A level Physics · Edexcel 9PH0 · Topic 4C

Hooke's law and the Young modulus

Key points

Hooke's law: extension is proportional to force up to the limit of proportionality: $\Delta F = k\Delta x$ , where $k$ is the stiffness (N m $^{-1}$ ).
Elastic deformation is reversed when the load is removed; plastic deformation is permanent.
Elastic strain energy stored = area under the force–extension graph; in the Hooke's law region $\Delta E_{el} = \frac{1}{2}F\Delta x$ .
Tensile stress $\sigma = \frac{F}{A}$ (Pa), tensile strain $\varepsilon = \frac{\Delta x}{x}$ (no units), Young modulus $E = \frac{\sigma}{\varepsilon}$ = gradient of the linear part of a stress–strain graph.
Stress–strain graphs show the elastic limit, yield point, ultimate tensile stress and breaking stress. Ductile materials stretch a lot plastically; brittle materials snap with little plastic change.
Core practical: load a long thin wire, measure extension against a reference marker, and find $E$ from the gradient; measure the diameter in several places with a micrometer.

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When forces stretch or squash a solid, it changes shape. This sub-topic covers stiffness, elastic and plastic behaviour, stress, strain, the Young modulus, elastic strain energy and core practical 5.

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