Pull on a wire and it lengthens. How much depends on the force, the dimensions and the material. Hooke law handles the spring; stress, strain and the Young modulus strip away the shape to describe the material itself.
Below the limit of proportionality, extension is proportional to load: F = kx, with k the spring constant. To describe the material, use tensile stress σ = F / A and tensile strain ε = x / L. Their ratio is the Young modulus, E = stress / strain, a property of the material independent of the sample size.
Add load to the wire and trace the force-extension graph. While it is straight the wire obeys Hooke law; the gradient is the spring constant. Read off the stress, strain and Young modulus as you go.
The spring constant describes one sample; the Young modulus describes the material.
| Relation | Meaning | Unit |
|---|---|---|
| F = kx | Hooke law | spring constant k in N m⁻¹ |
| σ = F / A | tensile stress | pascal (Pa) |
| ε = x / L | tensile strain | no unit |
| E = σ / ε | Young modulus | pascal (Pa) |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
Hooke law states that, below the limit of proportionality, the extension of a spring is:
A spring extends by 0.040 m under a load of 8.0 N. Its spring constant is:
The tensile stress in a wire of cross-sectional area A carrying a tension F is:
Tensile strain is defined as the:
The standard experiment turns four measurements into one material constant.
Keep the limits straight: the limit of proportionality is where the graph stops being straight, while the elastic limit is where permanent deformation begins; they are close but not the same. Stress uses the cross-sectional area (A = πd²/4 for a round wire), not the diameter or length. Strain is a ratio and has no units, so an answer with units of metres is wrong.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
A wire of cross-sectional area 2.0 × 10⁻⁷ m² carries a tension of 40 N. The tensile stress is:
A wire of original length 2.5 m stretches by 1.0 mm. The strain is:
A material has a stress of 1.2 × 10⁸ Pa at a strain of 6.0 × 10⁻⁴. Its Young modulus is:
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