Young Modulus

The Young modulus E of a material is its tensile stress divided by its tensile strain, E = σ/ε. It measures the stiffness of the material itself.Since stress = F/A and strain = ΔL/L, the Young modulus can be written E = FL/(AΔL), where F is the tension, L the original length, A the cross-sectional area and ΔL the extension. Its unit is the pascal (Pa), the same as stress, because strain has no units.The Young modulus is a property of the material, not of a particular sample. A thicker or longer wire of the same material has a different spring constant but the same Young modulus. It only applies in the region where stress is proportional to strain.On a stress-strain graph, the Young modulus is the gradient of the straight-line section. A stiff material such as steel has a large Young modulus, about 2 × 10¹¹ Pa, while rubber has a very small one.To measure it, a long thin wire is loaded with increasing masses. The diameter is measured with a micrometer at several points to find A, the original length with a metre rule, and the extension with a vernier scale or a marker against a fixed ruler.