Force-Displacement Graphs

A force-displacement graph will have force (in N) on the vertical axis and displacement (in m) on the horizontal axis. The area of the graph is = Fs. This quantity represents the work done on the object.

From a force-displacement graph we can:

  • Read forces directly from the graph.
  • Read displacements directly from the graph.
  • Use the area under the graph to find the work done by the force. This is equal to the kinetic or potential energy the object gains due to the application of the force.

Example 1:

The graph below shows the force applied to an object as it was moved a distance of 10m. Answer the following:

a) When was a constant force applied to the object?

b) What force was applied at a displacement of 6m?

c) How much work was done on the object?

a) Reading directly from the graph, a constant force of 10N was applied between a displacement of 0-5m.

b) At a displacement of 6m, a force of 5N was applied to the object

c) To calculate the work done on the object, we must calculate the area under the graph. This is done by dividing the graph into a series of rectangles and triangles and calculating the sum of these areas;

  • Area 1 =10\times 5=50
  • Area 2 =\cfrac { 1 }{ 2 } \times 2\times 10=10

Total area =50+10=60

Therefore W=60\quad J