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AS & A-Level Physics 06 — Materials and Deformation

AS & A-Level Physics 06 — Materials and Deformation

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 6 of 26: Materials and deformation. Concepts, worked applications and misconception checks.

Physics EN AS & A-Level
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Load, Extension, and the Limit of Proportionality

In the study of materials, the external force applied to an object is often called the 'load'. This load causes deformation. If the object is stretched, the increase in its length is called the 'extension', calculated as the new length minus the original length. If it is squashed, the decrease in length is the 'compression'. When we plot a graph of load against extension for many materials, we initially see a straight line passing through the origin. This indicates that the extension is directly proportional to the load. However, this relationship only holds up to a certain point, known as the 'limit of proportionality'. Beyond this limit, the graph starts to curve, and the extension is no longer proportional to the applied load.

Key points

  • Load (FF) is the force applied to an object, causing it to deform.
  • Extension (xx) is the change in length of an object under a tensile load: x=Lfinal−Loriginalx = L_{final} - L_{original}.
  • Compression is the change in length under a compressive load: x=Loriginal−Lfinalx = L_{original} - L_{final}.
  • The limit of proportionality is the point on a load-extension graph beyond which the load is no longer directly proportional to the extension.

Worked example

Question

An elastic strip has unloaded length 18.0 cm. During a test its clamped end is at the 8.0 cm mark of a ruler and its free end at 30.0 cm. A learner reports an extension of 12.0 cm. Identify the error and determine the extension.

Solution

1. A ruler coordinate is not a length unless the other end is at zero. The stretched length is 30.0−8.0=22.030.0-8.0=22.0 cm.
2. Extension compares stretched and unloaded lengths: 22.0−18.0=4.022.0-18.0=4.0 cm.
3. The learner subtracted 18.0 cm directly from the free-end coordinate and ignored the clamp coordinate.

The extension is 4.0 cm, or 0.040 m.

Common pitfalls

  • Using the final length instead of the change in length for extension. Always subtract the original length from the new length.
  • Confusing the limit of proportionality with the elastic limit. While often close, the limit of proportionality is where the graph ceases to be linear, whereas the elastic limit is where permanent deformation begins.

Prerequisites

  • Introduces the concepts of tensile and compressive deformation.
  • Requires the ability to interpret a simple linear graph and understand the concept of proportionality.
Further resources