What is force? Pushes, pulls and the newton, explained

In physics, a force is a push or a pull on an object that can change how it moves: start it, stop it, speed it up, slow it down or turn it. Force is what a kick, a magnet, a rope and gravity have in common. It is measured in newtons and always has a direction as well as a size. When several forces act at once, what counts is their total, the net force.

In short

• A force is a push or pull with a size and a direction. One newton is the force that speeds up 1 kg by 1 meter per second every second.
• Forces add like arrows. Equal forces pulling opposite ways cancel, and only a net force changes motion.
• Every force in nature comes from four fundamental ones, and all the everyday pushes except weight are electromagnetic.

How is force measured?

The unit of force is the newton, N, named after Isaac Newton. The International System of Units defines it from the base units as a kilogram meter per second squared: one newton is the force that makes a 1 kg mass speed up by 1 m/s every second. That comes from Newton's second law, F = ma, force equals mass times acceleration, which is covered with the other two laws in the Newton's laws note.

A newton is small. A medium apple, about 100 grams, weighs about 1 newton, since gravity pulls on each kilogram with about 9.8 newtons at Earth's surface. An adult of 70 kg weighs about 690 newtons. In the United States, force is often given in pounds (strictly pound-force), and 1 pound-force is about 4.45 newtons.

Force is easy to confuse with three related ideas, because everyday speech uses all of them loosely:

Quantity	What it is	Unit	Example
Force	A push or pull, with a direction	Newton (N)	The 690 N with which a 70 kg person presses down on the floor
Pressure	Force spread over an area	Pascal (Pa), 1 N per square meter	The same person on stiletto heels presses far harder per square centimeter than in flat shoes
[[what-is-energy	Energy]]	The capacity to do work, which is force times distance moved	Joule (J), 1 N over 1 meter
[[what-is-momentum	Momentum]]	Mass times velocity, how hard something is to stop	Kilogram meter per second

A moving object doesn't "have" a force. It has momentum and energy, and a force is what changes them.

How do forces add up?

Because forces have direction, they add like arrows, not like plain numbers. Physicists draw a free-body diagram, a sketch of one object with an arrow for every force on it, and then add the arrows.

• Same direction: two people push a stalled car forward, one with 300 N and one with 200 N. The net force is 500 N forward.
• Opposite directions: in a tug of war, one team pulls with 2,000 N and the other with 2,000 N. The net force is zero, and the rope doesn't accelerate, even though each team is straining hard.
• At an angle: one rope pulls a box east with 30 N and another pulls it north with 40 N. The net force points between them, at about 53° north of east, and its size is the long side of a right triangle: √(30² + 40²) = 50 N, not 70 N.

A book resting on a table has forces on it; they just cancel. Gravity pulls it down, and the table pushes it up with an equal force, the normal force. Zero net force means no change in motion, which is why it stays put. It does not mean no forces are acting.

A worked example: what stops a braking car?

Take a 1,000 kg car moving at 20 m/s, about 72 km/h, on a flat, dry concrete road. Walk through the forces on it.

1. Down: its weight, mass × gravity = 1,000 × 9.81 = 9,810 N.
2. Up: the normal force from the road, also 9,810 N. Up and down cancel, so the car neither sinks nor lifts off.
3. Backward: friction between the tires and the road. The brakes grip the wheels, but it is the road pushing back on the tires that slows the car.
4. A gentle stop: to slow at 5 m/s², the net backward force must be mass × deceleration = 1,000 × 5 = 5,000 N. The car stops in 20 ÷ 5 = 4 seconds and covers 20² ÷ (2 × 5) = 40 meters.

How hard could it stop? Friction has a limit: the friction coefficient times the normal force. OpenStax College Physics gives rubber on dry concrete a static coefficient of 1.0 while the tire still grips, but only 0.7 once it is skidding, and 0.5 for a skid on wet concrete.

Situation	Most friction available	Deceleration	Stopping distance from 20 m/s
Dry, tires gripping	1.0 × 9,810 = 9,810 N	9.8 m/s²	About 20 m
Dry, wheels locked and skidding	0.7 × 9,810 = 6,870 N	6.9 m/s²	About 29 m
Wet, wheels locked and skidding	0.5 × 9,810 = 4,905 N	4.9 m/s²	About 41 m

Two things fall out of the arithmetic. First, a gripping tire stops the car in less distance than a skidding one, which is why anti-lock brakes pulse to keep the wheels turning. Second, the car's mass cancels: a heavier car has more weight pressing its tires down and so more friction available, but also more mass to stop. In this simple model, a truck and a hatchback on the same tires would stop in the same distance. Real vehicles differ because of their tires, brakes and load, and these idealized figures leave out reaction time and air resistance.

What are the four fundamental forces?

Every force known, from a handshake to the pull that holds a galaxy together, comes from one of four fundamental interactions:

Force	Strength compared with the strong force	Range	What it does
Strong nuclear	1	About the width of a nucleus	Binds quarks into protons and neutrons, and those into nuclei
Electromagnetic	About 10⁻²	Unlimited	Holds electrons to atoms and atoms to each other; light, electricity, magnetism
Weak nuclear	About 10⁻⁶	Less than 10⁻¹⁸ m	Drives some radioactive decay and the first step of fusion in the Sun
Gravity	About 10⁻³⁸	Unlimited	Pulls every mass toward every other mass

The strengths, from OpenStax's overview of the four basic forces, are rough comparisons at the scale of a nucleus. To see how weak gravity is, compare two protons. Their electric repulsion is k × e² ÷ r² and their gravitational attraction is G × m² ÷ r², so the distance cancels in the ratio: (8.99 × 10⁹ × (1.60 × 10⁻¹⁹)²) ÷ (6.67 × 10⁻¹¹ × (1.67 × 10⁻²⁷)²), which is about 10³⁶. The electric push is a trillion trillion trillion times stronger.

Gravity rules the large scale anyway, for two reasons: it only ever attracts, and it builds up with mass. Electric charges come in positive and negative and mostly cancel in bulk matter, so a planet is almost perfectly neutral, but its gravity adds up atom by atom.

Where do everyday forces come from?

The forces in daily life go by many names: friction, the normal force, tension in a rope, air resistance, the push of a spring, the lift on a wing. Apart from weight, which is gravity, every one of them is electromagnetic. When your hand presses a table, no atoms touch in the way the word suggests; the electrons on the surface of your hand and those on the table repel each other. Friction comes from atoms at two surfaces attracting and catching on each other. Tension is the electrical bonds between a rope's molecules resisting being pulled apart, which is the subject of the chemical bond note.

Physicists have already shown that two of the four are connected: at very high energies the electromagnetic and weak forces merge into one electroweak force, work that earned Sheldon Glashow, Abdus Salam and Steven Weinberg the 1979 Nobel Prize in Physics. The Standard Model describes the strong, weak and electromagnetic forces with carrier particles: gluons, the W and Z bosons, and the photon. Gravity is described separately, by Einstein's general relativity, as the bending of space and time by mass and energy, and no one has yet joined it to the other three.

Check yourself

• Without looking back, explain why a book resting on a table has forces on it but doesn't move.
• In the braking example, what actually pushes the car backward, and why does a skidding tire stop it in a longer distance?
• If the electric force between two protons is about 10³⁶ times stronger than gravity, why does gravity dominate the motion of planets?

Sources

• International System of Units (SI): units — National Institute of Standards and Technology
• Development of force concept — OpenStax, College Physics 2e
• Friction — OpenStax, College Physics 2e
• The four basic forces: an introduction — OpenStax, College Physics 2e
• The Nobel Prize in Physics 1979 — Nobel Prize Outreach
• Fundamental interaction — Wikipedia