2.1.2Interactions Over Small and Large Distances

Resultant Forces (HT Only) — AQA GCSE Combined Science Synergy 8465 - Physical Sciences Revision Notes & Topical Questions

5 min read 8 parts Lesson 3 of 26

📚 AQA GCSE Combined Science Synergy 8465 - Physical Sciences Hub / Topical Revision

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Part 1 of 7The resultant force

When several forces act on one object, we can replace them with one force having the same effect: the resultant force. It is the vector sum of the forces. For forces along a straight line, choose one direction as positive, add forces that way, subtract forces the other way.

Resultant = (forces in the positive direction) − (forces in the negative direction)

Part 2 of 7Balanced forces

If the resultant force is zero the forces are balanced. Then, by Newton's first law, the object either stays at rest or keeps moving at constant velocity in a straight line. A parachutist falling at steady speed, a lift moving up at steady speed and a book resting on a desk all have zero resultant force.

Notice that balanced forces do not mean no forces. They mean the forces add up to zero.

A classic example is a book on a table.

Balanced forces

Weight acts down and the normal contact force acts up.

These two forces are equal and opposite, but they are not a Newton third law pair, because they act on the same object.

The partner of the weight is the book's pull on the Earth, and the partner of the table's push on the book is the book's push on the table.

Part 3 of 7Unbalanced forces

If the resultant is not zero, the object accelerates in the direction of the resultant. A resultant force in the direction of motion speeds the object up; against the direction of motion it slows it down; at an angle it changes the direction. The size of the acceleration is found from F = ma, covered in the next lesson.

It is the resultant force that causes the acceleration, not any individual force.

Unbalanced forces

If a car engine pushes with 2000 N, but resistive forces total 1500 N, the car does not accelerate as if 2000 N were acting; the resultant is 500 N.

As the car speeds up, drag rises, the resultant falls and acceleration falls until the car reaches a top speed where the driving force equals the resistive forces.

Part 4 of 7Forces at right angles

When two forces act at 90° to each other, draw a right-angled triangle and use Pythagoras:

F_R² = F₁² + F₂²

The direction is found from tan θ = F₂ / F₁. For forces at other angles a scale drawing, with the vectors joined head to tail and the resultant measured, is used.

A boat pulled by two tugs at right angles, or a kite string pulling up and sideways, are typical situations.

Example of a scale drawingfor a 3 N force east and a 4 N force at 60° north of east, draw the first arrow 3 cm long, then the second at 60° from its end, 4 cm long, and measure the line from start to finish.

Forces at right angles

This gives a resultant of about 6.1 N at about 34° north of east.

Exact calculation uses components, which belong to a later stage.

Part 5 of 7Finding an unknown force

If an object moves at constant velocity, the resultant is zero, so an unknown force can be found by balancing. For a car at steady speed, driving force = resistive forces. A cyclist travelling at constant speed against a drag of 40 N must provide a 40 N driving force.

If the object accelerates, resultant = m × a, so the unknown force equals the resultant plus or minus the known forces.

Part 6 of 7Summary of the method

Draw the object with all forces on it.

Choose a positive direction.

Add the forces with their signs.

Zero means balanced; otherwise the sign shows the direction of the resultant.

Always state the direction of the resultant.

Summary of the method

A good habit is to write the answer as, for example, "40 N to the left", and to check that the sign of your number agrees with the arrow you drew.

When more than two forces act along a line, add all those to the right first,

then all those to the left, and subtract the smaller total from the larger.

Part 7 of 7Worked examples

A rocket sled has a thrust of 2500 N forwards and a total resistance of 1800 N backwards. Find the resultant force.
Two forces of 9.0 N and 12 N act on a block at right angles. Find the resultant and its angle to the 12 N force.
A crate is pulled along the floor at constant speed by a 60 N horizontal force. What is the friction force?

Key terms

Term	Meaning
Resultant force	Single force with the same effect as all forces acting.
Balanced forces	Forces whose resultant is zero.
Equilibrium	State where the resultant force on an object is zero.
Net force	Another name for resultant force.

Avoid these mistakes

Saying that if an object is moving there must be a resultant force in the direction of motion.

Adding forces without regard to direction.

Using Pythagoras when the forces are in the same line.

Forgetting that zero resultant allows constant velocity, not just rest.

Writing the answer without a direction.

Last updated: 20 October 2026