Mechanical Properties of Matter

Stress (σ) The restoring force per unit cross-sectional area within a deformed material. Stress quantifies the internal forces that neighbouring particles exert on each other. For a wire under tension, stress = F/A, where F is the applied force and A is the original cross-sectional area. SI unit: pascal (Pa) or N m⁻². Example: A steel cable supporting a lift experiences tensile stress proportional to the load. Strain (ε) The fractional change in dimension of a material due to stress. Strain is dimensionless, defined as ΔL/L₀ for length changes (tensile or compressive strain). It describes deformation relative to original size. Example: Stretching a 2 m rubber band by 4 cm gives a strain of 0.02 (2%). Young’s Modulus (E or Y) The ratio of tensile stress to tensile strain within the elastic limit. Young’s modulus measures a material’s stiffness. A high E means the material deforms very little under load. For a wire: E = (F/A) / (ΔL/L₀) = FL₀ / (AΔL). Example: Steel (E ≈ 200 GPa) is much stiffer than rubber (E ≈ 0.01 GPa).