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Materials

The Young modulus and calculations with it

  • 1 thing to know
  • Papers 2 and 3

Overview

Recall questions on the definition and unit of the Young modulus, what a large value means, and how it differs from the stiffness of one sample.

What you need to know

Answer each one before you reveal it.

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What is the unit of the Young modulus, what does a large value mean, and how does it differ from stiffness?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is the Young modulus, and what equation is used to calculate it for a wire?

    Model answer

    The Young modulus is tensile stress divided by tensile strain in the region where the material obeys Hooke's law, given by E = Fl/(AΔl).

  2. 2

    What is the unit of the Young modulus?

    Model answer

    It has the same unit as stress, the pascal, and values for metals are usually quoted in GPa.

  3. 3

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

    Model answer

    The material is stiff, since a large stress produces only a small strain.

  4. 4

    What is the difference between the stiffness k of a sample and the Young modulus E of the material it is made from?

    Model answer

    Stiffness depends on the dimensions of the particular sample as well as the material, whereas the Young modulus is a property of the material alone.

  5. 5

    How are the stiffness of a wire and the Young modulus of its material related?

    Model answer

    They are linked by k = EA/l, where A is the cross-sectional area and l the original length of the wire.

  6. 6

    A cable of cross-sectional area 2.0 × 10⁻⁵ m² supports a load of 500 N. What is the tensile stress in it?

    Model answer

    Stress = F/A = 500/(2.0 × 10⁻⁵) = 2.5 × 10⁷ Pa.

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