Stress, strain and the Young modulus Cambridge International AS & A Level Physics revision
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In plain words
How much a wire stretches depends on how long and thick it is, as well as what it is made of. To compare materials fairly we use stress (force per area) and strain (stretch per length). Their ratio, the Young modulus, belongs to the material itself: steel has one value whatever shape it is in.
Three things to know
- Stress σ = force ÷ cross-sectional area, in Pa. Strain ε = extension ÷ original length, which has no units.
- Young modulus E = stress ÷ strain, in Pa. It is the gradient of the straight part of a stress–strain graph.
- To measure it: load a long, thin wire. Measure its diameter with a micrometer (to get the area), its original length with a metre rule, and its extension for each load. Plot stress against strain and find the gradient.
Worked example
A wire 2.0 m long with a cross-sectional area of 1.0 × 10⁻⁶ m² extends by 1.0 mm under a load of 100 N. Find the Young modulus of its material.
- Stress = 100 ÷ 1.0 × 10⁻⁶ = 1.0 × 10⁸ Pa.
- Strain = 1.0 × 10⁻³ ÷ 2.0 = 5.0 × 10⁻⁴.
- E = 1.0 × 10⁸ ÷ 5.0 × 10⁻⁴ = 2.0 × 10¹¹ Pa.
Tips and tricks
- Area comes from the diameter: A = πd² ÷ 4. Measure the diameter in several places and take a mean.
- Extension and original length must be in the same units before you divide.
It lands in your notebook with its questions as flashcards.
Stress, strain and the Young modulus: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is stress?
It is measured in pascals.
What are the units of strain?
It is a length divided by a length.
What is the gradient of the straight part of a stress–strain graph?
E = stress ÷ strain.
A wire of cross-sectional area 2.0 × 10⁻⁶ m² carries a load of 100 N. What is the stress in it?
100 ÷ 2.0 × 10⁻⁶.
Two wires of the same material and length carry the same load. Wire X has twice the diameter of wire Y. How do their extensions compare?Stretch
X has four times the area, so a quarter of the stress and a quarter of the strain.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Stress, strain and the Young modulus
Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org
Name ______________________________ Date ______________
State the units of stress, strain and the Young modulus.[2]
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Stress: Pa (N m⁻²). Strain: no units. Young modulus: Pa.
A steel wire 3.0 m long with a cross-sectional area of 5.0 × 10⁻⁷ m² supports a load of 50 N. The Young modulus of steel is 2.0 × 10¹¹ Pa. Find the extension.[3]
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1.5 mm. Stress = 1.0 × 10⁸ Pa, so strain = 5.0 × 10⁻⁴, and 5.0 × 10⁻⁴ × 3.0 m = 1.5 × 10⁻³ m.
Explain why a long, thin wire is used when measuring the Young modulus.[2]
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It gives a larger extension for a given load, so the percentage uncertainty in the extension is smaller.
Answers: Stress, strain and the Young modulus
- 1. Stress: Pa (N m⁻²). Strain: no units. Young modulus: Pa.
- 2. 1.5 mm. Stress = 1.0 × 10⁸ Pa, so strain = 5.0 × 10⁻⁴, and 5.0 × 10⁻⁴ × 3.0 m = 1.5 × 10⁻³ m.
- 3. It gives a larger extension for a given load, so the percentage uncertainty in the extension is smaller.