What is a force?

One newton is about the weight of a small apple held in your hand.

Pushes and pulls

In everyday language a force is a push or a pull. You push a door, pull a drawer, kick a ball, lean on a wall. In physics a force is anything that can change an object’s motion or shape: start it moving, stop it, speed it up, slow it down, turn it, squash it or stretch it. A force always acts between two objects. Your hand pushes the door; the Earth pulls the apple; the road pushes on the tyres. If you cannot name the second object, you have probably not found a real force.

Some forces need contact: friction between a box and the floor, the tension in a rope, the push of the floor holding you up (called the normal force, because it acts at right angles to the surface), and the drag of air or water. Others act across empty space: gravity, the electric force between charges and the magnetic force between magnets. The Sun’s gravity reaches across 150 million kilometres of near-empty space to hold the Earth in its orbit.

Measuring force in newtons

Force is measured in newtons (N), named after Isaac Newton. One newton is the force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N = 1 kg·m/s². That sounds abstract, but it is a small, everyday amount. A small apple of about 100 g weighs about 1 N on Earth. Holding a 1 kg bag of sugar takes about 9.8 N. A spring scale, the kind used to weigh luggage, measures force directly: the spring stretches in proportion to the pull.

Forces add like arrows

Force is a vector, so direction matters. Two people pulling a cart the same way with 30 N and 20 N give a total of 50 N. If they pull in opposite directions, the total is 30 − 20 = 10 N towards the stronger one. The total of all the forces on an object is called the net force. When forces at right angles combine, you add them as the sides of a right triangle: 3 N east and 4 N north make 5 N towards the north-east, by Pythagoras.

When the forces on an object cancel, the net force is zero and the forces are balanced. A book resting on a table is a good example: gravity pulls it down and the table pushes it up just as hard. In a tug of war where neither side moves, both teams may be pulling with hundreds of newtons, but the net force on the rope is zero. Unbalanced forces are the ones that change motion, which is the subject of Newton’s laws in the next lesson.

Free-body diagrams

Physicists sort out forces with a free-body diagram: draw the object as a box or a dot, then draw one arrow for each force acting on it, starting at the object and pointing the way the force acts. The arrow lengths show the sizes. For a crate being pushed across a floor there are four arrows: the weight W pulling down, the normal force N pushing up, your push F, and friction f pointing back against the motion.