Question

Work done in stretching the spring from x= .10 m to x= .20 m?

The force, in Newtons, required to stretch a spring, is given by `F=(3000N/m)x`, where x is in meters. Find the work done in stretching the spring from x= .10 m to x= .20 m.

Answer 1

`90J`

Explanation:

work done = force * extension

here, the extension would be actually be the change in length of the spring's extension.

the final length in question is `0.2m` and the starting length in question is `0.1m`.

the increase in length is `0.1m`, so the added extension of the spring is `0.1m`.

when reading off the `y`-axis of the graph, which goes up by a scale of `100` each time, the force at `0.10m` is `300N`, and the force at `0.20m` is `600N`.

the work done from `0.10m` to `0.20m` is the change in energy from `0.10m` to `0,20m` extension.

energy at `0.10m = 0.10 * 300N = 30J`
energy at `0.20m = 0.20 * 600N = 120J`

change in energy `= 120J - 30J = 90J`

hence, the work done is `90J`.