Free-body force diagrams

A free-body diagram shows all the forces acting on one object. It is the first step in almost every forces question.

Drawing one

Draw the object on its own (often as a dot or box).
Draw each force acting on it as an arrow starting from the object, in the right direction.
Label each force (W, N or R, F, T, D, U).
Make arrow lengths roughly show the relative sizes.

Never include forces the object exerts on other things.

Common forces

Weight (W = mg), normal contact force (reaction, perpendicular to a surface), friction (along a surface, opposing sliding), tension (along a string), drag or air resistance (opposing motion through a fluid), upthrust (upwards in a fluid) and thrust.

Centre of gravity

The centre of gravity of an extended body is the point at which its whole weight can be considered to act. For a uniform, symmetrical object it is at the geometric centre. On a free-body diagram, draw weight from the centre of gravity.

Objects on slopes

For a block on a slope at angle θ, resolve its weight: mg sin θ down the slope and mg cos θ into the slope. If the block is at rest, friction = mg sin θ and the normal force = mg cos θ.

Worked example

A 5.0 kg box rests on a ramp inclined at 20°. Find the friction force and the normal contact force.

Weight = 5.0 x 9.81 = 49.05 N
Friction balances the component down the slope: 49.05 sin 20° = 16.8 N
Normal force balances the component into the slope: 49.05 cos 20° = 46.1 N

Answer: Friction = 17 N; normal force = 46 N

Key idea: One object, every force acting on it, arrows from the object, weight from the centre of gravity.

Check yourself

A book rests on a table. Which forces belong on the book's free-body diagram?
- Its weight and the force of the book on the table
- Only its weight
- The normal contact force and the weight of the table
- Its weight and the normal contact force from the table
Show answer
Its weight and the normal contact force from the table. Only forces acting on the book are drawn: the Earth's pull (weight) and the table's push (normal force).
What is the centre of gravity of an object?
- The point where its mass is greatest
- The point at which its whole weight can be considered to act
- Always the lowest point of the object
- The point about which it is pivoted
Show answer
The point at which its whole weight can be considered to act. That is the definition used in the specification.
A 12 kg crate rests on a slope at 30° to the horizontal. Find the friction force on it in N, to 3 s.f.
Show answer
58.9 N. Friction = mg sin θ = 12 x 9.81 x 0.5 = 58.9 N.
For the same crate (12 kg on a 30° slope), find the normal contact force in N, to 3 s.f.
Show answer
102 N. N = mg cos θ = 12 x 9.81 x 0.866 = 102 N.
A skydiver falls at terminal velocity. How do the arrows on her free-body diagram compare?
- Air resistance is larger than weight
- Weight is larger than air resistance
- Air resistance and weight are equal and opposite
- Only weight is shown
Show answer
Air resistance and weight are equal and opposite. At terminal velocity the resultant force is zero, so the two forces balance.
Where is the centre of gravity of a uniform metre rule?
- At the 50 cm mark
- At the 0 cm mark
- At the 100 cm mark
- It depends on where it is pivoted
Show answer
At the 50 cm mark. For a uniform object the centre of gravity is at its geometric centre.

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Last updated 7 November 2026. Spotted a mistake? Tell us.