Work from a graph
A graph shows a push along a distance. That distance is the displacement. Where is the work on it?
Loading lab…
- Force goes up the side. Displacement goes along the bottom.
- A steady 8 N for 1.5 m. The shaded area is 8 × 1.5 = 12 J.
- A force that rises from 0 to 6 N over 2 m. The area is ½ × 2 × 6 = 6 J.
- A force that rises from 2 N to 6 N over 3 m. The area is 12 J.
Rule
Rule: Work is the area under the force–displacement graph. For a steady force, the area is force × displacement.
Work is in joules. One joule is one newton times one metre.
A steady force does not change in size. So it gives a flat line. The area under it is a rectangle. A force that grows evenly gives a slanted line. The area is a triangle or a trapezium. The force must point along the movement.
A trapezium has four sides, and two of them are parallel. The area of a triangle is ½ × base × height. The base is the displacement. The height is the force.
The area of a trapezium is (sum of parallel sides) ÷ 2 × width. In graph three, the parallel sides are 2 N and 6 N. The width is the displacement, 3 m.
| Force | Shape of the area | Work |
|---|---|---|
| Steady 8 N for 1.5 m | Rectangle | 8 × 1.5 = 12 J |
| 0 N rising to 6 N over 2 m | Triangle | ½ × 2 × 6 = 6 J |
| 2 N rising to 6 N over 3 m | Trapezium | (2 + 6) ÷ 2 × 3 = 12 J |