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Mechanics · Forces & Newton's laws

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Statics — equilibrium under several forces

A particle in equilibrium has zero resultant, so resolving in two perpendicular directions gives two equations — used to find unknown forces or angles, including on rough slopes where friction is at its limit (F = μR) on the point of moving.

Mechanics · Forces & Newton's laws

Statics — equilibrium under several forces

A particle in equilibrium has zero resultant, so resolving in two perpendicular directions gives two equations — used to find unknown forces or angles, including on rough slopes where friction is at its limit (F = μR) on the point of moving.

Why it works

A particle in equilibrium is the resolving idea pushed to its most useful form: the resultant force is zero, so the forces balance in every direction. Resolve in two perpendicular directions and each total is zero — two equations, enough for two unknowns.

The skill in "applications" problems is choosing the directions and handling friction correctly:
  • On a slope, resolve along and perpendicular to the slope.
  • The normal reaction comes from the perpendicular balance (often R=mgcos⁡αR = mg\cos\alpha,
adjusted by any other perpendicular force).
  • Friction takes whatever value is needed to keep equilibrium, up to μR\mu R. Only
when the particle is on the point of slipping is F=μRF = \mu R, acting against the direction it is about to move.

A particle "on the point of slipping" is the bridge between statics and motion: it is still in equilibrium, but friction is maxed out, so you get the extra equation F=μRF = \mu R to pin down an unknown (μ\mu, a force, or an angle).