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For forces in the same direction add them, and for opposite directions subtract the smaller from the larger. Free GCSE Physics notes and 15 FAQs.
Calculating Resultant Forces is part of Forces and their interactions in GCSE AQA Higher Physics.
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For forces in the same direction add them, and for opposite directions subtract the smaller from the larger. Free GCSE Physics notes and 15 FAQs.
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Use this lesson to stay inside Forces and their interactions while connecting the detail back to the wider Forces topic.
Read the core explanations from Calculating Resultant Forces before testing yourself from memory.
Picture a tug-of-war match. Team A pulls with 500 N to the right, Team B pulls with 300 N to the left. Who wins and by how much? The answer lies in calculating the resultant force — the single force that shows the overall effect.
This isn't just playground physics. Engineers designing bridges need to know how wind forces combine with weight. Pilots must understand how thrust, drag, and gravity work together. Every moving object experiences multiple forces, and the resultant determines what actually happens.
When forces act along the same line, calculating the resultant becomes straightforward. Think of it like a number line — forces in one direction are positive, forces in the opposite direction are negative.
For forces in the same direction: add them together. A 50 N push combined with a 30 N push in the same direction gives 80 N total. For forces in opposite directions: subtract the smaller from the larger. The resultant points in the direction of the larger force.
Worked example: Calculating Resultant Force - Same Direction
A car engine provides 2000 N forward thrust. The wind provides an additional 150 N push from behind. Calculate the resultant force.
Answer: 2150 N forward
Worked example: Calculating Resultant Force - Opposite Directions
A box experiences 80 N friction opposing its motion and 120 N applied force in the direction of motion. Find the resultant force.
Answer: 40 N in the direction of motion
Notice how we always specify direction. A force of '40 N' tells you nothing useful — you need to know which way it acts.
Real life isn't always so neat. Forces often act at angles to each other. A boat's engine pushes forward while the current pushes sideways. How do we find the resultant then?
This is where we need vector addition. Unlike simple numbers, forces have both size (magnitude) and direction. We can't just add 50 N east plus 30 N north and get 80 N — the direction matters.
For perpendicular forces, we use Pythagoras' theorem to find the magnitude and trigonometry to find the direction. The resultant forms the hypotenuse of a right-angled triangle.
Worked example: Resultant of Perpendicular Forces
A ship experiences 600 N thrust eastward and 800 N current force northward. Calculate the resultant force.
Answer: 1000 N at 53° north of east
Sometimes we need to work backwards. Instead of combining forces, we break a single force into components. This is called resolution — splitting one force into two perpendicular parts.
Why would we do this? Imagine pushing a lawnmower. Your push acts at an angle — part of it moves the mower forward, part pushes it down into the ground. Resolving the force shows you how much actually contributes to motion.
Worked example: Resolving a Force into Components
A person pushes a lawnmower with 100 N force at 30° below horizontal. Find the horizontal and vertical components.
Answer: Horizontal: 86.6 N, Vertical: 50 N downward
The key insight: these two component forces together have exactly the same effect as the original 100 N force. That's the power of resolution — we can replace one angled force with two perpendicular ones.
What happens when the resultant force is zero? The object is in equilibrium — either stationary or moving at constant velocity. No acceleration occurs because there's no net force.
Think of a book on a table. Weight pulls down, normal force pushes up. They're equal and opposite, so the resultant is zero. The book stays put. This is static equilibrium.
A car at constant speed on a motorway is also in equilibrium. Engine force forward equals air resistance backward. Resultant force is zero, so velocity stays constant — this is dynamic equilibrium.
Force calculations are mark-heavy in exams. Here's how to secure every point available.
Common exam traps: mixing up sine and cosine in resolution (horizontal uses cosine), forgetting to convert angles to the correct reference, and adding perpendicular forces arithmetically instead of using Pythagoras.
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-03-20.
Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
Equilibrium is the state when all forces acting on an object are balanced, giving zero resultant force, so the object is either stationary or moving at constant velocity. A book on a table is in static equilibrium; a car at constant speed on a motorway is in dynamic equilibrium.
To resolve a force, split it into two perpendicular components: the horizontal component uses cosine and the vertical uses sine. A 100 N push angled 30° down from the horizontal has a horizontal component of 86.6 N and a vertical component of 50 N downward.
Static equilibrium is when the resultant force is zero and the object stays still, like a book on a table. Dynamic equilibrium is when the resultant force is zero and the object moves at constant velocity, like a car at constant speed on a motorway.
For forces in the same direction, add them; for forces in opposite directions, subtract the smaller from the larger, and the resultant points in the direction of the larger force. An applied force of 120 N against 80 N of friction gives a resultant of 40 N in the direction of motion.
For perpendicular forces, use Pythagoras' theorem for the magnitude and trigonometry for the direction, since the resultant is the hypotenuse. A ship with 600 N thrust east and an 800 N current north has a resultant of 1000 N at 53° north of east.
Forces are resolved to see how much of an angled force actually contributes to motion. When pushing a lawnmower at an angle, part of the push moves the mower forward and part pushes it down; the two component forces together have exactly the same effect as the original force.
Forces acting in the same direction are added, so a 2000 N forward engine force and a 150 N push from the wind behind give a resultant force of 2150 N forward. The direction must always be included.
A 120 N applied force against 80 N of friction gives a resultant force of 40 N in the direction of motion. Taking forward as positive, (+120) + (−80) = +40 N, so the box accelerates forward.
Perpendicular forces cannot simply be added: 50 N east plus 30 N north does not give 80 N. Pythagoras' theorem gives the magnitude of the resultant, which forms the hypotenuse of a right-angled triangle, and trigonometry gives its direction.
The horizontal component of a force at angle θ to the horizontal is F cos θ, and the vertical component is F sin θ. Mixing up sine and cosine is a common trap when resolving forces.
A 100 N push angled 30° down from the horizontal has a horizontal component of 100 cos 30° = 86.6 N and a vertical component of 100 sin 30° = 50 N downward. Together they have exactly the same effect as the original 100 N force.
Vector addition is the process of combining forces by considering both their magnitude and direction to find the net effect. Forces in a straight line add or subtract, while perpendicular forces are combined using Pythagoras' theorem.
A tug of war with Team A pulling 500 N right and Team B pulling 300 N left gives a resultant force of 200 N to the right, so Team A wins. For forces in opposite directions, the smaller is subtracted from the larger.
Force components are checked with Pythagoras: they should recreate the original force. For components of 86.6 N and 50 N, √(86.6² + 50²) = √(7500 + 2500) = 100 N, matching the original force.
The direction of a resultant force must be given because a force of '40 N' alone says nothing about which way it acts. The direction shows which way the object will accelerate, such as 40 N in the direction of motion.