Mechanics: Statics, Kinematics, Dynamics and Fluid Flow
Mechanics questions mix several topics, so first decide which principle applies. In statics, add vectors by components, take moments M = Fd, and apply equilibrium conditions ΣF = 0 and ΣM = 0. The centre of gravity is the point where the weight may be taken to act.
Kinematics uses v = u + at, s = ut + ½at² and v² = u² + 2as for constant acceleration. Distinguish speed from velocity and distance from displacement. Dynamics rests on Newton's laws: F = ma, weight W = mg, momentum p = mv, and impulse Ft = Δp. Work is W = Fs cosθ, power P = W/t, kinetic energy ½mv² and gravitational potential energy mgh. Circular motion needs a centripetal acceleration a = v²/r directed towards the centre.
In fluid dynamics, the continuity equation A₁v₁ = A₂v₂ expresses conservation of volume flow rate for an incompressible fluid. Bernoulli's equation, p + ½ρv² + ρgh = constant along a streamline, applies to steady, ideal flow. Viscosity and Reynolds number indicate whether flow is laminar or turbulent.
Traps: mass is not weight; constant velocity means zero net force, not zero force on each object; Newton's third-law pairs act on different bodies; Bernoulli's equation requires its assumptions; and continuity conserves volume flow rate, not speed.
Worked example: a 1000 kg car accelerates uniformly from rest to 20 m/s in 5 s. a = (20 − 0)/5 = 4 m/s²; F = ma = 4000 N; distance s = ½at² = 50 m; work = Fs = 200 kJ; average power = 200 kJ / 5 s = 40 kW.