M10.1MechanicsCore

Force Diagrams

A force diagram shows every force acting on an object as an arrow. Drawing one correctly — weight, normal reaction, tension, friction — is the essential first step of almost every mechanics problem.

25 min Video by Zeeshan Zamurred Forces and Motion

Edexcel AS Level Maths: 10.1 Force DiagramsWatch the full walkthrough before the notes below.

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What you'll be able to do

Identify the common forces
Draw a clear force diagram
Know the direction of each force
Recognise equilibrium

The common forces

The forces you meet are: $weight$ ( $W = m g$ , always downward), the $normal reaction$ ( $R$ , perpendicular to the surface), $tension$ (along a string, pulling), $thrust$ (along a rod, pushing) and $friction$ (along the surface, opposing motion).

W = m g

Weight = mass × gravity, acting straight down.

Drawing the diagram

Represent the object as a dot (particle) and draw each force as an arrow $from$ the object in the correct direction. Label every arrow. Only include forces actually acting on the object.

Tip — Always include weight (mg) — it’s the most commonly forgotten force.

Equilibrium

If an object is in $equilibrium$ (at rest or moving at constant velocity), the forces balance: they sum to zero. Resolving in perpendicular directions then gives equal-and-opposite force pairs.

equilibrium \Rightarrow resultant force = 0

Balanced forces ⟶ no acceleration.

1Equilibrium vertically:

R = W = m g = 2 \times 9.8

Answer

R = 19.6

Formula recap

W = m g

Weight (downward).

R ⊥ surface

Normal reaction.

equilibrium \Rightarrow Σ F = 0

Balanced forces.

Common mistakes to avoid

Forgetting to include the weight on a force diagram.

Weight (mg) always acts — include it pointing straight down.

Drawing the normal reaction vertically on a slope.

The normal reaction is perpendicular to the SURFACE, not always vertical.

Key takeaways

Common forces: weight (mg, down), normal reaction (⟂ surface), tension, thrust, friction.
Draw each force as a labelled arrow from the particle.
Equilibrium means the forces sum to zero.

Test yourself

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