Mechanics and Properties of Matter
Mechanics and properties of matter tests motion, forces, energy and the behaviour of materials under load. Numerical problems dominate, often combining Newton's laws with stress and strain.
Motion and force
Use v = u + at, s = ut + ½at² and v² = u² + 2as for constant acceleration. Newton's second law is ΣF = ma, with weight W = mg. Momentum p = mv is conserved in collisions and explosions; impulse FΔt = Δp.
Circular and rotational motion
Centripetal force F = mv²/r acts towards the centre. The moment of a force is Fd; for equilibrium, the resultant force and the resultant moment are both zero.
Work, energy and power
Work = Fs cosθ; kinetic energy = ½mv²; gravitational potential energy = mgh; power = work/time = Fv. Energy is conserved but may be dissipated as heat.
Materials
Stress = F/A, strain = e/L, and Young modulus E = stress/strain. A force–extension graph is linear only up to the limit of proportionality; the elastic limit is where permanent deformation begins. Density ρ = m/V, pressure p = F/A, and viscosity and surface tension explain flow and capillary effects.
Worked example
A steel wire of length 2.00 m and diameter 0.50 mm extends by 1.0 mm under a load of 20 N. A = π(d/2)² = π(0.25 × 10⁻³)² = 1.96 × 10⁻⁷ m². Stress = 20/1.96 × 10⁻⁷ = 1.02 × 10⁸ Pa. Strain = 1.0 × 10⁻³/2.00 = 5.0 × 10⁻⁴. E = 1.02 × 10⁸/5.0 × 10⁻⁴ = 2.0 × 10¹¹ Pa.
Traps
Using diameter instead of radius, forgetting to convert mm to m, and treating stress as force.