.
Common mistakes
Confusing tensile stress with tensile strain
Why it happens: Students often mix up the definitions of tensile stress and tensile strain, leading to incorrect calculations.
Fix: 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
Why it happens: Students sometimes use the diameter of the wire directly instead of converting it to the cross-sectional area using A = π(d/2) 2 .
Fix: 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
Why it happens: Students often forget to ensure that all measurements are in consistent units (e.g., meters for length and newtons for force) before performing calculations.
Fix: Check that all units are consistent throughout the calculation. Convert units as necessary to maintain consistency.
Misinterpreting the slope of the stress-strain graph
Why it happens: Students may incorrectly identify the slope of the entire graph as the Young modulus, rather than just the linear portion.
Fix: 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
Why it happens: Students sometimes use incorrect formulas, such as E = F / (A × ΔL) instead of E = (F × L 0 ) / (A × ΔL).
Fix: Review and memorize the correct formula for Young modulus: E = (F × L 0 ) / (A × ΔL).
Not accounting for the original length in strain calculations
Why it happens: Students may forget to use the original length (L 0 ) when calculating tensile strain, leading to incorrect results.
Fix: Always include the original length (L 0 ) in the strain calculation: ε = ΔL / L 0 .
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Young Modulus | Find the Young modulus of a wire from its dimensions, applied force, and extension. | 4 |
| Calculate Young Modulus | Find the Young modulus of a wire from its dimensions, applied force and extension. | 4 |
| Calculate Young Modulus | Find the Young modulus from force, area, original length, and extension data. | 4 |
| Calculate Young Modulus | Find a material's Young modulus from wire dimensions, applied force, and resulting extension. | 4 |
| Total across these question types | 16 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.