The big idea: A force is a push or a pull, measured in newtons (N). It has a size and a direction — so it's a vector.
A free-body diagram is a simple sketch of one object as a dot, with an arrow for every force acting on it.
When the arrows cancel out — the total force is zero — the object is in equilibrium: it stays still or keeps moving at a steady velocity.
| 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 |
[Diagram: phys-free-body] - Available in full study mode
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'.
[Diagram: phys-vector-components] - Available in full study mode
- 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.
Worked example — resolve a pull on a sledge
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)
Solution
- Horizontal — start with the given formula:
- Put in the numbers (A = 50, θ = 37°):
- So the horizontal part is:
- Vertical — start with the given formula:
- Put in the numbers and solve — keep the unit:
Final answer
horizontal = 40 N (drags it forward), vertical = 30 N (lifts it up).
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How this is tested: Forces in equilibrium are everywhere in Theme A.
- Paper 1A: draw or pick the free-body diagram — the right arrows, the right directions (e.g. the forces on a floating cork or a hanging sign). - Paper 2: an object in equilibrium held by ropes — resolve the tensions and set each direction to zero.
Classic trap: a rope pulled nearly straight still has to balance the weight with 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.
IB-style question — tension in a sagging washing line
A small bird of weight 6.0 N lands at the exact middle of a washing line. The line sags so each half makes an angle of 5.0° with the horizontal. By balancing the vertical forces, find the tension T in the line. (sin 5.0° = 0.087)
Solution
- Both halves of the line pull up on the bird at 5.0°. Their vertical parts must balance the weight. Resolve each tension vertically with the given formula:
- Two halves share the load, so vertical balance gives:
- Rearrange for T:
- Work it out — keep the unit:
Final answer
T ≈ 34 N — far bigger than the 6.0 N weight, because a nearly-horizontal rope has only a tiny vertical part to do the lifting.