Mechanics and Materials
This domain tests how you model motion and forces, then connect force to deformation in materials. Expect suvat and graphical kinematics, Newton’s three laws, momentum conservation, work–energy and power, equilibrium and moments, plus stress, strain and the Young modulus.
Core rules and concepts
- Use v = u + at, s = ut + ½at², v² = u² + 2as only for constant acceleration. On a v–t graph, gradient is acceleration and area is displacement.
- Resolve forces along and perpendicular to motion; include friction and weight components on inclines. For equilibrium, resultant force and resultant moment are zero.
- Momentum is conserved in collisions and explosions when external impulse is negligible; kinetic energy is conserved only in elastic collisions.
- Stress σ = F/A, strain ε = ΔL/L0, Young modulus E = σ/ε. Hooke’s law applies only up to the limit of proportionality.
- The area under a force–extension graph is elastic strain energy.
Worked example
A 2.0 m steel wire of diameter 0.50 mm stretches 1.2 mm under a 40 N load. Find E. Radius = 0.25 × 10⁻³ m, so A = πr² = 1.96 × 10⁻⁷ m². Stress = 40 / 1.96 × 10⁻⁷ = 2.04 × 10⁸ Pa. Strain = 1.2 × 10⁻³ / 2.0 = 6.0 × 10⁻⁴. Then E = 2.04 × 10⁸ / 6.0 × 10⁻⁴ = 3.4 × 10¹¹ Pa. The reasoning depends on converting mm to m before dividing.
Traps
- Using diameter as radius in A = πr².
- Mixing stress, measured in Pa, with force, measured in N.
- Applying suvat when acceleration changes.
- Quoting E without units or with strain inverted.
- Assuming a material behaves elastically after the yield point.