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.
| Force | What it is | Which way it points |
|---|---|---|
| Weight (Fg) | the pull of gravity | always straight down |
| Normal (N) | a surface pushing back | perpendicular to the surface |
| Tension (T) | a pull along a rope or string | along the rope, away from the object |
| Friction / drag | a surface or fluid resisting motion | opposes the motion |
Free-body diagram of a box on a rough surface: one arrow per force acting ON the box — weight down, the table's normal push up, the applied pull along, and friction opposing it.
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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.
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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'.
Splitting a slanted force into a sideways part F cos θ and an up/down part F sin θ.
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- size (magnitude) of the force (N)
- angle the force makes with the horizontal (°)
- horizontal component of the force (N)
- vertical component of the force (N)
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.
A child pulls a sledge with a 50 N force on a rope at 37° above the horizontal. Find the horizontal and vertical components of the pull. (cos 37° = 0.80, sin 37° = 0.60)
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How this is tested — forces in equilibrium are everywhere in Theme A. It comes up two ways:
Paper 1A
- Draw or pick the free-body diagram.
- The right arrows, the right directions — a floating cork, a hanging sign.
Paper 2
- An object in equilibrium held by ropes.
- Resolve the tensions, set each direction to zero.
The classic trap: A rope pulled nearly straight still has to balance the weight with only a tiny vertical part — so the tension becomes huge. A small sag means a very big pull.
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.
This is the free-body diagram the exam wants: the bird as a dot, the two rope tensions pulling up-and-out at a shallow angle, and its weight down. The ropes are drawn long because T turns out much bigger than the 6.0 N weight (the sag angle is exaggerated here so the arrows are readable).
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A small bird of weight 6.0 N lands at the exact middle of a washing line. The line sags so each half makes 5.0° with the horizontal. Find the tension T in the line. (sin 5.0° = 0.087)
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