GCSE · Physics · AQA · Spec 8463

Resultant forces and resolving forces

Every force battle on an object can be settled by one winning force — the resultant.

What you need to know

  • The resultant force is the single force that has the same effect as all the individual forces acting on an object combined.
  • For forces in a straight line: add forces in the same direction; subtract forces in opposite directions to find the resultant.
  • If the resultant force is zero, the forces are balanced — the object is in equilibrium (stationary or moving at constant velocity).
  • Higher tier: a single force can be resolved into two perpendicular components, and a scale vector diagram can find the resultant of two non-collinear forces.

The big picture

When more than one force acts on an object, you can replace them all with a single resultant force that has exactly the same effect. For forces acting along the same straight line, you simply add or subtract them depending on direction. If the resultant force is zero, the object is in equilibrium — it will not accelerate. At Higher tier, a single force can be split into two perpendicular components, and a scale vector diagram can find the resultant of forces acting at an angle.

TONIGHT'S REVISION

Resultant Forces

Replace any number of forces with one — and predict exactly what an object will do.

Forces on a car travelling along a flat road

Tap each arrow to see what that force does and why it matters. Notice which forces are balanced and which are not.

CarDriving force (thrust)Friction / air resistanceWeightNormal contact force

Tap a force to see what it does.

Predict, then check

Look at the force diagram above — commit to an answer before you reveal.

A car has a driving force of 3000 N to the right and a friction force of 3000 N to the left. The weight is 12 000 N downward and the normal contact force is 12 000 N upward. What is the resultant force on the car?

Resultant forces — the causal chain

?

Reason it through

Why does increasing the driving force of a car (while friction stays the same) change how the car moves?

Link 1 of 3

First link · your turn

What happens to the two horizontal forces when the driver presses the accelerator harder?

2
Locked — reveal the link above first
3
Locked — reveal the link above first
Higher

Relationship matrix

Tap any cell to reveal it. Tap a column header to read one property down every item.

Method to find resultantSize of resultant vs each forceScale diagram needed?
Two forces, same directione.g. 5 N right + 3 N right
Two forces, opposite directionse.g. 10 N right + 6 N left
Two forces at right anglesHigher tier — e.g. 3 N right + 4 N up

Each cell hides a short answer and the reason behind it. Predict before you tap.

AQA 8463 — Resultant forces

AQA mark scheme practice

Read the student answer — which phrases earn marks?

Question

A boat engine provides a forward thrust of 800 N. Water resistance is 500 N backward. Explain what the resultant force is and what effect it has on the boat's motion. [4 marks]

Student answer

The resultant force is 300 N in the forward direction because 800 N minus 500 N equals 300 N. The forces are unbalanced so there is a resultant force. This means the boat will accelerate in the direction of the resultant force. The boat speeds up because the driving force is greater than the resistive force.

Method marks0/4

Key points

1Resultant force = the net single force that replaces all forces acting on an object.
2Same direction: add the magnitudes. Opposite directions: subtract — resultant acts in the direction of the larger force.
3Resultant = 0 N means equilibrium; the object does not accelerate.
4Higher tier: use a scale drawing (tip-to-tail vector triangle) to find the resultant of two forces at an angle — measure the closing side and its angle.
5Higher tier: resolving a force means splitting it into a horizontal component and a vertical component acting at right angles to each other.

Worked example

Problem

A book sits on a table. The Earth pulls it downward with a weight of 15 N. The table pushes it upward with a normal contact force of 15 N. What is the resultant force on the book, and what does this tell you about its motion?

🧠

Memory hook

Think of a tug-of-war: one team pulls left with 300 N, the other right with 200 N — the rope 'feels' a single 100 N pull to the left. That 100 N IS the resultant.

★ Exam tip

On AQA Paper 2, if a question gives you two forces in a straight line, always assign a positive direction first (e.g. right = positive), then give each force a sign before adding. Write 'Taking right as positive: resultant = +8 N + (−5 N) = +3 N to the right.' Showing the sign convention earns the method mark even if you slip on arithmetic.

⚠ Watch out

Forgetting that forces in opposite directions must be SUBTRACTED — students often add all magnitudes regardless of direction and get a resultant that is too large.

✓

Check yourself

Two horizontal forces act on a crate: 60 N to the right and 25 N to the left. Without calculating — in which direction does the resultant act, and is it larger or smaller than 60 N?

Flashcards

(22)
What is the resultant force?
The single force that has the same effect as all the individual forces acting on an object combined.
How do you find the resultant of two forces acting in the same direction?
Add their magnitudes together. The resultant acts in the same direction as both forces.
How do you find the resultant of two forces acting in opposite directions?
Subtract the smaller magnitude from the larger. The resultant acts in the direction of the larger force.
What does a resultant force of 0 N mean?
The forces are balanced — the object is in equilibrium. It is either stationary or moving at constant velocity.
A force of 10 N right and 6 N left act on a box. What is the resultant?
10 − 6 = 4 N to the right.
What is equilibrium?
The state where the resultant force on an object is zero — no acceleration occurs.
Can a moving object have a resultant force of zero?
Yes — if it moves at constant velocity in a straight line, the resultant force is zero.
What is a diagram showing an object with all forces drawn as labelled arrows called?
A force diagram (sometimes called a force arrow diagram). It shows the direction and relative size of every force acting on the object.
In a force diagram, what does the length of an arrow represent?
The magnitude (size) of the force — a longer arrow means a larger force.
Two forces of 7 N upward and 7 N downward act on an object. What is the resultant?
0 N — the forces are balanced and the object is in equilibrium.
What is the AQA term for the single replacement force that has the same effect as multiple forces?
The resultant force.
Higher tier: What does resolving a force mean?
Splitting a single force into two components that act at right angles to each other, usually horizontal and vertical.
Higher tier: What is a scale vector diagram used for in force problems?
To find the resultant of two forces that do not act along the same straight line, by drawing them tip-to-tail to scale and measuring the closing side.
Higher tier: How do you find the resultant of two forces at right angles using a scale diagram?
Draw the two forces tip-to-tail forming two sides of a right-angled triangle. The resultant is the hypotenuse — measure its length using the scale and its angle with a protractor.
Higher tier: What does it mean for forces to be in equilibrium on a vector diagram?
The force vectors form a closed triangle — there is no closing side — so the resultant is zero.
Name two forces that commonly act vertically on a stationary object.
Weight (downward, due to gravity) and normal contact force (upward, from the surface).
A car engine provides 4000 N forward; friction is 1500 N backward. What is the resultant?
4000 − 1500 = 2500 N in the forward direction.
What direction is the resultant when 12 N acts right and 20 N acts left?
To the left, with magnitude 20 − 12 = 8 N.
Why must you always state the direction of a resultant force?
Force is a vector quantity — without direction, the answer is incomplete and could lose a mark.
Three forces act on an object: 5 N right, 3 N right, 4 N left. What is the resultant?
(5 + 3) − 4 = 4 N to the right.
What is the difference between balanced and unbalanced forces?
Balanced forces have a resultant of zero (no acceleration). Unbalanced forces have a non-zero resultant (the object accelerates).
Higher tier: If two perpendicular forces of 3 N and 4 N act on an object, what is the magnitude of the resultant shown on a scale vector diagram?
5 N — the resultant is the hypotenuse of a 3-4-5 right-angled triangle.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

Learn Resultant forces and resolving forces properly — interactive practice, marked questions and flashcards.

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