# Solids under stress: Unit 1.5(a)

> define stress, strain and the Young modulus and relate them for an elastic material

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Specification statement (Unit 1.5(a)): define stress, strain and the Young modulus and relate them for an elastic material

## Explanation

1. **Stress** σ = force ÷ cross-sectional area = F/A (unit Pa). **Strain** ε = extension ÷ original length = x/L (no unit).
2. The **Young modulus** E = stress ÷ strain = FL/(Ax) (unit Pa). It is a property of the material, not of one sample: a thicker or longer wire of the same steel has the same E.
3. E applies in the region where stress is proportional to strain. A large E means a stiff material.

## Worked example

A steel wire 2.0 m long and 0.50 mm in diameter extends by 2.5 mm under a 50 N load. Find the stress, strain and Young modulus.

1. A = π(0.25 × 10⁻³)² = 1.96 × 10⁻⁷ m².
2. Stress = 50 / 1.96 × 10⁻⁷ = 2.55 × 10⁸ Pa.
3. Strain = 2.5 × 10⁻³ / 2.0 = 1.25 × 10⁻³.
4. E = 2.55 × 10⁸ / 1.25 × 10⁻³ = 2.0 × 10¹¹ Pa.

Answer: E ≈ 2.0 × 10¹¹ Pa.

## Check

A second wire of the same steel has twice the length. Under the same load, what happens?

- Same extension and same Young modulus
- Twice the extension, same Young modulus
- Twice the extension and twice the Young modulus
- Half the extension, same Young modulus

The answer and its explanation are shown in the app once you choose an option.

## Apply it

Explain why the diameter of the wire must be measured at several points and in different directions when determining the Young modulus.

The model answer is shown in the app after you have tried it.

## Related

- [Solids under stress lesson](https://revise-gray.vercel.app/lesson?subject=wjec-alevel-physics&topic=wjec-alevel-physics.materials)
- [Solids under stress in the library](https://revise-gray.vercel.app/library?topic=wjec-alevel-physics.materials)