Forces and Newton's laws

Hit the same puck across a carpet and it stops almost at once. So something about the surface matters. But notice the bigger puzzle. Once the stick leaves the puck, nothing is pushing it forward. Why does it keep moving at all?

Aristotle's answer was that moving things need a steady push, and they stop when the push ends. That matches everyday life: stop pedaling and a bike slows down. It took Galileo and then Isaac Newton to see that everyday life was hiding something. This lesson covers Newton's three laws of motion, which explain why things move the way Lesson 1 described (Urone & Hinrichs, 2022).

A force is a push or a pull. A stick hitting a puck, a magnet tugging a paper clip, and Earth pulling you down are all forces. A force has a size and a direction, so it is a vector, the same kind of quantity as velocity in Lesson 1. Physicists draw forces as arrows.

Force is measured in newtons (N), named for Isaac Newton. One newton is about the weight of a small apple in your hand.

Usually several forces act on an object at once. What matters is the net force: all the forces added together, arrows and all. Two equal pulls in opposite directions add up to zero. Figure 2.1 shows a tug-of-war both ways.

Galileo answered with a thought experiment. Roll a ball down one ramp and up a second ramp facing it. On very smooth ramps, the ball climbs back to nearly the height it started from. Now make the second ramp less steep. The ball still climbs to the same height, so it rolls farther to get there. Lay the second ramp flat, and the ball never reaches its starting height. It just keeps rolling (Galilei, 1638/1914). Figure 2.2 draws the three cases.

Newton made this his first law of motion: an object stays at rest, or keeps moving at the same speed in a straight line, unless a net force acts on it (Newton, 1687/1999). This tendency to keep its current motion is called inertia.

You feel inertia all the time. When a car brakes hard, your body keeps going forward until the seatbelt pushes back on you. In the old tablecloth trick, a quick yank pulls the cloth out while the dishes, with their inertia, barely move.

Inertia depends on mass, the amount of matter in an object, measured in kilograms. A loaded truck has far more inertia than a bicycle. It takes more force to get it moving, and more force to stop it.

Because a force is acting on it after all. Friction is the force between two surfaces that resists their sliding past each other. It always points against the direction of sliding (Urone & Hinrichs, 2022). Air resistance, from Lesson 1, adds a little more drag.

Carpet grips a puck hard, so friction is large and the puck stops fast. Ice is very slippery, so friction is small and the puck slides a long way. Why ice is so slippery is still being studied. A very thin, liquid-like layer on the surface of ice plays a big part (Rosenberg, 2005).

So Aristotle had it backward. Moving things do not need a force to keep going. They need a force to stop. On Earth, friction is almost always there, which is why it looked as if motion simply runs down.

Newton's second law of motion answers this. The acceleration of an object equals the net force on it divided by its mass. It is usually written the other way around:

net force = mass × acceleration (F = ma)

Double the force and you double the acceleration. Double the mass and the same force gives only half the acceleration. Push an empty shopping cart and it jumps forward. Give a full cart the same push and it barely gets going. This also defines the newton: 1 newton is the force that gives a 1-kilogram mass an acceleration of 1 m/s² (Urone & Hinrichs, 2022). Figure 2.3 works through the numbers.

In Figure 2.4, a puck is pushed to 10 meters per second, about 22 mph, and then let go. After that, the only sideways force on it is friction. Choose a surface and press Push. Watch the friction arrow, and watch what happens with no friction at all.

No. Mass is how much matter an object has, and so how much inertia. Weight is a force: the pull of gravity on that mass. By the second law, weight equals mass times g, the 9.8 m/s² from Lesson 1.

weight = mass × g

A 70-kilogram person weighs about 690 newtons on Earth. On the Moon, where gravity is about one sixth as strong, the same person weighs about 113 newtons. Their mass is still 70 kilograms, so they are just as hard to push sideways or to stop.

This finishes the story from Lesson 1. A bowling ball has more mass than a baseball, so gravity pulls on it with more force. But it also has more inertia, in exactly the same proportion. Divide the bigger pull by the bigger mass, and the acceleration comes out the same: g. That is why, without air, everything falls together.

A free-body diagram draws one object and every force acting on it, as arrows. Figure 2.5 is the free-body diagram of the puck while it slides. Gravity pulls it down. The ice pushes it up with an equal force called the normal force. Friction points backward.

Notice what is missing: there is no forward arrow. The stick's force ended the moment the stick lost contact. The puck keeps moving forward by inertia, not because a force carries it along.

Always. Newton's third law of motion says that forces come in pairs. When object A pushes on object B, B pushes back on A with a force of the same size in the opposite direction (Newton, 1687/1999; Urone & Hinrichs, 2022).

A skater who shoves a wall rolls backward, because the wall pushes on the skater. When you walk, your foot pushes the ground backward and the ground pushes you forward. A rocket pushes hot gas out of its nozzle, and the gas pushes the rocket the other way. It needs no air to push against, which is why rockets work in space.

Then why don't the two forces cancel out? Because they act on different objects. The skater's push acts on the wall. The wall's push acts on the skater. Only forces on the same object add up to that object's net force. Figure 2.6 shows the pair.

Inertia. Once the stick lets go, no force pushes the puck forward, and none is needed. By the first law, it would keep its velocity forever. What stops it is a backward force, mostly friction with the ice. Friction on ice is small, so by the second law the puck slows only gently. That is why it can cross a whole rink.

Newton's laws tell you how forces change motion. Lesson 3 follows something that forces carry from one object to another: energy. It also covers momentum, which explains what happens when pucks, cars, and planets collide.

And these laws are not only for hockey rinks. In Lesson 4, the same three laws, plus Newton's law of gravity, explain why the Moon circles Earth and Earth circles the Sun.