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Work Done in Springs and Elastic Materials:
When elastic materials are compressed or stretched, work is done. If the applied force is F and the extension produced is e, then,
The work done = average Force × extension
⇒ \( \scriptsize Average\:force = \normalsize \frac{initial\: force \: + \: final \: force}{2} \)
= \(\left( \frac {0 \:+\: F}{2} \right) \scriptsize \times e \)
⇒ \(\scriptsize Average\: Work\: done = \normalsize \frac{1}{2}\scriptsize Fe \)
But from Hooke’s law,
F = k.e
∴ \(\scriptsize Work\: done = \normalsize \frac{1}{2}\scriptsize ke.e \\ = \frac{1}{2}\scriptsize ke^2 \)
- k = elastic constant
- e = extension or compression produced
- Work done is in JoulesJoule is the SI (International System of Units) unit of energy and work. It is equal to the amount of work done when a force of 1 newton displaces a mass... More
Example 6.4.1:
Calculate the work done when a force of 20 N stretches a spring by 50 mm.
Solution:
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