Resultant forces and free body diagrams (net force)
Add forces to find the resultant (net) force, draw free body diagrams and calculate weight, with worked examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolCurriculum fit: GCSE Physics and Combined Science (forces). US: middle and high school physical science (forces and interactions).
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What is it?
A force is a push or a pull, measured in newtons (N). Forces have both size and direction, so they are vectors. When several forces act on an object, you can replace them with one force, the resultant force, that has the same effect.
A free body diagram shows a single object with arrows for all the forces acting on it. The length of each arrow represents the size of the force.
Key formulas and ideas
- Resultant force: add forces in the same direction; subtract forces in opposite directions.
- If the resultant force is zero, the forces are balanced and the object stays at rest or moves at constant velocity.
- Weight W = mass × gravitational field strength = mg (g ≈ 9.8 N/kg on Earth).
- Resultant force = mass × acceleration (F = ma).
Worked examples
Example 1: Opposite forces
Question: A box is pushed right with 20 N and friction pulls left with 12 N. Find the resultant force.
- The forces act in opposite directions, so subtract.
- 20 − 12 = 8.
Answer: 8 N to the right
Example 2: Weight
Question: Find the weight of a 5 kg object on Earth (g = 9.8 N/kg).
- W = mg.
- = 5 × 9.8 = 49.
Answer: 49 N
Example 3: Terminal velocity
Question: Explain why a skydiver reaches a constant speed.
- As speed increases, air resistance increases.
- Eventually air resistance equals weight, so the resultant force is zero.
- With no resultant force, the speed stays constant.
Answer: Forces are balanced at terminal velocity
Common mistakes
- Adding forces that act in opposite directions.
- Confusing mass (kg) with weight (N).
- Saying a moving object must have a resultant force. Constant velocity needs zero resultant force.
- Drawing force arrows from the wrong object.
Practice questions
Frequently asked questions
What is the difference between mass and weight?
Mass is the amount of matter and does not change. Weight is the force of gravity on that mass, which changes with the gravitational field.
What is equilibrium?
A state where the resultant force is zero.
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Reviewed by StudyMorrow editorial review on 5 Nov 2026.