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Application of Hooke’s law

Assuming a spring obey’s Hooke’s law, and assuming a ten-pound force stretches a spring \frac{1}{12} feet, calculate how much work is done to stretch the spring 1 foot.

First, we have stretching the spring \frac{1}{12} feet requires 10 pounds of force, so by Hooke’s law,

    \[ f \left( \frac{1}{12} \right) = \frac{c}{12} = 10 \quad \implies \quad c = 120. \]

Then, we compute the work done stretching the spring 1 foot,

    \[ W = \int_0^1 120x \, dx = \left. \frac{x^2}{60} \right|_0^1 = 60 \text{ foot-pounds}. \]

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