Define and use the term 'limit of proportionality' for a load-extension graph and identify this point on the graph (an understanding of the elastic limit is not required)

Cambridge IGCSE Physics 0625 – 1.5.1 Effects of Forces

Objective

Define and use the term limit of proportionality for a load–extension graph and identify this point on the graph.

Key Concept: Limit of Proportionality

The limit of proportionality is the point on a load–extension (or stress–strain) graph at which the material’s response is no longer strictly proportional to the applied load. Up to this point the graph is a straight line, indicating Hooke’s law holds: \$F = kx\$ where \$F\$ is the applied force, \$x\$ is the extension and \$k\$ is the spring constant. Beyond this point the graph deviates from the straight line, signalling the onset of non‑elastic behaviour.

How to Identify the Limit of Proportionality

1. Plot the load (\$F\$) on the vertical axis and the extension (\$x\$) on the horizontal axis.
2. Draw the best straight‑line fit through the initial data points.
3. Locate the point where the experimental data first diverges from this straight line.
4. Mark this point as the limit of proportionality.

Illustrative Example

Consider a metal wire stretched by increasing loads. The following table shows a typical set of measurements:

Plotting these points gives a straight line up to about \$30\ \text{N}\$, after which the data points lie below the line. The point at \$30\ \text{N}\$, \$0.70\ \text{mm}\$ is therefore the limit of proportionality.

Practical Tips

• Use a ruler or digital instrument to ensure accurate extension measurements.
• When drawing the straight line, include as many initial points as possible to minimise error.
• Remember that the limit of proportionality is distinct from the elastic limit; the latter is the maximum load the material can withstand and still return to its original shape.