Net Forces

Resultant force — the single force that would have the same effect as all the forces acting on a body combined. Because forces are vectors, they are added by vector addition, not arithmetic.

Newton's second law — a resultant force produces an acceleration in the direction of that force:

F = ma

Example: a 1500 kg car has a driving force of 3000 N and total resistive forces of 1200 N. The resultant is 3000 − 1200 = 1800 N forwards, so a = 1800 ÷ 1500 = 1.2 m s⁻². Only the resultant appears in F = ma — using the driving force alone is the standard mistake.

Free-body diagrams — draw the body as a dot or simple outline and mark every force acting on it, with arrows from the point of action, labelled with what each force is. Leave out forces the body exerts on other things: those act elsewhere and belong on a different diagram.

Adding perpendicular forces — use Pythagoras for the magnitude and trigonometry for the direction.

Forces on a slope — resolve the weight into components parallel and perpendicular to the surface, because that is the natural pair of directions for the problem. For a slope at angle θ to the horizontal:

component down the slope = mg sinθ

component perpendicular to the slope = mg cosθ

The normal contact force balances the perpendicular component, not the whole weight — which is why the normal force on a slope is always less than mg.

Example: as the slope steepens, sinθ grows and cosθ shrinks. The force pulling the object down the slope increases while the force pressing it into the surface decreases, so friction falls just as the driving force rises. That is why things slip suddenly rather than gradually.