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Mechanical Properties of Materials

Hooke's law and force-extension graphs

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

Overview

Recall questions on Hooke's law and F = kx, stiffness from a force–extension graph, the limit of proportionality, springs joined end to end and side by side, rubber band loading loops and the energy they represent, polythene strips, measuring a spring's force–extension characteristic, unloading, plotting extension, and safety precautions and pointers.

What you need to know

Answer each one before you reveal it.

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Key term

State Hooke's law.

Key term

Write Hooke's law as a relationship and define the constant in it.

Numbers

A spring extends by 50 mm when a force of 4.0 N is applied. Calculate its stiffness.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State Hooke's law.

    Model answer

    The extension of a specimen is directly proportional to the force applied, provided the limit of proportionality is not exceeded.

  2. 2

    Write Hooke's law as a relationship and define the constant in it.

    Model answer

    F = kx, where k is the stiffness or spring constant measured in N m⁻¹ and x is the extension in metres.

  3. 3

    What does the gradient of a force–extension graph give?

    Model answer

    It gives the stiffness k of that particular specimen.

  4. 4

    What is meant by the limit of proportionality?

    Model answer

    It is the point beyond which the force–extension graph is no longer a straight line.

  5. 5

    A spring extends by 50 mm when a force of 4.0 N is applied. Calculate its stiffness.

    Model answer

    k = 4.0/0.050 = 80 N m⁻¹.

  6. 6

    A spring of stiffness 25 N m⁻¹ is stretched by 80 mm. Calculate the force applied.

    Model answer

    F = 25 × 0.080 = 2.0 N.

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