Applied Mechanics
Applied Mechanics tests whether you can replace a real machine or structure with a free body diagram and solve it: force composition and resolution, moments, equilibrium, friction and simple motion.
Core rules
- Resultant of two forces at right angles: R = √(P² + Q²), direction θ = tan⁻¹(P/Q) measured from Q.
- Parallelogram law: R = √(P² + Q² + 2PQ cos α), where α is the included angle.
- Resolution: Fx = F cos θ, Fy = F sin θ, with θ measured from the x-axis. Resolve forces before summing; never add magnitudes directly.
- Equilibrium of a coplanar concurrent system: ΣFx = 0 and ΣFy = 0. For a non-concurrent system also ΣM = 0 about any point.
- Lami's theorem applies only to three concurrent forces in equilibrium: P/sin α = Q/sin β = R/sin γ, with each angle opposite its force.
- Friction: limiting friction F = μN; angle of friction φ = tan⁻¹ μ. Friction always opposes impending motion.
- Uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
Worked example
Forces of 60 N and 80 N act at a point at right angles. R = √(60² + 80²) = √(3600 + 6400) = 100 N. Angle from the 80 N force: θ = tan⁻¹(60/80) = 36.9°. The equilibrant is 100 N acting at 180° to the resultant.
Traps that cost marks
Skipping the free body diagram; leaving out a reaction at a hinge or roller; using sin for the wrong angle; mixing kgf and N (1 kgf ≈ 9.81 N); applying Lami's theorem to four forces or to forces that are not concurrent.