Statics (Forces in Equilibrium) — Quick Summary

Mr Toogood's Physics · Mechanics

AQA 3.4.1.1
ΣF = 0
Equilibrium condition
ΣFx = 0
Horizontal balance
ΣFy = 0
Vertical balance
Closed triangle
Graphical check

Free-body diagrams

Free-body diagram showing the forces acting on an airplane

Schematic, not lifelike — arrows show force magnitude (length) and direction.

Free-body diagrams are schematic: the object is drawn as a box or dot, with force arrows from its edge (or point of action), drawn to scale, pointing the correct way, and labelled with what's producing each force. A well-drawn one lets you resolve forces, check equilibrium, find unknown forces, or spot missing ones.

The equilibrium condition

ΣF = 0

An object at rest, or moving at constant velocity, has forces summing to zero — no resultant, no acceleration. If forces don't cancel, there's a resultant force and the object accelerates.

Two forces can only be in equilibrium if equal, opposite, and acting along the same line (parallel/colinear). Three forces: the resultant of any two must be equal and opposite to the third.

Checking equilibrium: graphical method

Arranging three force vectors into a closed triangle to check for equilibrium

A closed head-to-tail triangle means equilibrium; meeting arrowheads don't count.

Arrange the force vectors head-to-tail without rotating them. If they form a closed triangle, the object is in equilibrium. If two arrowheads meet instead of head-to-tail, it isn't equilibrium — even if the shape closes. Parallel forces can never form a triangle at all.

Checking equilibrium: mathematical method

Resolve every force along two perpendicular directions (horizontal/vertical, or parallel/perpendicular to a slope), then check both sums are zero:

ΣFx = 0     ΣFy = 0

Worked example: suspended camera

A camera suspended by two cables A and B over pulleys, at different angles to the horizontal

Cable A: 430 N at 35° to horizontal. Cable B: 12° to horizontal.

The camera is stationary, so it's in equilibrium. Resolving horizontally, the two horizontal tension components must be equal and opposite:

TA cos35° = TB cos12°
TB = (TA cos35°)/cos12° = 360 N

Reasoning about changes (no recalculation)

If the camera moves further from cable A's pulley, θA decreases and θB increases. The weight hasn't changed, so the vertical components must still sum to support it. Since A is now shallower, each newton of tension in it contributes less vertical support — so B must take up more of the weight, meaning TA decreases.

Exam tip: "increase or decrease" questions like this often want qualitative reasoning about angles and components, not a full recalculation from scratch.

Exam essentials

Key equations

  • ΣF=0
  • ΣFx=0, ΣFy=0

Recognising equilibrium

  • 2 forces: equal, opposite, colinear.
  • 3 forces: closed head-to-tail triangle, or resolved components sum to zero both ways.

Common slips

  • A closed shape only proves equilibrium if arrows run head-to-tail all the way round — check for meeting arrowheads.
  • Choose sensible perpendicular axes — horizontal/vertical isn't always simplest (e.g. along/perpendicular to a slope).
  • For "does it increase/decrease" questions, reason qualitatively about angles first rather than jumping to a full recalculation.