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Forces

The spring constant, and work done in stretching

  • 2 things to know
  • Paper 11 (Physics)

Overview

What the spring constant measures and its unit, force = spring constant × extension with calculations and stiffness comparisons, work done in stretching as stored energy, work done = ½ × spring constant × extension², the area under a force-extension graph, and the effect of doubling the extension.

What you need to know

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Key term

What is meant by the spring constant of a spring?

Key term

State the unit of the spring constant.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is meant by the spring constant of a spring?

    Model answer

    The force needed to produce each metre of extension, which is a measure of how stiff the spring is.

  2. 2

    State the unit of the spring constant.

    Model answer

    Newtons per metre (N/m).

  3. 3

    Write, in words, the relationship between the force applied to a spring, its spring constant and its extension.

    Model answer

    Force = spring constant × extension.

  4. 4

    Why must the extension, rather than the total stretched length, be used when finding a spring constant?

    Model answer

    The spring constant relates the force only to the increase in length, so the unstretched length has to be subtracted first.

  5. 5

    A force of 12 N stretches a spring by 0.30 m. Calculate the spring constant.

    Model answer

    40 N/m, because 12 N ÷ 0.30 m = 40 N/m.

  6. 6

    A force of 2.0 N stretches a spring by 4.0 cm. Calculate the spring constant.

    Model answer

    50 N/m, because 4.0 cm is 0.040 m and 2.0 N ÷ 0.040 m = 50 N/m.

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