Meet the Free-Body Diagram

Free-Body Diagram (FBD)

A free-body diagram isolates an object and shows all external forces. It is the starting map for force problems.

Key Characteristics:

  • Draw the object as a simple dot or box, separate from surroundings.
  • Attach arrows from the centre; each arrow represents one external force with correct direction.
  • Label every arrow: weight, normal, tension, friction, push, etc.

Example:

Block on table — arrows for weight (down), normal (up), friction (left), applied push (right).

Forces on a Stationary Block

Block on table with three coloured arrows (W, N, f)

Identify each force

Weight \(W\) acts vertically downward due to gravity.

The table pushes upward with an equal normal reaction \(N\).

Static friction \(f\) lies along the surface, resisting any push.

Key Points:

  • Weight \(W = mg\) downward
  • Normal reaction \(N\) upward
  • Static friction \(f\) along the surface

Label the Forces Yourself

Practice: Drag each force name to its arrow on the block, then hit “Check Answers” to self-check your labels.

Draggable Items

Weight \(mg\)
Normal Reaction \(N\)
Applied Pull \(F_{\text{pull}}\)
Kinetic Friction \(f_k\)

Drop Zones

Arrow 1

Arrow 2

Arrow 3

Arrow 4

Tip:

Start with weight; it always points straight down from the block.

Link Forces to Motion

\[F_{\text{net}} = m a\]

Variable Definitions

\(F_{\text{net}}\) Net force (N)
\(m\) Mass (kg)
\(a\) Acceleration (m s⁻²)

Applications

Net Force ≠ 0

When forces stop balancing, \(F_{\text{net}}\) appears and the block’s speed starts to change.

Predict Acceleration

Use \(a = F_{\text{net}}/m\). Bigger net force or smaller mass means faster acceleration.

Check Units

1 N applied to 1 kg produces 1 m s⁻², confirming Newton’s Second Law.

Worked Example: Push That Block

We push a 2 kg block with 10 N. Kinetic friction is 2 N. Find the acceleration.

1

List the forces

Forward push 10 N, backward kinetic friction 2 N. Choose forward as positive.

2

Find net force

\(F_{\text{net}} = 10\,\text{N} - 2\,\text{N} = 8\,\text{N}\) forward.

3

Apply \(F = ma\)

\(a = \dfrac{F_{\text{net}}}{m} = \dfrac{8}{2} = 4\ \text{m/s}^2\) forward.

Pro Tip:

Always subtract opposing friction before using \(F = ma\).

Quick Check: Did You Get It?

Question

A 5 kg block has 15 N rightward and 5 N leftward forces. What is its acceleration?

1
2 m/s² rightward
2
2 m/s² leftward
3
3 m/s² rightward
4
10 m/s² rightward

Hint:

First find net force, then apply \(a = F_{\\text{net}}/m\).

Key Takeaways

Begin by sketching a clear free-body diagram of the block.

On a level plane, weight \(mg\) downward balances normal force \(N\) upward.

Static or kinetic friction acts opposite the intended or actual motion.

Net horizontal force \( \Sigma F_x = ma \); its direction sets the block’s acceleration.

Thank You!

We hope you found this lesson informative and engaging.