Stretching Materials

• Hooke's Law: extension is directly proportional to applied force, up to the limit of proportionality (ΔF = kΔx).
• Stress is force per unit cross-sectional area (σ = F/A); strain is extension per unit original length (ε = Δx/x).
• The Young Modulus (E) is the ratio of stress to strain — a measure of a material's stiffness that doesn't depend on the sample's size or shape.
• Force-extension graphs reveal the limit of proportionality, elastic limit, and yield point — and their gradient (in the straight region) gives the spring constant.
• Stress-strain graphs show the same key points as force-extension graphs, plus breaking stress, and their gradient gives the Young Modulus.
• Core Practical 3 uses a stretched wire, a metre ruler and a pulley/clamp set-up to experimentally determine the Young Modulus of a metal.
• Elastic strain energy is the work done stretching a material — found as the area under a force-extension graph.

Imagine you're hanging weights from the bottom of a metal wire that's fixed at the top. As you add each weight, the wire stretches a little more. Hooke's Law simply describes the pattern in that stretching — for small enough forces, the extension is directly proportional to the force you apply.

"Directly proportional" means: double the force, and you double the extension. Triple it, and the extension triples too. If you plotted force against extension, you'd get a perfectly straight line passing through the origin — that straight-line relationship is the entire content of Hooke's Law.

Hooke's Law isn't just about stretching either — it applies equally to compression. The only difference is which direction the length changes: extension means the object got longer, compression means it got shorter.