Forces, balanced & unbalanced

What you will learn

what a force is, its units (newtons), and how to draw it as an arrow,
the main types of force: gravity, normal, friction, tension, air resistance, applied,
how to draw a free-body diagram and calculate the net force,
the difference between balanced and unbalanced forces and what each does to motion,
how mass and net force determine acceleration (conceptually: Newton’s second law).

Worked example 0 Real-world example: why a book on a desk is still

A textbook sits on a table. Gravity pulls it down with a force of $10$ N. What holds it up?

The table pushes back on the book with an equal upward force — called the normal force — of $10$ N.
The two forces are equal in size and opposite in direction.
Net force $= 10 - 10 = 0$ N.
With zero net force, motion does not change — the book stays still.

Key idea: “at rest” does not mean “no forces” — it means the forces balance out to zero. Whenever the net force is zero, motion is unchanged.

1. What is a force?

A force is a push or a pull. It can:

Start something moving,
Stop something moving,
Change an object’s direction or shape.

Force is measured in newtons (N). On Earth, an object of mass $1$ kg weighs about $10$ N. Forces are drawn as arrows: the length shows size, the direction shows which way the force pushes.

2. Types of force

Contact forces require touching:

Friction — opposes sliding between surfaces.
Normal (support) force — a surface pushes back on an object resting on it.
Tension — pull along a rope, string or cable.
Air resistance — a friction-like force from the air on a moving object.
Applied force — a push or pull that you apply directly.

Non-contact forces act across space:

Gravity — attraction between masses.
Magnetic — between magnets or between a magnet and iron/steel.
Electrostatic — between electric charges.

Worked example 1 Classifying forces in a real situation

A gymnast swings on a rope. List the forces on the gymnast.

Gravity — downward (non-contact).
Tension in the rope — along the rope toward where it is tied (contact).
Air resistance — small, opposite to motion (contact).

Key idea: nearly every real situation involves several forces at once. Always ask “is there a surface touching the object? Is there a rope? Is gravity acting?“

3. Free-body diagrams and net force

A free-body diagram shows the object as a dot or box with every force drawn as an arrow from it.

Free-body diagrams. Left: book at rest on a table (balanced). Right: box being dragged across a floor with friction (unbalanced forward).

The net force is the single force that has the same effect as all the individual forces combined.

Net force (one dimension)

Forces along a line

Take one direction as positive (e.g. right). Add forces in that direction; subtract forces in the opposite direction.

F_{\text{net}} = F_1 + F_2 + \ldots - F_{\text{opposite}}

Worked example 2 Adding forces along one direction

A box is pulled right with $30$ N; friction pulls left with $10$ N. Find the net force.

F_{\text{net}} = 30 - 10 = 20 \text{ N to the right}.

Net force is not zero, so the box accelerates to the right.

Worked example 3 Tug-of-war

Team A pulls right with $250$ N. Team B pulls left with $220$ N. What is the net force and which team moves?

F_{\text{net}} = 250 - 220 = 30 \text{ N to the right}.

The rope (and everyone holding it) accelerates to the right — Team A wins.

4. Balanced vs unbalanced forces

Balanced: forces cancel; net force is zero; motion does not change. The object stays at rest or keeps moving at constant speed in a straight line.
Unbalanced: there is a leftover net force; the object’s motion changes — it speeds up, slows down, or changes direction.

Worked example 4 Cyclist at constant speed

A cyclist pedals at steady $20$ km/h on flat ground. Air resistance + friction together add up to $40$ N backwards. What forward force is the cyclist producing?

Steady speed → balanced forces → net force is zero.

Therefore the forward force from pedalling = $40$ N.

Key idea: constant speed in a straight line means the forces are balanced, even though the cyclist is working hard.

5. Mass, weight and acceleration

Mass is how much matter is in an object, measured in kilograms. Constant everywhere.
Weight is the force of gravity on that mass, measured in newtons. Depends on where you are.

Weight

Weight from mass

W = m g

where $g$ is the gravitational field strength. On Earth $g \approx 10$ N/kg.

Worked example 5 Mass vs weight

Your mass is $50$ kg. Find your weight on Earth and on the Moon (where $g \approx 1.6$ N/kg).

Earth: $W = 50 \times 10 = 500$ N.
Moon: $W = 50 \times 1.6 = 80$ N.

Mass stays at $50$ kg in both places — only the pull of gravity changes.

Newton’s second law (conceptually): the bigger the unbalanced force, the bigger the acceleration. The bigger the mass, the smaller the acceleration for the same force.

F_{\text{net}} = m \times a

Practice: Year 7

Fluency

Tier 1: recall and identify

What is a force? Give its unit.
Give two contact forces and two non-contact forces.
Define “net force”.
What is the difference between mass and weight?
A box is pushed right with $25$ N and friction pulls left with $10$ N. Find the net force.
A bag weighs $200$ N on Earth. What is its mass?
Explain what a free-body diagram shows.
Two students pull on a rope; each pulls $50$ N in opposite directions. What is the net force? Describe the motion.
An object in space has no air resistance. If a small thruster pushes it for one second and then stops, what happens next?
A person has a mass of $60$ kg. What is their weight on Earth? ( $g = 10$ N/kg.)

Reasoning

Tier 2: explain and reason

Explain why a book on a table stays still even though gravity pulls it down.
A car travels at a constant $80$ km/h in a straight line. Are the forces on it balanced or unbalanced? Justify.
A parachutist falls at terminal velocity. Draw a labelled free-body diagram and describe the net force.
Why does it take more force to push a heavy box than a light one to the same acceleration?
Explain why your mass is the same on the Moon but your weight is less.
A satellite orbiting Earth moves at constant speed in a curve. Is the net force zero? Justify.

Problem solving

Tier 3: apply to a novel context

A rocket engine provides $5000$ N upward. The rocket’s weight is $4000$ N. Find the net force and describe what happens.
A $3$ kg trolley is pushed with a net force of $12$ N. Find its acceleration using $F = ma$ .
A skydiver initially accelerates downward. Describe the forces at (a) the moment of jumping, (b) mid-fall as speed rises, (c) at terminal velocity.
Two dogs pull on a lead attached to a post. Dog A pulls north with $80$ N; Dog B pulls east with $60$ N. Describe qualitatively the direction the post would be pulled (assume the post is only loosely set).

Challenge

Reasoning

Harder reasoning

A car of mass $1200$ kg accelerates from $0$ to $20$ m/s in $10$ seconds. Find its acceleration and the net force required. How is this force generated?
Explain using forces why a person in a lift feels momentarily “heavier” when the lift starts going up and “lighter” when it starts going down.
A rock with weight $50$ N on Earth is taken to a planet where gravity is $3\times$ Earth’s. State its mass, weight on that planet, and one everyday consequence for the astronaut.
Two skaters push off from each other on smooth ice: a $40$ kg skater and a $60$ kg skater. Predict which moves faster and justify using forces and mass.