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Free Body Diagrams (FBD)

Key idea: Draw accurate free-body diagrams, identify external forces, avoid Newton's third-law traps, and use the diagram in O Level and A Level calculations.

  • SEC G3 Physics 2027
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Learning objectives

  • Distinguish contact forces from non-contact forces
  • State that mass measures the amount of matter in a body
  • Describe a gravitational field as a region where a mass experiences gravitational force
  • Define gravitational field strength as gravitational force per unit mass
  • Apply weight = mass × gravitational field strength
  • Distinguish mass from weight
  • Describe the effect of balanced and unbalanced forces on a body
  • Describe ways a force may change motion
  • Identify action–reaction pairs on interacting bodies
  • Draw free-body diagrams for force systems in at most two dimensions
  • Solve three-force static equilibrium graphically
  • Apply resultant force = mass × acceleration
  • Relate mass to resistance to change in motion
  • Explain the effects of friction on motion
  • Describe falling with and without air resistance, including terminal velocity
  • Describe a moment as a force's turning effect in everyday examples
  • Apply moment = force × perpendicular distance from the pivot
  • State the principle of moments for a body in equilibrium
  • apply the principle of moments to new situations or to solve related problems
  • show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity
  • Explain qualitatively how centre-of-gravity position affects stability

1. Definition

A free body diagram (FBD) is a diagram of an object (or point mass) showing all the external forces acting on it.

What you need for this course

You should be able to identify the forces acting on an object and draw free-body diagrams in no more than two dimensions.

Prerequisite

If you’re unsure what each force means, revise: What Is A Force?

2. Key Ideas

  • Draw the object as a simple shape (box, dot, etc.).
  • Show forces as arrows starting on the object.
  • Label every force clearly (e.g. W, N, T, f).
  • Include directions and keep the diagram uncluttered.
  • Only include forces that act on the object (not forces the object exerts on something else).
Sign convention (for calculations)

If you need to calculate a resultant force or acceleration, choose a positive direction first (e.g. right/up).

Use signs consistently; the sign of your final answer tells you the direction.

Four common free-body diagramsA book on a table, a pulled block on rough ground, a block sliding down a rough slope, and a hanging mass. Each object has labelled external force arrows.1. Book at restnormal, Nweight, W2. Pulled on rough groundNWpullfriction3. Sliding down a rough slopeNfrictionWmotion4. Mass hanging at resttension, Tweight, W
Start with one isolated body. Draw only the external forces acting on it; motion arrows and resultant force are not extra forces.

3. Detailed Explanations

A. Common forces you should recognise

  • Weight (W): gravitational force on the object, acts vertically downwards. (W = mg)
  • Normal contact force (N): perpendicular to the surface of contact.
  • Friction (f): parallel to the surface, opposes motion or impending motion.
  • Tension (T): pull along a string/rope, away from the object.
  • Air resistance / drag: opposite to the direction of motion through air.

B. Contact vs non-contact forces

  • Contact forces require physical contact (e.g. normal force, friction, tension, air resistance).
  • Non-contact forces act at a distance (e.g. gravitational, electrostatic, magnetic).

C. How to draw an FBD (step-by-step)

  1. Identify the body you are analysing (one object at a time).
  2. Sketch the body as a simple shape.
  3. List all external interactions (surface, string, Earth, air, etc.).
  4. Convert each interaction into a force arrow on your diagram.
  5. Choose axes (often horizontal/vertical) and label directions (e.g. right is positive).
What to do after the FBD (exam workflow)
  1. Choose a positive direction (or axes).
  2. Add forces along the line of motion using signs. For example, with forward positive, subtract the backward-force magnitudes.
  3. Apply Fᵣₑₛᵤₗₜₐₙₜ = ma (or set Fᵣₑₛᵤₗₜₐₙₜ = 0 for constant velocity / equilibrium).
  4. Check units and use your sign to state the direction.

4. Common Mistakes

  • Drawing action–reaction pairs on the same FBD (they act on different bodies).
  • Forgetting the weight force.
  • Drawing friction in the wrong direction (it opposes motion/impending motion).
  • Mixing “resultant force” into the diagram as if it is an extra force.
  • Automatically writing N = mg (not true on slopes, in lifts, or when there is vertical acceleration).
  • Drawing forces without labelling them (labels are often the marks).

5. Exam Tips

  • If an object is at rest / moving at constant velocity, the resultant force is zero: ΣF = 0.
  • For an accelerating object, show the forces first, then use F = ma on the resultant.
  • When drawing a diagram, ask yourself: “What is touching it? What is pulling it? What is attracting it? What is resisting its motion?”
If the question says…Translate it into…
constant speed in a straight linea = 0, so the vector resultant force is zero
slowing while moving rightacceleration and resultant force point left
smooth surfaceneglect friction unless another resistive force is stated
rough surfaceinclude friction opposite relative motion or the tendency to move
draw the forces on Xisolate X and omit forces exerted by X on other bodies

6. Worked Examples

Hidden assumptions to watch for
  • “smooth”: friction is negligible.
  • “rough”: include friction, opposite motion/impending motion.
  • “light string” / “smooth pulley”: tension is the same throughout the string.
  • “ignore air resistance”: do not include drag.

Modelled example 1

Block on a rough horizontal surface

Core

Problem

A 6.0 kg block is pulled right with 18 N on a rough horizontal surface at constant speed. Draw the FBD and calculate friction.
Study the worked solution

  1. Isolate the block and list interactions

    Method

    Draw weight down, normal force up, pull right and friction left.

    Reason

    Only external forces acting on the block belong on its FBD; friction opposes its rightward motion.

    Working

    Label the four arrows W, N, 18 N and f.

  2. Use the motion condition

    Method

    Set the horizontal resultant to zero.

    Reason

    Constant velocity means a = 0.

    Working

    18-f = 0 ⇒ f = 18 N left

Guided practice 2

Object sliding down a slope (directions only)

About 5 min

Problem

A block slides down a rough slope. State each force on the block and its direction.

Build the diagram from interactions

Friction direction
Normal-force direction

Hints

Hint 1: start with Earth and surface
Earth supplies weight; the surface supplies normal force and friction.
Hint 2: orient each force
Weight is vertical, normal is perpendicular to the slope and friction opposes motion.
View solution step by step

  1. Draw the three external forces

    Method

    Draw W vertically down, N perpendicular away from the slope and f up the slope.

    Reason

    Each arrow represents one external interaction acting on the isolated block.

    Working

    Friction points up the slope because the relative motion is down the slope.

Common misconception 3

Newton’s 3rd law (paired FBDs for two bodies)

Find and correct the mistake

Learner response

Two blocks A and B touch on a smooth horizontal surface; A is pushed right. A student draws both contact forces on block A’s FBD because they are an action–reaction pair. Locate the error and construct the paired FBDs.

Assign every force to its target body

Where do the contact-force pair members act?

View solution step by step

  1. Draw block A's forces

    Method

    Include weight down, normal up, applied push right and B-on-A contact left.

    Reason

    These are the external forces whose target is block A.

    Working

    Do not add A-on-B to A’s diagram.

  2. Draw block B's forces

    Method

    Include weight down, normal up and A-on-B contact right.

    Reason

    The contact-force partner acts on block B and belongs on B’s separate FBD.

    Working

    The two contact forces are equal and opposite but act on different blocks.

Examiner practice 4

Person in a lift (compare forces)

3 marks

Examination question

A person stands on a scale in a lift accelerating upward. State the two forces on the person and compare the scale reading with the person’s weight. [3 marks]

Name forces on the person and use acceleration direction

View solution step by step

  1. Identify the two forces

    2 marks

    Method

    Draw weight W down and normal contact force N up.

    Reason

    Earth attracts the person and the scale pushes on the person.

    Working

    The scale reading is the normal force N.

  2. Use the upward acceleration

    1 mark

    Method

    Make the upward force larger.

    Reason

    An upward acceleration requires an upward resultant force.

    Working

    N-W > 0 ⇒ N > W

Challenge 5

Falling object (with air resistance)

Minimal support

Motion-to-force transfer

A ball moves downward through air but is slowing. State the forces and determine which is larger.

Infer resultant direction before comparing forces

Larger force at this instant

Hints

Hint 1: infer acceleration direction
If downward speed decreases, acceleration points upward.
Hint 2: compare the FBD arrows
The upward resultant requires upward drag to exceed downward weight.
View solution step by step

  1. Draw the two forces

    Method

    Draw weight downward and air resistance upward.

    Reason

    Gravity and interaction with the air are the stated external interactions.

    Working

    The ball’s downward velocity does not determine the resultant direction by itself.

  2. Use the slowing condition

    Method

    Set the resultant upward.

    Reason

    Acceleration is opposite to the downward velocity while speed decreases.

    Working

    Air resistance is greater than weight at that instant.

7. Mind Stretchers

Mind stretcher 1: Static friction (“about to move”)Extension

A heavy box is on a rough floor. You push it to the right, but it does not move.

  1. Which horizontal forces act on the box?
  2. What can you say about their magnitudes?
Show Answer

  1. Horizontal forces on the box:

    • your push to the right
    • static friction to the left

  2. Since the box is at rest, the resultant force is zero, so the horizontal forces balance:

static friction = push (as long as the box does not start moving).

Mind stretcher 2: Don’t mix up “pairs”Extension

For a block on a table, weight W and normal reaction N can balance.

Are they an action–reaction pair? Explain.

Show Answer

No.

An action–reaction pair acts on different objects.

  • W acts on the block (Earth on block).
  • N acts on the block (table on block).

They can be balanced, but they are not an action–reaction pair.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027