Forces, equilibrium, moments and friction
Forces, equilibrium, moments and friction
This domain tests statics of particles and rigid bodies: resolving forces, equilibrium conditions, moments and couples, and limiting friction. It rewards clear diagrams and correct choice of pivot.
Core rules
- A particle in equilibrium has zero resultant force: sum of horizontal components = 0 and sum of vertical components = 0.
- A rigid body in equilibrium also has zero resultant moment about any point. Moment = force × perpendicular distance from pivot.
- A couple consists of two equal, opposite, parallel forces; its moment is one force times the perpendicular distance between them.
- Friction opposes impending motion and satisfies F ≤ μR; at limiting equilibrium F = μR. R is perpendicular to the surface.
- On a slope of angle θ, the weight components are mg sin θ down the slope and mg cos θ perpendicular to it.
- Toppling occurs when the line of action of the weight falls outside the base.
Worked example
A 5 kg block on a rough horizontal plane is just moved by a horizontal force P; μ = 0.4. Vertically, R = mg = 5 × 9.81 = 49.05 N. At limiting friction, F = μR = 0.4 × 49.05 = 19.62 N, so P = 19.62 N.
Common traps
Using F = μR when friction is not limiting; forgetting that R changes if an applied force has a vertical component; using the wrong perpendicular distance for a moment; omitting the weight of a ladder or beam; and reversing the friction direction.