Resultant force and balanced motion
Key idea: The resultant combines all forces on a body with their directions. Zero resultant means constant velocity or rest; a non-zero resultant changes velocity.
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Guided lessons · coming soon
Guided lesson
Guided steps
- Choose a positive direction before adding the forces.
- Follow how the opposite forces combine into one resultant.
- Explain why a moving car can have balanced forces.
- Add every horizontal force and predict how velocity changes.
- Decide whether balanced forces require rest, then find the new resultant.
- Compare the resultant’s direction with the direction of motion.
- Predict the satellite’s path and speed when the force disappears.
- Compare how the same resultant changes opposite velocities.
- Find the resultant and decide whether the lift slows down.
- Find the new resultant and the lift’s immediate speed change.
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ContinueA tug of war can stay still even though both teams are pulling hard: their pulls cancel. What decides how an object moves is not any single force but all of them added together, the resultant force. Starting from a free-body diagram, you add the forces to find the resultant, and its size and direction tell you whether the object keeps moving as it is, speeds up, slows down or turns.
Resultant force: balanced or unbalanced
Add the forces with their directions
The resultant force is the single force that has the same effect as all the forces on the body together.
For forces along one line:
- choose a positive direction, such as “to the right”;
- add the forces in that direction;
- subtract the forces in the opposite direction.
A positive answer means the resultant points in your chosen direction; a negative answer means it points the other way.
Worked example 1
Resultant force on a pushed box
Problem
A box on a floor is pushed to the right with 50 N. Friction on the box is 20 N to the left. Find the resultant force.
Show full solution
Choose a positive direction
Method
Take right as positive.Reason
Forces along one line add with signs, so one direction must count as positive.Working
Answer
Push: + 50 N; friction: -20 N
Add the forces with their signs
Method
Add the push and subtract the friction.Reason
Friction acts to the left, against the chosen direction.Working
Answer
Resultant force = 50 - 20 = 30 N
Read the direction from the sign
Working
Answer
The answer is positive, so the resultant force is 30 N to the right.
If two people push the box to the right with 40 N and 30 N, and friction is 20 N, the resultant is 40 + 30 - 20 = 50 N to the right. The largest single force is not the resultant.
When forces act both horizontally and vertically, find the resultant in each direction separately. For a box sliding along a level floor, the vertical forces (weight and normal force) balance, so only the horizontal forces decide how it speeds up or slows down.
Balanced and unbalanced forces
The forces on a body are balanced when the resultant force is zero. They are unbalanced when it is not zero.
| Resultant force | Forces are | What happens to the body’s motion |
|---|---|---|
| zero | balanced | no change: it stays at rest, or keeps moving at the same speed in the same direction |
| not zero | unbalanced | its velocity changes: it accelerates in the direction of the resultant force |
Balanced forces do not mean the body is at rest. A cyclist on a straight road with a 120 N driving force and 120 N of resistance has zero resultant force. If the cyclist is already moving, the cyclist keeps moving at a constant speed.
Worked example 2
Constant velocity
Problem
A car travels along a straight, level road at a constant 20 m/s. The driving force is 1500 N. What is the total resistive force on the car?
Show full solution
Read the motion
Method
Constant speed in a straight line is constant velocity.Reason
Neither the speed nor the direction changes, so the acceleration is zero.Working
Answer
a = 0
Link motion to the resultant
Method
Zero acceleration means zero resultant force.Reason
A resultant force would change the car’s velocity.Working
Answer
Driving force - resistive force = 0
Balance the forces
Working
Answer
The forces are balanced, so the resistive force equals the driving force: 1500 N, backward.
Check your understanding 1
A boat moves forwards with 540 N thrust, opposed by 410 N water resistance and 130 N air resistance. Find the horizontal resultant. How does its velocity change?
Show answer
Take forward as positive: resultant force = 540 - 410 - 130 = 0. The forces are balanced, so the boat keeps moving forward at a constant speed. It does not stop.
Check your understanding 2 Balanced means at rest?
A crate has a 30 N push right and 30 N friction left. Must it be at rest? The push rises to 45 N while friction stays at 30 N. Find the new signed resultant, taking right as positive.
Show answer
Not necessarily. The resultant force is zero, so the crate’s velocity does not change. It could be at rest, or moving to the right at a constant speed. With a 45 N push, the resultant is 45 - 30 = 15 N to the right, so the crate accelerates to the right: it speeds up, or starts moving if it was at rest.
How a force changes motion
An unbalanced force changes a body’s velocity. Velocity has a size (the speed) and a direction, so a resultant force can:
- start a body moving from rest;
- speed it up;
- slow it down or stop it;
- change its direction.
Which of these happens depends on the direction of the resultant force compared with the direction of motion.
| Resultant force compared with the motion | Effect on the body | Example |
|---|---|---|
| on a body at rest | starts moving | a kick sets a ball rolling |
| same direction as the motion | speeds up | a car accelerates as the driver presses the pedal |
| opposite to the motion | slows down | brakes slow a moving bicycle |
| sideways to the motion | changes direction | a car turns a corner |
A body that changes direction is accelerating, even if its speed stays the same. A car going round a bend at a constant 15 m/s has a resultant force on it, pointing sideways towards the inside of the bend.
Check your understanding 3 Constant speed in a circle
In a model, a satellite moves in a circle at constant speed. At one instant the inward force is removed and no forces then act on it. Predict its subsequent path and speed. Would it stop, continue round the circle, or move in a straight line?
Show answer
It moves in a straight line at the same speed, in the direction it was travelling when the force was removed: along a tangent to the circle. With zero resultant force its velocity stays constant. It does not stop, and it cannot keep turning round the circle without an inward force.
Worked example 3
Same forces, different motion
Problem
A trolley has an 18 N force to the right and a 7 N force to the left. Describe what happens (a) if it is moving to the right, (b) if it is moving to the left.
Show full solution
Find the resultant
Method
Take right as positive and add the forces.Reason
The resultant does not depend on which way the trolley moves.Working
Answer
Resultant force = 18 - 7 = 11 N to the right
(a) Moving to the right
Method
Compare the resultant’s direction with the motion.Reason
The resultant points the same way as the motion.Working
Answer
The trolley speeds up.
(b) Moving to the left
Working
Answer
The resultant is opposite to the motion, so the trolley slows down. If the forces stay the same, it stops and then starts moving to the right.
The resultant force tells you the direction of the acceleration, not the direction of motion.
Check your understanding 4
A lift moves downwards with 5200 N tension upwards and 5000 N weight downwards. Find the signed resultant, taking up as positive. Does it speed up or slow down at that instant?
Show answer
Take upward as positive: resultant force = 5200 - 5000 = 200 N upward. The lift moves downward, so the resultant is opposite to its motion: the lift slows down.
Check your understanding 5 What information does the force sum leave open?
A lift has 600 N tension upwards and 600 N weight downwards, with no other vertical forces. Which motions are possible? While it moves upwards, tension falls to 500 N. Find the new resultant, taking up as positive, and predict the immediate speed change.
Show answer
The first resultant is 0 N, so the velocity is unchanged; the lift could be stationary, moving steadily up or moving steadily down. Its initial velocity is needed to choose among those possibilities. With 500 N tension the signed resultant is 500 − 600 = −100 N, or 100 N downward. Since the lift is then moving upward, it slows down immediately. Downward acceleration does not mean it is already travelling downward.
Common mistakes
- Saying a moving body needs a forward resultant force. A forward resultant makes it speed up; constant velocity needs a zero resultant.
- Saying zero resultant force means the body is at rest. It means its velocity does not change.
- Taking the largest force as the resultant. Add all the forces with their directions.
- Saying constant speed means zero resultant force. If the direction changes, there is a resultant force.
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Syllabus and review details
- SEC G2 Science Physics component 2027 · 2027
Physics section, PDF pages 8–23
Last reviewed: