When a load (force) is applied to a spring or a rod, it stretches (or compresses) by an amount called the extension \$x\$. The relationship between the load \$F\$ and the extension is often plotted as a graph with \$F\$ on the vertical axis and \$x\$ on the horizontal axis.
For many materials, the initial part of this graph is a straight line, described by Hooke’s Law:
\$F = kx\$
where \$k\$ is the spring constant.
The limit of proportionality is the point on the load‑extension graph at which the straight‑line (Hooke’s Law) behaviour ends. Beyond this point, the material no longer follows the simple linear relationship.
Exam tip: The LoP is always the first point where the graph deviates from a straight line. It is not the same as the elastic limit (which is the maximum load before permanent deformation). For the IGCSE, you only need to identify the LoP.
Think of it like stretching a rubber band: as you pull, it stretches linearly until it starts to feel “stiff” and the stretch no longer increases proportionally with the pull.
Imagine a playground swing. While you push gently, the swing’s motion is predictable and proportional to your push. If you push too hard, the swing’s motion becomes erratic and no longer follows the simple push‑to‑movement rule. The point where the swing’s behaviour changes is like the LoP.
Question: A spring has a load‑extension graph that is linear up to 10 N, after which it bends. Identify the limit of proportionality and explain how you would find it on the graph.
Answer: The limit of proportionality is at 10 N, the point where the graph stops being a straight line. On the graph, you locate the first point where the curve deviates from the initial straight line.
| Feature | Description |
|---|---|
| Hooke’s Law | \$F = kx\$ – linear relationship. |
| Limit of Proportionality | First deviation from the straight line. |
| Elastic Limit | Maximum load before permanent deformation (not required for IGCSE). |
Tip 1: Always look for the first point where the graph bends – that’s the LoP.
Tip 2: Remember that the LoP is purely about the shape of the graph, not about the material’s strength.
Tip 3: Practice by sketching a simple load‑extension graph and marking the LoP yourself.
The limit of proportionality is a key concept in understanding how materials behave under load. By recognising the first deviation from a straight line on a load‑extension graph, you can answer exam questions confidently.