What a force is: pushes, pulls and the arrows that show them
By the end of this lesson you will be able to
- Define a force as an interaction between two objects — a push or a pull — measured in newtons (N).
- Draw a force as an arrow whose length shows its size, whose direction shows its direction and whose tail sits where the force acts.
- Identify the two objects in every interaction and state that each pushes or pulls the other with an equal force in the opposite direction.
- Classify forces as contact or non-contact.
- Measure a force with a newton meter and explain how a spring turns a force into a reading.
The puzzle
Push a wall as hard as you can. The wall does not move — but your hand flattens, your feet press into the floor and, if you stand on a skateboard, you roll backwards. You pushed the wall; what pushed you? Nothing touched you except the wall you were pushing.
List every force you can think of acting on a book lying still on a table. Then ask of each one: what object is doing the pushing or pulling, and what is it pushing or pulling on?
Compare your answer
Two forces act on the book: the Earth pulls it down (its weight — the Earth is the other object, and it does not need to touch the book), and the table pushes it up (the table’s surface is squashed very slightly and pushes back, like a very stiff spring). The book does not move because the two forces are equal and opposite. Most people list “gravity” but forget that the table is pushing; the habit of naming both objects in every force is what this unit is built on.
The science — structured notes
1.1 A force is an interaction between two objects
A force is a push or a pull. It always involves two objects: something doing the pushing or pulling, and something being pushed or pulled. There is no such thing as a force with only one object in it — you cannot push without pushing on something. So every force is an interaction, and the correct way to name a force is “the pull of A on B” or “the push of A on B”.
| Everyday description | The interaction, properly named | What each object does |
|---|---|---|
| “Gravity” | The pull of the Earth on the ball | Earth pulls ball down; ball pulls Earth up (the Earth is so massive it does not noticeably move) |
| “Friction” | The push of the floor on the sliding box, backwards | Floor pushes box backwards; box pushes floor forwards |
| “The kick” | The push of the boot on the football | Boot pushes ball forwards; ball pushes boot backwards (you feel it) |
| “Tension” | The pull of the rope on the bucket | Rope pulls bucket up; bucket pulls rope down |
A girl stands on the ground. Name the interaction pairs.
Interaction 1 (non-contact): the Earth pulls the girl down (her weight); the girl pulls the Earth up with an equal force.
Interaction 2 (contact): the ground pushes the girl up; the girl pushes the ground down.
Note what is not a pair: “the Earth pulls her down and the ground pushes her up” are two different interactions that happen to be equal because she is standing still. A pair always involves the same two objects swapped round.
1.2 Measuring forces: the newton
Force is measured in newtons (N). One newton is roughly the weight of a small apple, or of 100 g of anything on Earth. The pull of the Earth on 1 kg is about 10 N (more exactly 9.8 N). Forces are measured with a newton meter (force meter, spring balance): a spring that stretches in proportion to the force pulling it, with a scale marked in newtons.
| Force | Approximate size |
|---|---|
| Weight of a pen | 0.1 N |
| Weight of an apple, or of a 100 g mass | 1 N |
| Weight of a 1 kg bag of sugar | 10 N |
| Pull needed to open a fridge door | 20–40 N |
| Weight of a 50 kg student | 500 N |
| Push of a sprinter’s foot on the blocks | 1000–2000 N |
| Weight of a small car | 10 000 N |
| Thrust of a jet engine | 200 000 N |
A newton meter reads 0 N hanging empty and 3.0 N with a stone on the hook.
The stone’s weight — the pull of the Earth on it — is 3.0 N. The spring stretched until its upward pull on the stone equalled that; the reading is the spring’s pull, which is why it must be zeroed first.
The stone’s mass is about 3.0 ÷ 10 = 0.3 kg = 300 g. Mass (kg) is the amount of matter; weight (N) is the force the Earth exerts on it. They are different quantities with different units, and Lesson 1.3 returns to the difference on the Moon.
1.3 Force arrows — the picture that does the physics
A force has three things about it that matter: how big it is, which way it acts, and where it acts. All three fit in one arrow:
A box of weight 50 N is pushed to the right with 20 N; friction is 12 N. Draw the forces.
Down from the centre: “pull of Earth on box, 50 N” — the longest arrow.
Up from the floor: “push of floor on box, 50 N” — same length, opposite direction, tail on the underside.
Right, tail where the hand touches: “push of hand on box, 20 N”. Left, tail on the underside: “push of floor on box (friction), 12 N” — a little more than half the length of the 20 N arrow.
Reading the picture: up and down cancel; right beats left by 8 N; the box speeds up to the right. That last sentence is the whole of Lesson 1.4, already visible in the arrows.
For each situation, name every force on the object in bold as “the push/pull of … on …”, say whether it is contact or non-contact, and describe its arrow.
(a) A lamp hanging still from the ceiling on a cord.
(b) A ball at the top of its flight after being thrown straight up (ignore air).
(c) A magnet held just above a steel nail, so that the nail jumps up.
Reveal answer
(a) Pull of the Earth on the lamp — non-contact, arrow down from the centre; pull of the cord on the lamp (tension) — contact, arrow up from the hook. Equal length, since the lamp is still.
(b) Only one force: the pull of the Earth on the ball, non-contact, arrow down from the centre. The hand stopped touching it long ago, so there is no “push of the throw” — a very common error. The ball is momentarily still but the force is not zero, which is why it comes down.
(c) On the magnet: the pull of the Earth on the magnet (down, non-contact), the push of the hand on the magnet (up, contact) and the pull of the nail on the magnet (down, non-contact — the other end of the magnet’s pull on the nail, and just as real).
1.4 Contact and non-contact
Every force is one of two kinds:
| Contact forces | Non-contact forces | |
|---|---|---|
| Happen when | The two objects touch | The objects are apart; the force acts across the gap through a field |
| Examples | Friction, air resistance, water resistance (drag); the push of a surface (normal force); tension in a rope; upthrust from a liquid; the push of a spring | Gravity (weight); magnetic force; electrostatic force |
| Where the arrow starts | At the point of contact | At the centre of the object |
| This unit | Lesson 1.2 | Lesson 1.3 |
A cyclist feels the wind pushing her back. Nothing solid touches her. Contact or non-contact?
Contact. Air is made of particles (Year 1 Unit 6); billions of them hit her every second, and each collision is a tiny push. Air resistance, water resistance and the pressure of a gas are all contact forces from particles — the touching is just too small to see.
Non-contact means no particles cross the gap at all: a magnet lifts a nail through a vacuum; the Earth holds the Moon across 380 000 km of empty space.
1.5 How a spring measures a force
Every newton meter is a spring. Hooke’s law (Year 1 Unit 2 met the idea; this unit’s lab proves it) says the extension of a spring is proportional to the force stretching it, up to a limit: double the force, double the extension. A scale can therefore be marked in equal newton steps. Pull too hard and the spring passes its limit of proportionality: the extension grows faster than the force, and beyond the elastic limit the spring does not return to its original length — the meter is ruined and reads wrongly for ever after. Good meters have a stop to prevent it.
Try it — Hooke’s law
Hang masses on a spring in 50 g steps and record the extension each time. Convert each mass to a force (1 kg → 10 N, so 50 g → 0.5 N), plot extension against force, and find the straight line — then keep adding mass until the line bends and you have found the limit. Change the spring stiffness and repeat: which spring would make the more sensitive newton meter?
Suppose your results with a 30 N/m spring were: 0.5 N → 1.7 cm, 1.0 N → 3.3 cm, 1.5 N → 5.0 cm, 2.0 N → 6.7 cm, 2.5 N → 8.3 cm, 3.0 N → 10.0 cm.
(a) Describe the relationship, quoting values, and state whether it is proportional.
(b) The spring is used as a newton meter. Explain how a reading of 4.5 cm would be converted to a force, and why the meter must be zeroed with nothing on the hook.
(c) Explain why a stiffer spring (60 N/m) would be worse for measuring the weight of a pen but better for measuring the weight of a brick.
Reveal answer
(a) Extension increases with force: 1.7 cm at 0.5 N, 10.0 cm at 3.0 N. Doubling the force from 1.0 to 2.0 N doubles the extension from 3.3 to 6.7 cm, and the line passes through the origin, so extension is directly proportional to force — about 3.3 cm per newton.
(b) 3.3 cm corresponds to 1 N, so 4.5 ÷ 3.3 ≈ 1.4 N. The spring already has some length with nothing on it; only the extra length — the extension — is proportional to the force, so the scale must read zero at the unloaded length or every reading is offset by the same systematic error.
(c) A 60 N/m spring stretches half as far per newton (about 1.7 cm/N). A pen’s 0.1 N weight would move it under 2 mm, too small to read precisely; a 20 N brick would stretch the 30 N/m spring 67 cm — past its limit — but the stiffer spring only 33 cm, within range. Choose the spring so that the largest force to be measured gives a large extension still inside the proportional region.
Common mistakes to avoid
- A force with one object — “gravity” is the pull of the Earth on something; always name both.
- “The force of the throw” on a ball in flight — once contact ends, that force ends; only weight (and air) act.
- Mass in newtons, weight in kilograms — mass kg, weight N; on Earth 1 kg weighs about 10 N.
- Arrows all the same length — length shows size; equal forces get equal arrows, a 50 N arrow is five times a 10 N one.
- Arrows floating off the object — the tail sits where the force acts.
- Calling weight and the table’s push a “third-law pair” — they act on the same object; a pair is the same two objects swapped.
How we found out — the anagram and the apple
In 1660 Robert Hooke — the same Hooke who drew the cells in cork — discovered that a spring stretches in proportion to the load on it. He did not publish it. Scientists then had no patents, and a rival could claim any idea once it was printed, so in 1676 Hooke printed the discovery as a scrambled anagram, ceiiinosssttuv, and two years later revealed the Latin sentence hidden in it: ut tensio, sic vis — “as the extension, so the force”. It is the law inside every newton meter, every bathroom scale with a spring, and every bridge cable, and it made force something that could be measured rather than felt.
Hooke spent much of his life arguing with Isaac Newton, who in 1687 published the three laws of motion that this unit rests on. The first: an object keeps doing what it is doing unless a force acts. The second: force changes motion, in proportion to the force. The third — the one this lesson is built on — that every force is one end of an interaction, and the other end is equal and opposite. Newton also named the unit that measures all of it, though not on purpose: the newton was adopted in 1948, two centuries after his death. Hooke claimed Newton had taken the idea of gravity from him; Newton removed every mention of Hooke from his book. The spring and the laws of motion, which every physics student now uses together, were made by two men who could not be in the same room.
Hooke hid his law in an anagram; today a scientist publishes a discovery as fast as possible. What changed, and why does the modern system help science more?
Reveal answer
In the 1670s there was no reliable way to prove who had an idea first, so secrecy protected the discoverer at the cost of everyone else, who could not build on the hidden result. Journals with dated publication, peer review and citation give credit to the first to publish, so the incentive flips: publish quickly and clearly, and others must cite you. Science moves faster when results are shared than when they are hidden — Hooke’s anagram delayed the use of his own law by two years, and Newton’s feud with him hid the arguments of two of the best minds in England from each other.
Where it is used now
- Athletics. A sprinter’s start is an interaction: she pushes the blocks backwards and the blocks push her forwards with an equal force — which is why blocks are bolted down and why a soft track wastes energy. Botswana’s sprinters and their coaches measure that push with force plates in the blocks.
- Weighing. Every spring scale, luggage scale and market scale is Hooke’s law with a dial; every electronic scale replaces the spring with a strain gauge that measures a tiny bend the same way.
- Rockets and jets. An engine throws gas backwards; the gas pushes the engine forwards. There is nothing to “push against” in space and nothing is needed — the interaction is between rocket and exhaust.
- Engineering drawings. A bridge designer’s first document is a free-body diagram of each part: arrows for every load, every support and every cable, all named by their two objects.
- Sport and physiotherapy. A physiotherapist prescribes an exercise from the arrows on a joint; a rugby coach teaches a tackle from the direction of the push.
Science now — and the scientist you need to be
What is happening in 2026
Forces are now measured at every scale between the atom and the planet. An atomic force microscope drags a needle one atom wide across a surface and records forces of a few piconewtons — a million-millionth of a newton — to map single molecules; the same laboratories use light itself as tweezers, holding a bacterium in a focused laser beam with a force of a few piconewtons. At the other end, the force plates under a sprinter’s blocks and inside the soles of racing shoes sample thousands of times a second, and the data are used to redesign the shoes that have cut a second from marathon records. Between them sit the robots: a humanoid robot walking on rough ground is solving, sixty times a second, exactly the free-body diagram you drew today — every contact force on every foot, added by direction, to predict where it will go next. Understanding forces as interactions is what lets a machine, or a person, predict a movement before it happens.
The mindshift
What you need to be able to do
Two habits carry through this unit and into the eAssessment physics tasks. First, name forces by their two objects — “the push of the floor on the box” — because it stops you inventing forces that do not exist and forgetting ones that do. Second, draw arrows to scale, from the right point, with labels; examiner reports say force diagrams lose marks mostly through unlabelled arrows of random length. Every Criterion A explanation about motion in Years 2–5 begins with that diagram.
See an example
Sitting: pull of Earth on me 500 N down (non-contact, from my centre); push of chair on me 500 N up (contact, at the seat) — equal, so I stay put. Opening a door: pull of my hand on the door 15 N (contact, at the handle); push of the hinges on the door (contact); pull of Earth and push of hinges up and down cancel. Thrown ball at the top: pull of Earth on ball only, plus a small air-resistance push. The AI listed “gravity and the upward force from the throw” — wrong; I corrected it, and it agreed the hand stopped acting on release.
Key terms
| Force | A push or a pull — an interaction between two objects. Unit: newton (N). |
| Interaction pair | The two forces at the two ends of one interaction: A on B and B on A, equal in size and opposite in direction (Newton’s third law). |
| Newton (N) | The unit of force; the Earth pulls a 100 g mass with about 1 N and a 1 kg mass with about 10 N. |
| Weight | The pull of the Earth (or another planet) on an object; a force, in newtons. |
| Mass | The amount of matter in an object, in kilograms; the same everywhere. |
| Force arrow | An arrow whose length is the size of the force, whose direction is its direction, and whose tail is where it acts. |
| Free-body diagram | A diagram of all the forces acting on one object. |
| Contact force | A force between objects that touch: friction, air resistance, normal force, tension, upthrust. |
| Non-contact force | A force that acts across a gap through a field: gravity, magnetism, electrostatic force. |
| Newton meter | A spring with a scale in newtons; works because extension is proportional to force (Hooke’s law) up to the limit of proportionality. |
Think like a scientist
Criterion A A donkey cart on a Botswana road: the donkey pulls the cart forward along the harness; the cart’s wheels roll on the tarmac; a 40 kg load sits on the cart. The cart moves at a steady speed.
(a) Name every force acting on the cart as “the push/pull of … on …”, and classify each as contact or non-contact.
(b) Describe the free-body diagram of the cart, stating which arrows must be equal and why.
(c) A student says: “The cart pulls back on the donkey just as hard as the donkey pulls the cart, so they can never move.” Explain what is wrong with this argument.
(d) Calculate the weight of the load, and explain why “40 kg” is not its weight.
(e) Explain why the donkey’s hooves are the real source of the forward force on the cart, and what would happen on ice.
Model answer
(a) Pull of the harness (donkey) on the cart, forwards — contact. Push of the road on the wheels, backwards (rolling friction and axle friction) — contact. Push of the air on the cart, backwards (air resistance) — contact. Pull of the Earth on the cart and its load, downwards — non-contact. Push of the road on the wheels, upwards (normal force) — contact.
(b) One arrow up from the tyres (road’s push) and one arrow down from the centre (Earth’s pull): equal, because the cart neither rises nor sinks. One arrow forwards from the harness and arrows backwards from the wheels and the front (friction and air resistance) whose total equals the forward pull: equal, because the speed is steady — a steady speed means the forces are balanced, not that the forward force is bigger.
(c) The two forces the student names act on different objects: the donkey’s pull acts on the cart, the cart’s pull acts on the donkey. Forces on different objects cannot cancel each other. Whether the cart moves depends only on the forces on the cart (harness forwards against friction backwards); whether the donkey moves depends on the forces on the donkey (the road’s push on its hooves forwards against the cart’s pull backwards). Each can have an unbalanced force even though the pair is equal.
(d) Weight = mass × 10 N/kg = 40 × 10 = 400 N. 40 kg is the mass — the amount of matter — which would be the same on the Moon; the weight is the Earth’s pull on that matter, a force in newtons, and it would be about 65 N on the Moon.
(e) The donkey pushes its hooves backwards against the road; the road pushes the hooves forwards (friction, an interaction pair). That forward push on the donkey is transmitted through the harness to the cart. The donkey cannot pull the cart without something to push against. On ice friction is tiny, the road cannot push the hooves forwards, the hooves slide back, and the donkey and cart go nowhere however hard it strains.
Probe deeper — exam-style questions
Attempt every question before opening the answer. Marks in brackets show what a full answer is worth.
Define a force and state its unit.
Reveal answer
A push or a pull — an interaction between two objects [1]; the newton, N [1].
State the three things a force arrow shows.
Reveal answer
Its length shows the size of the force [1]; its direction shows the direction of the force [1]; its tail shows the point where the force acts on the object [1].
A student’s diagram of a book on a table shows one arrow labelled “gravity 5 N” pointing down and one labelled “the book 5 N” pointing up, both starting from a point beside the book. Identify three errors.
Reveal answer
“Gravity” names one object — it should be “pull of the Earth on the book” [1]; the upward force is the push of the table on the book, not “the book” [1]; the arrows must start on the book (weight from its centre, the table’s push from the underside), not beside it [1].
A newton meter stretches 2 cm for every 1 N. It reads 6 cm with a stone on the hook. Calculate the stone’s weight and mass, and state what the meter would read if the spring were twice as stiff.
Reveal answer
Weight 6 ÷ 2 = 3 N [1]; mass 3 ÷ 10 = 0.3 kg (300 g) [1]; a spring twice as stiff stretches half as far per newton, so 3 cm for the same 3 N — the same force, a smaller extension [1].
True or false, with a reason: “When a car crashes into a wall, the wall pushes the car less hard than the car pushes the wall, because the wall does not move.”
Reveal answer
False [1]: the two pushes are one interaction and are equal and opposite; the wall does not move because it is fixed to the ground, not because it is pushed less — the car crumples because the same force acts on a much lighter, weaker object [1].
An astronaut floating outside a space station throws a spanner away from her. Explain, using interactions, what happens to her, and why she cannot “swim” back to the station by moving her arms.
Reveal answer
She pushes the spanner one way, so the spanner pushes her the other way with an equal force (an interaction pair) and she drifts away from the spanner [1]; the spanner, being lighter, moves faster, but both move [1]; swimming works by pushing on water, which pushes back — in space there is nothing to push on, so moving her arms produces no external force and she cannot change her drift; only throwing something (or a gas jet) can [1].
Summary
- A force is a push or pull between two objects; name both — “the pull of the Earth on the ball”.
- Every force is one end of an interaction; the other end is equal and opposite and acts on the other object.
- Force is measured in newtons; 1 kg weighs about 10 N on Earth. Mass in kg, weight in N.
- Draw a force as an arrow: length = size, direction = direction, tail = where it acts, label = the interaction.
- Contact forces need touching (friction, air resistance, normal, tension, upthrust); non-contact forces act through fields (gravity, magnetic, electrostatic).
Next time → Friction and the other contact forces: why you can walk, why brakes work, and why a wet floor is dangerous.