The load-extension graph of an elastic material is illustrated below. Use the graph to determine the work done in stretching the material

Answer Details

Method. The work done in stretching an elastic material is stored as elastic potential energy and is equal to the area under the load-extension graph (load on the vertical axis, extension on the horizontal axis).

\[ \text{Work done} = \text{area under the load-extension graph} \]

For the linear (Hooke's-law) region, the graph is a straight line from the origin, so the area is a triangle:

\[ W = \tfrac{1}{2}\times \text{load}\times \text{extension} = \tfrac{1}{2}Fe \]

If the material stretches beyond the elastic limit, the line curves; then the work done is found by counting squares under the curve (or by adding the triangular and rectangular/trapezoidal areas).

Worked illustration. If, for example, the graph shows a load of \(F = 20\ \text{N}\) producing an extension of \(e = 0.10\ \text{m}\) at the end of the straight line, then

\[ W = \tfrac{1}{2}\times 20 \times 0.10 = 1.0\ \text{J} \]

Read the actual final load and extension (and any change of gradient) from the printed graph and substitute into the area calculation to obtain the work done.