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Materials

Force-extension graphs and work done

  • 4 things to know
  • Papers 1 and 3

Overview

Recall questions on plotting force-extension graphs, work done from the area under them, E = ½Fx, loading and unloading curves, rubber band behaviour and hysteresis, and a metal wire stretched beyond its elastic limit.

What you need to know

Answer each one before you reveal it.

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Numbers

State the formula for work done in stretching a material that obeys Hooke's law, explain why it is ½Fx rather than Fx, and state how work done is found from a force-extension graph.

Key term

What graph should be plotted after collecting force-extension data?

Key term

How can the work done in stretching a spring or wire be determined from a force-extension graph?

Key term

Describe the shape of a force-extension graph for a metal wire as it is stretched beyond its elastic limit.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What graph should be plotted after collecting force-extension data?

    Model answer

    A force-extension graph

  2. 2

    How can the work done in stretching a spring or wire be determined from a force-extension graph?

    Model answer

    The work done equals the area under the force-extension graph

  3. 3

    State the formula for work done when stretching a material that obeys Hooke's law.

    Model answer

    E = ½Fx, where E is work done (or energy stored), F is force, and x is extension

  4. 4

    Why is the formula for work done E = ½Fx rather than E = Fx for a spring obeying Hooke's law?

    Model answer

    Because the force increases linearly from zero to F as the spring extends, so the average force is ½F

  5. 5

    What does the area between the loading and unloading curves on a force-extension graph represent?

    Model answer

    Energy dissipated as heat

  6. 6

    Describe two characteristic features of the force-extension behaviour of rubber bands.

    Model answer

    Rubber bands show non-linear force-extension behaviour and exhibit hysteresis when loading and unloading

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