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A spring has a natural length of 20 cm. A 40 N force is required to stretch (and hold the spring) to a length of 30 cm. How much work is done in stretching the spring from 35 cm to 38 cm?

This example will require Hooke’s Law to determine the force. Hooke’s Law tells us that the force required to stretch a spring a distance of *x* meters from its natural length is,

where

is called the spring constant.The first thing that we need to do is determine the spring constant for this spring. We can do that using the initial information. A force of 40 N is required to stretch the spring 30cm-20cm = 10cm = 0.10m from its natural length. Using Hooke’s Law we have,

So, according to Hooke’s Law the force required to hold this spring *x* meters from its natural length is,

We want to know the work required to stretch the spring from 35cm to 38cm. First we need to convert these into distances from the natural length in meters. Doing that gives us *x*’s of 0.15m and 0.18m.

The work is then,

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