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Mechanical Properties of Materials

Elastic strain energy

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on elastic strain energy, the area under a force–extension graph, E = ½kx² and why it is ½Fx rather than Fx, calculations for springs, bungee cords and catapults, doubling the extension, materials that do not obey Hooke's law, energy beyond the elastic limit, and why a stretched rubber band warms.

What you need to know

Answer each one before you reveal it.

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Key term

State the relationship for the energy stored in a specimen obeying Hooke's law.

Key term

Explain why the energy stored is ½Fx rather than Fx.

Numbers

A spring of stiffness 80 N m⁻¹ is stretched by 50 mm. Calculate the energy stored.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define elastic strain energy.

    Model answer

    Elastic strain energy is the energy stored in a material as it is elastically deformed, which is recovered when the load is removed.

  2. 2

    What does the area under a force–extension graph represent?

    Model answer

    It represents the work done in stretching the specimen, which is the energy stored if the deformation is elastic.

  3. 3

    State the relationship for the energy stored in a specimen obeying Hooke's law.

    Model answer

    E = ½kx², where k is the stiffness and x the extension.

  4. 4

    Explain why the energy stored is ½Fx rather than Fx.

    Model answer

    The force grows steadily from zero to F as the specimen extends, so the mean force is F/2 and the work done is the mean force multiplied by the extension.

  5. 5

    A spring of stiffness 80 N m⁻¹ is stretched by 50 mm. Calculate the energy stored.

    Model answer

    E = ½ × 80 × 0.050² = 0.10 J.

  6. 6

    A force of 4.0 N stretches a spring obeying Hooke's law by 50 mm. Calculate the energy stored.

    Model answer

    E = ½Fx = ½ × 4.0 × 0.050 = 0.10 J.

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