What is a force?

A force is a push or a pull. Every force has a size and a direction, so we draw it as an arrow: the longer the arrow, the bigger the force. Quantities with a direction are called vectors.

Force is measured in newtons (N). One newton is the push that makes 1 kg speed up by 1 m/s every second. It is about the weight of a small apple (100 g). Lifting a 1 litre bottle of water takes about 10 N; your whole body weighs several hundred.

You can measure a force with a spring scale, or newton meter. Pull on it and the spring stretches in proportion to the force (that's Hooke's law, see HookeClear), so the marks are evenly spaced.

When several forces act on one thing, you add them as arrows: put them tip to tail, and the arrow from the start to the end is the net force (or resultant). Two equal forces in opposite directions add up to zero: the forces are balanced. A pull of 30 N and a push of 40 N at right angles add up to 50 N, not 70 N.

Only the net force changes how something moves: a = F ÷ m, Newton's second law (see NewtonClear). Engineers draw a free-body diagram: one object, with every force on it as an arrow. Here the table pushes up (the normal force) exactly as hard as gravity pulls down (the weight), so those two cancel.

Mass is how much stuff something is made of, in kilograms. Weight is a force: the pull of a planet on that mass, in newtons. W = m × g, where g is the pull on each kilogram: 9.81 N/kg on Earth, 1.62 on the Moon and about 24.8 at Jupiter’s cloud tops. A 5 kg bag of rice weighs 49 N here, 8 N on the Moon and 124 N on Jupiter, yet it is the same rice.

A spring balance measures the force, so it reads differently on each world. A pan balance compares one mass with another, so it balances anywhere.

A bathroom scale doesn’t measure your weight directly either. It measures how hard it has to push up on your feet: the normal force. In a lift that is speeding up on the way up, the floor must push you up harder than gravity pulls you down, so the scale reads more: N = m (g + a). As the lift slows at the top, it reads less. The steel ropes carry the whole car the same way: their pull, the tension, is about 11,000 N for a small lift with one passenger.

Squeeze a spring and it pushes back, harder the more you squeeze it. The little spring in a click pen pushes back with about 2 N when the tip is out, enough to snap the refill back when you click again (see PenClear and HookeClear).

Machines are force movers. On a bicycle, your foot pushes down on the pedal, the crank turns the chainring, and the chain carries the pull back to the wheel. Because the chainring is smaller than the crank is long, the chain tension is bigger than your push: stand on a pedal with 700 N and the chain pulls with about 1,300 N (see CycleClear). Only the part of your push at right angles to the crank counts, so the pull peaks when the crank is level and drops to nothing at the top and bottom.

A car stops because its tyres grip the road. The road pushes back on each tyre with friction, and the most it can give is about μ × weight: roughly 10,000 N for a 1,300 kg car on a dry road, far less on ice. The same force decides the stopping distance, v² ÷ (2 μ g). Inside, the seat belt pulls you back with the force needed to slow you with the car: about 550 N in hard braking, but about 7,500 N in a 50 km/h crash (see CarClear, and the seat belt in NewtonClear).

A washing machine spinning at 1,000 rpm has to push every sock towards the middle of the drum, or the sock would fly off in a straight line. That inward push is F = m ω² r: about 250 N on a 100 g wet sock, the weight of a 25 kg bag. Water gets no such push through the holes, so it leaves. A heavy lump of towels on one side pulls the whole drum around with thousands of newtons, which is why machines shuffle the load before they spin (see WasherClear).

Forces always come in pairs. If the rocket pushes the hot gas down, the gas pushes the rocket up just as hard. If your foot pushes the ground backwards, the ground pushes your foot forwards. A fan throws air forwards, and the air pushes the fan back. This is Newton's third law (see NewtonClear). The trick is that the two forces of a pair act on different objects, so they never cancel each other out.

A rocket's push, its thrust, is the mass of gas thrown out each second times how fast it goes: F = ṁ × v. It lifts off only when thrust is bigger than its weight. On slippery ice the ground can't push your foot forwards hard enough, so you can't walk. A desk fan pushes with only a newton or two, but on a skateboard that is enough to roll it backwards (see FanClear).

When the forces on one object add up to zero, they are balanced and the object stays still. A bridge is a balancing act: the two supports push up exactly as hard as the deck and the traffic push down, and the support nearer the car takes more of its weight. A bookshelf bracket does the same job for your books.

On a ramp, it helps to split the weight into two parts, called components: one along the slope, mg sin θ, trying to slide the crate down, and one into the slope, mg cos θ, which the ramp pushes back against. Friction holds the crate until the slope gets too steep: that happens when tan θ is bigger than μ.

Friction, springs, the push of a chair, the tension in a rope: they seem like many kinds of force. Deep down, physicists know of only four fundamental forces. The strong force glues the nucleus of every atom together. The electromagnetic force acts between electric charges and magnets, and it is behind almost every everyday push and pull, because touching is really electrons repelling electrons. The weak force changes one kind of particle into another in radioactive decay. Gravity pulls every mass towards every other mass.

Gravity is by far the weakest: between two protons, the electric push is about 10³⁶ times stronger than their gravity. A fridge magnet lifts a paper clip against the pull of the entire Earth. Gravity wins on big scales only because it always attracts and never cancels out.

Myth: you need a force to keep something moving. It feels true, because friction and air slow everything down. But a force changes motion, it doesn't maintain it. Push a crate with exactly as much force as friction and it glides at a steady speed: the net force is zero. Without friction it would keep going with no push at all, like a spacecraft coasting.

Myth: centrifugal force flings things outwards. Whirl a ball on a string and it seems to pull outwards. Really the string pulls the ball inwards, bending its path into a circle. Let go and the ball flies off in a straight line along the tangent, not outwards. The outward "force" is just your hand feeling the ball's inertia.

Myth: heavier things need more force to fall, so they fall faster. A heavier ball does get more pull: exactly as much more as it has more mass to move. So everything falls with the same acceleration, g. Only air resistance slows a feather (see NewtonClear for the hammer and feather dropped on the Moon, and MotionClear for falling).