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Material Science

Stress, strain and the Young modulus

  • 3 things to know
  • AS 5

Overview

Stress, strain and the Young modulus with worked calculations for wires, rods and bone, and measuring the Young modulus of a metal wire safely and accurately.

What you need to know

Answer each one before you reveal it.

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Numbers

A load of 40 N hangs from a wire of diameter 0.50 mm. Calculate the stress in the wire.

Key term

Describe an experiment to determine the Young modulus of a metal wire.

Key term

Define stress and give its unit.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define stress and give its unit.

    Model answer

    Stress is the force acting per unit cross-sectional area. The unit is the pascal, Pa, which equals one newton per square metre.

  2. 2

    Define strain and explain why it has no unit.

    Model answer

    Strain is the change in length divided by the original length. Both lengths are in the same unit, so the units cancel.

  3. 3

    Define the Young modulus and give its unit.

    Model answer

    The Young modulus is the ratio of stress to strain for a material deformed elastically. The unit is the pascal, Pa.

  4. 4

    What does a high Young modulus tell you about a material?

    Model answer

    A high Young modulus means the material is stiff. A large stress is needed to produce a small strain.

  5. 5

    A load of 40 N hangs from a wire of diameter 0.50 mm. Calculate the stress in the wire.

    Model answer

    The stress is 2.0 × 10⁸ Pa. The area is π × (0.25 × 10⁻³)² = 1.96 × 10⁻⁷ m². The stress is 40 ÷ 1.96 × 10⁻⁷ = 2.0 × 10⁸ Pa.

  6. 6

    A wire of original length 2.000 m extends by 1.2 mm under load. Calculate the strain.

    Model answer

    The strain is 6.0 × 10⁻⁴. The working is 1.2 × 10⁻³ m ÷ 2.000 m = 6.0 × 10⁻⁴.

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