Forces

What does a thing do when the net force on it is zero? If it is at rest, it stays at rest. That much is obvious. The other half is not: if it is moving, it keeps moving, in a straight line at an unchanging speed. In other words it keeps a constant velocity. This is Newton’s first law of motion, published in 1687.

It seems to clash with experience, since a kicked ball soon stops. But the ball is not free of forces. Friction and air resistance act on it all the way. Remove them, as in deep space, and it would go on for ever.

The reluctance of any object to change its motion is called inertia. You meet it in a braking car: the car slows, and your body carries on forward until the seatbelt supplies a force to stop it.

When the net force is not zero, the object accelerates: it speeds up, slows down or turns. Newton’s second law says how much. The net force equals the object’s mass multiplied by its acceleration. Turned around, the acceleration is the net force divided by the mass.

So for one object, acceleration goes hand in hand with force. Push a shopping trolley twice as hard and it picks up speed twice as quickly.

The law also defines the unit of force. One newton is the force that gives a mass of one kilogram an acceleration of one metre per second, every second. It is a small force, about the weight of an apple. A hard shove on a trolley is perhaps 50 newtons, and the forward push on a car pulling away hard is several thousand.

The second law has mass on the bottom of the division, and that explains a familiar fact. An empty shopping trolley leaps forward at a touch. A loaded one, given the same push, barely stirs. Mass measures how hard an object is to accelerate, which is to say how much inertia it has.

The rule is exact. Keep the force the same and double the mass, and the acceleration is halved. Triple the mass, and it falls to a third. In numbers: a net force of 30 newtons on a mass of 5 kilograms gives an acceleration of 30 divided by 5, which is 6 metres per second every second. The same 30 newtons on 10 kilograms gives only 3.

Everyday speech treats mass and weight as the same thing. Physics keeps them apart. Your mass is the amount of matter in you, measured in kilograms, and it is the same wherever you go. Your weight is the force with which gravity pulls on that matter, and it is measured in newtons like any other force.

On Earth, gravity pulls with about 9.8 newtons on every kilogram. On the Moon, where gravity is about six times weaker, the pull is 1.6 newtons per kilogram. At the cloud tops of the giant planet Jupiter it is about 25. An astronaut with a mass of 80 kilograms still has a mass of 80 kilograms on the Moon and is just as hard to push around. But the astronaut’s weight has dropped from about 780 newtons to about 130, which is why astronauts there could bound along in heavy suits.

Press your palm against a wall. You push on the wall, and you can feel the wall pushing back on your hand. Newton’s third law says this always happens. Whenever one object pushes or pulls on a second, the second pushes or pulls on the first with a force of the same size in the opposite direction. If your push is called the action, the wall’s push is the reaction. No force ever appears alone.

If every force has an equal and opposite partner, why does anything ever move? Because the two forces in a pair never act on the same thing. They act on different objects: your push acts on the wall, and the wall’s push acts on you. Forces can only cancel when they act on one object, so a pair never cancels itself.

The third law is how everything that moves itself gets moving. When you walk, your foot pushes backward on the ground, and the ground, in reaction, pushes you forward. That forward push from the ground is the force that moves you. Step onto sheet ice and the foot cannot push backward, so the ground cannot push you forward, and you go nowhere. A car’s tyres and a swimmer’s hands do the same thing with the road and the water.

A rocket shows the law at its purest. In empty space there is no ground, no air and no water to push on. So a rocket carries its own material to push against. It burns fuel and moves by throwing the hot gas backward out of its engine at great speed. The gas, in reaction, pushes the rocket forward.

Slide a box across a floor and something resists you. The force that opposes two surfaces sliding over each other is called friction. Even surfaces that look smooth are rough on a tiny scale, and where their high points touch they catch and cling. Friction always acts against the sliding.

Friction comes in two strengths. While the box is at rest, friction matches your push exactly, growing as you push harder, so the box does not move. This holding kind is called static friction. It has a limit, and when your push passes the limit the box breaks free. Once the box is sliding, friction is usually weaker than it was at the limit. That is why a heavy box takes a hard shove to start and less effort to keep going.

Which is harder to stop, a tennis ball or a lorry, both moving at walking pace? The lorry, obviously, and the reason is not its speed. Stopping a moving thing depends on how much mass is moving as well as how fast. Physics combines the two in one quantity, momentum: an object’s mass multiplied by its velocity.

At the same speed, a 30-tonne lorry has twenty times the momentum of a one-and-a-half-tonne car, simply because it has twenty times the mass. And since speed counts too, light things can carry a great deal. A bullet weighing a few grams can have as much momentum as a brick tossed gently across a room, because it is moving a few hundred times faster.

Momentum matters because of what happens to it in a collision. When two objects collide, or push each other apart, and no outside force interferes, their total momentum afterwards is exactly what it was before. One may lose some, but the other gains precisely that amount. This is the law of conservation of momentum, and it follows from the third law: the two objects push on each other with equal and opposite forces for the same length of time.

Fire a rifle and you can feel it. Before the shot, bullet and rifle are at rest, and the total momentum is zero. The bullet leaves with forward momentum, so the rifle must take an equal amount backward. That backward kick is called recoil. The rifle is far heavier than the bullet, so it moves far more slowly.

To stop a moving object you must take away its momentum, and a force does that over time. The same change in momentum can come from a large force acting briefly or a small force acting for longer. Spread the stop over more time and the force needed shrinks in proportion.

You use this without thinking. Catching a fast ball, you let your hands move back with it, which stretches the stop from a few thousandths of a second to a few hundredths, and most of the sting goes. Jumping down from a wall, you bend your knees. Car designers use it deliberately. A crumple zone and an airbag do not reduce the momentum a passenger has to lose. They lengthen the time over which it is lost, and so cut the force on the body.

People were multiplying forces long before anyone wrote down the laws of motion. One of the oldest devices for it is the lever: a stiff bar that turns about a fixed point. The fixed point is called the fulcrum. Push down on the long end of a crowbar and the short end, on the other side of the fulcrum, pushes up on the load with a much larger force.

How much larger depends on the lengths. If your hand is five times as far from the fulcrum as the load is, the lever multiplies your force by five. The factor by which a machine multiplies force is called its mechanical advantage. A seesaw, a pair of scissors, a bottle opener and an oar are all levers, and so is your forearm, which turns about the elbow.

A machine can multiply force, but it cannot multiply work. Work is force times distance, and the work you get out of a machine can never be more than the work you put in. So a larger force has to be paid for with distance. The long end of a lever that multiplies force by five must move five times as far as the load does.

A sloping plank makes the same bargain. Rolling a barrel up a slope onto a cart takes less force than lifting it straight up, but the barrel travels further. The slope is a simple machine in its own right, called an inclined plane. A wedge is two inclined planes back to back: drive an axe blade a long way down into a log and it pushes the wood a short way apart, with great force.

Three more machines use turning. A pulley is a grooved wheel with a rope running over it. A single fixed pulley only changes the direction of your pull, so that you can haul down to lift a load up. Rig several pulleys together and the load hangs from several strands of rope, each carrying a share, so your pull is multiplied.

A wheel and axle is a large wheel fixed to a thin central shaft, the axle. Turn the rim of a steering wheel or a doorknob with a small force and the axle turns with a large one. A gear is a wheel with teeth that mesh with the teeth of another. A small gear driving a large one turns it slowly but with more force, which is what a low gear on a bicycle does for you on a hill.