Free-Body Diagrams and Net Force
A free-body diagram is a sketch that shows a single object as a point or box with arrows for all the forces acting on it, and the net force is the vector sum of those forces. In brief: draw only forces acting on the chosen object (not forces it exerts on others), label each arrow, choose axes, then add the components: ΣFx and ΣFy. If the net force is zero, the object has no acceleration; otherwise a = ΣF ÷ m.
Drawing a free-body diagram is the first step in almost every mechanics problem. This guide explains how to draw one, how to find the net force along a line and at angles, compares common forces and their arrows in a table, works through a block-on-a-table example and an incline, and corrects common mistakes.
How do you draw a free-body diagram?
- Choose the object (the “system”) and sketch it as a dot or box.
- List what touches it (contact forces: normal, friction, tension, push) and what acts at a distance (weight).
- Draw each force as an arrow starting at the object, in the direction in which it acts, with the length roughly proportional to its size.
- Label each arrow with its name and magnitude (W, N, f, T, Fapplied).
- Draw coordinate axes, with x along the direction of motion or the slope.
Do not include forces that the object exerts on other objects, the velocity or acceleration (they are not forces), or “forces” that are only the resultant of others.
How do you find the net force?
The net force is the vector sum of all forces: Fnet = ΣF. For forces along a line, add the forces with signs. For forces at angles, resolve each force into x and y components (F cos θ and F sin θ), add the components separately, and combine the totals with the Pythagorean theorem. Then use Newton’s second law: ΣF = ma. If ΣF = 0, the forces are balanced and the object is in equilibrium: at rest or moving at constant velocity.
Typical forces in diagrams
| Force | Symbol | Direction of the arrow |
|---|---|---|
| Weight | W or mg | Straight down |
| Normal force | N | Perpendicular to the surface, away from it |
| Friction | f | Parallel to the surface, opposing sliding |
| Tension | T | Along the rope, away from the object |
| Applied force | F | Where the push or pull acts |
Worked example: a pushed block and a box on a slope
Part A. A 10 kg block is pushed to the right along a floor with an applied force of 50 N. Friction is 20 N. Use g = 9.8 m/s2.
- Forces: applied 50 N right; friction 20 N left; weight W = 10 × 9.8 = 98 N down; normal force N up.
- Vertical: no acceleration, so N = 98 N.
- Horizontal net force: 50 − 20 = 30 N to the right.
- Acceleration: a = 30 ÷ 10 = 3.0 m/s2 to the right.
Part B. A 5.0 kg box rests on a smooth slope of 30°. Take x down the slope, y perpendicular to it.
- Weight: W = 5.0 × 9.8 = 49 N, pointing straight down.
- Components: along the slope W sin 30° = 49 × 0.50 = 24.5 N; perpendicular W cos 30° = 49 × 0.866 = 42.4 N.
- Normal force: N = 42.4 N (balances the perpendicular component).
- Net force along the slope: 24.5 N down the slope, so a = 24.5 ÷ 5.0 = 4.9 m/s2 (equal to g sin 30°).
How did the method develop?
Simon Stevin used the analysis of forces on an inclined plane in the 1580s, and the idea of isolating the object and listing all the forces on it became a standard method in mechanics and engineering in the 1800s. In teaching, “free-body diagram” became a standard term in the twentieth century.
Which mistakes are common?
Mistake 1: Including forces on other objects
Only draw forces acting on the chosen object.
Mistake 2: Drawing the normal force as always equal to weight
On a slope, N = W cos θ, which is less than W.
Mistake 3: Adding a force “in the direction of motion”
A moving object does not need a forward force. Include only real interactions.
Mistake 4: Forgetting to resolve angled forces
Split a slanted force into components before adding.