Linear & Non-Linear Extension
- Hooke’s law is the linear relationship between force and extension
- This is represented by a straight line on a force-extension graph
- Materials that do not obey Hooke's law, i.e they do not return to their original shape once the force has been removed, have a non-linear relationship between force and extension
- This is represented by a curve on a force-extension graph
- Any material beyond its limit of proportionality will have a non-linear relationship between force and extension
Linear and non-linear regions of a force-extension graph
In my experience, students can find the Hooke's law graph a bit tricky, because it changes shape and it has specific points that you need to be able to name and explain. I like to break it down for my students and tell the story of the graph.
At the origin (0, 0) the spring is unstretched. As the straight line slopes upwards on the graph, the spring is stretching under the influence of two opposing forces. If you remove the forces from the spring at any point on that straight line part of the graph, the spring will go back to its original length. At this part of the graph, force and extension are directly proportional. If you double one, the other also doubles. However, once you stretch the spring so far that its extension falls in the curved region of the graph, it will no longer go back to its original length. The point at which this happens is the limit of proportionality, that's the point where the graph starts to curve. Beyond this point, the relationship is no longer directly proportional.
You do need to understand this graph, because Hooke's law questions are very common in exams.