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Deformation of Solids

Strain energy and force–extension graphs

  • 3 things to know
  • Unit A2 1

Overview

Recall questions on what strain energy is, the two forms of the equation and why there is a factor of ½, the area under a force–extension graph, the effect of doubling the extension, finding the energy under a curved graph, what the area of a loading and unloading loop represents, and a catapult calculation.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

State the equation for strain energy in both of its forms and define every symbol.

Key term

What is meant by strain energy?

Key term

Why does the equation for strain energy carry a factor of ½?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is meant by strain energy?

    Model answer

    Strain energy is the elastic potential energy stored in a material because work has been done in stretching or compressing it.

  2. 2

    State the equation for strain energy in both of its forms and define every symbol.

    Model answer

    E = ½Fx = ½kx², where E is the strain energy in joules, F the final force in newtons, x the extension in metres and k the spring constant in N m⁻¹.

  3. 3

    Why does the equation for strain energy carry a factor of ½?

    Model answer

    The force grows steadily from zero to F as the material stretches, so the average force doing the work is F/2 rather than F.

  4. 4

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

    Model answer

    The area under the graph is the work done on the material, which is the strain energy stored in it, in joules.

  5. 5

    Calculate the strain energy stored in a spring of spring constant 200 N m⁻¹ extended by 4.0 cm.

    Model answer

    E = ½kx² = ½ × 200 × (0.040)² = 0.16 J.

  6. 6

    A force of 8.0 N produces an extension of 4.0 cm in a spring. Calculate the work done in stretching it.

    Model answer

    E = ½Fx = ½ × 8.0 × 0.040 = 0.16 J.

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