Free-body diagrams, equilibrium & resolving forces

The big idea: A book rests on a table and doesn't move. Why? Gravity pulls it down, the table pushes up just as hard — the two forces cancel.

That balance is called equilibrium. Here you'll draw the forces on an object and check they add up to zero.

Spot it: Draw only the forces on the object — not the forces it pushes back on.

Equilibrium = the forces balance, so the net force is zero. That can mean staying still or moving at steady speed.

A slanted force is hard to add up. The trick is to resolve it — split it into a horizontal part and a vertical part that, together, do the same job. Resolve just means 'break into perpendicular pieces'.

Which is cos, which is sin?: Measure the angle θ from the horizontal.

cos goes with the side next to the angle (the horizontal one); sin goes with the side across from it (the vertical one).

If the angle is given from the vertical instead, swap them.

How this is tested — forces in equilibrium are everywhere in Theme A. It comes up two ways:

The classic trap: The sag is how far a rope dips in the middle. A rope pulled nearly straight (a tiny sag) still has to balance the weight with only a tiny vertical part — so the tension becomes huge.

The exam's favourite scene for this: a bird lands on a washing line and the line barely dips. Watch what that does to the tension:

The equilibrium recipe: Equilibrium means the forces balance, so the net force is zero — and that must be true in each direction on its own.

So left pull = right pull and up pull = down pull.

Resolve every slanted force first, then balance each direction.

Back to that bird. In the exam you don't draw the posts and the line — you redraw the scene as a free-body diagram: the bird becomes a simple box, with one arrow for each force acting on it: