Force-displacement graph

A force-displacement graph measures:

Area under the graph

The area under a force-displacement graph gives the work done, in joules, J.

That’s because \text{work done} = \text{Force} \times \text{distance}, and the area under the graph is just the force multiplied by the distance (because the two axis multiply when finding the area).

Units of the area

To find the area under the graph, we multiply the force (in newtons, N) by the displacement (in metres, m).

That gives us newton-metres, Nm.

If we look at the SI units of newton-metres:

One joule is defined as kg\,\,m^2/s^2.

So the units are the same! That shows us that the area under the graph must be in joules, J, so represents the work done (or energy transferred).

flashcards

QuestionAnswer
What does a force-displacement graph measure?The force applied in newtons (N) on the y-axis, and displacement in metres (m) on the x-axis.
What does the area under a force-displacement graph represent?The work done, in joules (J).
Why does the area under a force-displacement graph give the work done?Because \text{work done} = \text{Force} \times \text{distance} and the area under the graph is force multiplied by displacement (since the two axes multiply when finding the area).
What are the units of the area under a force-displacement graph derived from multiplying the axes?Newton-metres (Nm).
How do you derive the units of a joule?N = kg\,\,m/s^2, so Nm = kg\,\,m/s^2 \times m = kg\,\,m^2/s^2. One joule is defined as kg\,\,m^2/s^2.
What do the identical units of newtons-metres and joules confirm about the area under a force-displacement graph?It confirms that the area represents the work done (or energy transferred), measured in joules (J).