Mechanics: Statics and Dynamics
This domain applies Newton's laws to particles and simple connected systems, together with the equilibrium of coplanar forces, friction, moments and projectile motion. Marks are lost far more often to a wrong diagram or a mixed sign convention than to the algebra itself, so draw and label before writing equations.
Core rules
- Constant acceleration: v = u + at, s = ut + (1/2)at^2, v^2 = u^2 + 2as, s = (1/2)(u + v)t.
- Newton's second law along the direction of motion: F(net) = ma; resolve into two perpendicular directions for a body on an incline.
- Equilibrium: the vector sum of forces is zero and the sum of moments about any point is zero. A couple has moment Fd independent of the pivot chosen.
- Limiting friction: F = μR, acting opposite to the tendency of motion; below limiting, F ≤ μR.
- Projectile: the horizontal component u cos α is constant while the vertical motion has acceleration -g. Time of flight is 2u sin α/g, range u^2 sin 2α/g, greatest height u^2 sin^2 α/(2g).
- Work–energy: work done by the net force equals the change in (1/2)mv^2; momentum is conserved when no external impulsive force acts.
Worked example
A particle is projected from level ground with speed 20 m s^-1 at 30° to the horizontal, with g = 10 m s^-2. The vertical component is 20 sin 30° = 10 m s^-1, so the time of flight is 2(10)/10 = 2 s. The horizontal component is 20 cos 30° = 10√3 m s^-1, so the range is 10√3 × 2 = 20√3, about 34.6 m.
Traps
- Mixing sign conventions inside one equation; fix a positive direction and keep it throughout.
- Drawing friction in the direction of motion rather than opposing the tendency of motion.
- Using g = 9.8 when the paper specifies 10, or the reverse.
- Resolving the weight along an incline as mg cos α instead of mg sin α.