Mechanics and Properties of Matter
Mechanics and Properties of Matter tests whether you can move between describing motion, explaining it with forces, and then applying the same ideas to solids and fluids. Expect calculations on projectiles, Newton's laws, momentum, moments and equilibrium, plus density, pressure, Hooke's law and the Young modulus.
Motion and force
Use v = u + at, s = ut + ½at² and v² = u² + 2as only when acceleration is constant. Resolve vectors into perpendicular components; on an incline the component of weight along the slope is mg sin θ. Newton's second law is ΣF = ma, and all the forces must act on the same body. Momentum is conserved in collisions and explosions when no external resultant force acts. For equilibrium, both ΣF = 0 and Σ moments about any point = 0; choose the point that eliminates an unknown.
Materials
Density ρ = m/V. Pressure in a fluid p = hρg. Hooke's law F = kx applies up to the limit of proportionality. Stress = F/A, strain = extension/original length (no units), Young modulus E = stress/strain.
Worked example
A steel wire 2.00 m long and 0.50 mm in diameter extends 1.20 mm under a 2.5 kg load. Find E. Radius r = 0.25 mm = 2.5 × 10⁻⁴ m, so A = πr² = 1.96 × 10⁻⁷ m². Force = mg = 2.5 × 9.81 = 24.5 N. Stress = 24.5 / 1.96 × 10⁻⁷ = 1.25 × 10⁸ Pa. Strain = 1.20 × 10⁻³ / 2.00 = 6.0 × 10⁻⁴. E = 1.25 × 10⁸ / 6.0 × 10⁻⁴ = 2.1 × 10¹¹ Pa.
Traps
Using diameter instead of radius in A = πr²; leaving millimetres unconverted; quoting strain with units; using mass instead of weight; measuring extension from the total length rather than the original length.