Two forces of 12\ N and 7\ N act on a box in opposite directions. Find the resultant force. [2 marks]

SEAB Original-style practice: A sled is pulled with a forward force of 50\ N while friction of 20\ N acts on it. The sled has a mass of 15\ kg. (a) Find the resultant force. (b) Find the acceleration.

(a) Friction opposes the pull, so the resultant force is 50 - 20 = 30\ N in the forward direction. (b) Using F = ma: a = Fm = 3015 = 2.0\ m s^-2. Markers reward subtracting friction to find the resultant force, stating its direction, and using F = ma to get the acceleration with units.

SingaporePhysicsSyllabus dot point

How do we combine several forces into a single resultant, and what role does friction play?

Find the resultant of forces acting in a line, and describe the effects of friction on motion

A focused answer to the O-Level Physics outcome on resultant force and friction. Adding forces in a straight line, balanced versus unbalanced forces, friction as a contact force opposing motion, and its useful and wasteful effects.

Generated by Claude Opus 4.87 min answerUpdated 2026-06-06

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

SEAB wants you to combine forces that act along the same straight line into a single resultant force, to tell balanced from unbalanced forces, and to describe friction as a contact force that opposes motion, including both its useful and its wasteful effects. The big idea is that motion depends on the resultant, not on the individual forces.

The answer

Adding forces in a line

When forces act along the same line, find the resultant by adding those in one direction and subtracting those in the opposite direction.

Forces in the same direction add.
Forces in opposite directions subtract; the resultant points the way of the larger.

F_{\text{resultant}} = \text{(forces one way)} - \text{(forces the other way)}

Balanced and unbalanced forces

If the resultant force is zero, the forces are balanced: the object stays at rest or keeps moving at constant velocity (Newton's first law). If the resultant is not zero, the forces are unbalanced and the object accelerates in the direction of the resultant.

What friction is

Friction is a contact force that acts along surfaces in contact and opposes motion or the tendency to move. It arises because no surface is perfectly smooth. Friction acts backward when an object slides forward, so it tends to slow things down and turn kinetic energy into heat.

Useful and wasteful friction

Friction is essential as well as a nuisance.

Useful: walking (shoes grip the ground), braking, gripping objects, writing.
Wasteful: friction in machine parts wastes energy as heat and wears surfaces.

To reduce unwanted friction, lubricate surfaces with oil, use rollers or ball bearings, or make surfaces smoother. To increase useful friction, make surfaces rougher (tyre tread, brake pads).

Air resistance and drag

Air resistance is friction with the air. It grows with speed, which is why a falling object eventually reaches terminal velocity when air resistance balances weight.

Worked example

A $20\ \text{kg}$ crate is pushed across a floor with a force of $80\ \text{N}$ . Friction between the crate and floor is $30\ \text{N}$ . (a) Find the resultant force. (b) Find the acceleration. (c) State what happens if the push is reduced to $30\ \text{N}$ .

Step 1: Find the resultant force

Friction opposes the push: $F_{\text{resultant}} = 80 - 30 = 50\ \text{N}$ forward.

Step 2: Find the acceleration

Use $F = ma$ : $a = \dfrac{50}{20} = 2.5\ \text{m s}^{-2}$ forward.

Step 3: Consider the reduced push

If the push is $30\ \text{N}$ , it exactly balances the $30\ \text{N}$ friction, so the resultant is zero. The crate then moves at constant velocity if already moving, or stays at rest if it was still.

So a $80\ \text{N}$ push accelerates the crate, but a $30\ \text{N}$ push only balances friction and produces no acceleration. The resultant force is what matters.

Examples in context

Example 1. A tug of war. Two teams pull a rope in opposite directions. The resultant force is the difference between the two pulls, and the rope (and flag) accelerates toward the stronger team. When the pulls are equal the resultant is zero and the flag stays put, a balanced-forces situation.

Example 2. Oil in an engine. Engine parts slide past each other thousands of times a second, and friction would wear them out and waste energy as heat. Oil lubricates the surfaces, cutting the friction so less energy is wasted and the parts last longer, a direct application of reducing unwanted friction.

Try this

Q1. Two forces of $12\ \text{N}$ and $7\ \text{N}$ act on a box in opposite directions. Find the resultant force. [2 marks]

Cue. $12 - 7 = 5\ \text{N}$ in the direction of the $12\ \text{N}$ force.

Q2. State what happens to an object when the resultant force on it is zero. [2 marks]

Cue. It stays at rest or continues to move at constant velocity in a straight line.

Q3. Give one example where friction is useful and one where it is unwanted. [2 marks]

Cue. Useful: gripping the ground when walking (or braking). Unwanted: heat and wear in the moving parts of a machine.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original4 marksA sled is pulled with a forward force of

50\ \text{N}

while friction of

20\ \text{N}

acts on it. The sled has a mass of

15\ \text{kg}

. (a) Find the resultant force. (b) Find the acceleration.

Show worked answer →

(a) Friction opposes the pull, so the resultant force is $50 - 20 = 30\ \text{N}$ in the forward direction.

(b) Using $F = ma$ : $a = \dfrac{F}{m} = \dfrac{30}{15} = 2.0\ \text{m s}^{-2}$ .

Markers reward subtracting friction to find the resultant force, stating its direction, and using $F = ma$ to get the acceleration with units.

Original4 marks(a) State two situations in which friction is useful and one in which it is a nuisance. (b) State one way to reduce unwanted friction between two surfaces.