Properties of Matter
Core concepts
This domain covers elasticity (stress, strain, Young's modulus, bulk and shear moduli, Poisson's ratio), Hooke's law and elastic potential energy, surface tension and capillarity, viscosity, and the behaviour of materials under load. You should understand the stress–strain curve: proportional limit, elastic limit, yield point, ultimate strength, and fracture, plus the difference between ductile and brittle materials.
Traps
- Confusing stress (force per area) with strain (dimensionless ratio).
- Forgetting that Young's modulus applies only in the linear elastic region.
- Mixing up surface tension (force per unit length, N/m) with surface energy (J/m²) - they are numerically equal but conceptually distinct.
- Using the wrong radius in capillary rise (h = 2T cosθ / ρgr) - r is the tube radius, not the meniscus radius.
- Ignoring that a wire's extension depends on original length and cross-section, not just the load.
Rule of thumb
For a wire, extension ΔL = FL/(AE). Doubling the length doubles the extension; doubling the diameter reduces it fourfold.
Worked example
A steel wire of length 2 m, diameter 1 mm, carries a 50 N load. Y = 2×10¹¹ Pa. Area A = π(0.5×10⁻³)² ≈ 7.85×10⁻⁷ m². ΔL = FL/(AY) = 50×2/(7.85×10⁻⁷ × 2×10¹¹) ≈ 100/(1.57×10⁵) ≈ 6.4×10⁻⁴ m, about 0.64 mm.