Galileo lived from 1564 to 1642. He calculated the law of free fall, conceived of an inertial principle, worked out the parabolic path of projectiles, and recognized that motion is relative. Isaac Newton, from 1642 to 1727, stated the three laws of motion that form the foundation of the science of how forces change motion. Behind such big ideas lay ramps, slopes, thought experiments and careful numbers.

Experiments with inclined planes led Galileo to the law of free fall. Under it, a body falling from rest travels a distance proportional to the square of the time. Doubling the time of the fall makes a ball drop four times as far. A thought experiment aimed at Aristotle's idea that heavier things fall faster. Join a heavy body and a light body and let them fall together. The light one should hold back the heavy one. But the joined pair weighs more than either alone, so it should fall faster. Both results cannot be true.

In a second experiment, a ball rolls down one slope and up another. Galileo reasoned that if the second slope were nearly flat, the ball would roll almost forever in its effort to reach the height where it started. That was a step toward the idea of inertia. A sled makes the point clearer. Imagine it sliding across a level field with no friction and no air resistance. Gravity and the upward push of the snow are the only forces on it, and they cancel. The sled would go on at the same speed in the same direction.

Astronauts could test the theory on the Moon. On Apollo 15, a hammer of 1.32 kilograms and a feather of 0.03 kilograms were let go from about 1.6 meters up. Both hit the lunar surface at about the same time, just as theory predicted. The Moon has almost no air, and where there is no air, heavy and light things fall the same way. Lunar gravity is about one-sixth of Earth's, so a person would weigh much less there, though a thing's mass is unchanged on Earth, in orbit and on the Moon.

Newton's second law is more precisely a statement about momentum. Force equals the change in momentum per change in time, where momentum is mass times velocity. The familiar F = ma applies when mass stays constant. In everyday terms, the amount a thing speeds up is set by the push and the mass: more force gives more change and more mass gives less. Where no unbalanced force acts, no change happens.

Forces add up. The net force is every force on a thing added together, and equal forces pointing in opposite directions cancel one another. Forces also come in pairs. If one thing pushes a second thing, the second thing pushes back on the first, equally and oppositely. A swimmer pushing against a pool wall travels away from it because the wall pushes back, and a fish moves ahead by pushing water backward.

Skydivers put these ideas to work. A falling skydiver speeds up until air pushes back as hard as gravity pulls, and after that the speed no longer changes. In one textbook example, a skydiver of 150 kilograms weighs more than one of 100 kilograms, so more air resistance is required to balance the weight. The heavier skydiver reaches a higher speed before terminal velocity. A 75-kilogram skydiver falling head first reaches about 350 km/h, or about 220 mph. Flat and spread out, the same skydiver reaches only about 200 km/h, and an open parachute reduces the speed much further.

A ramp, or inclined plane, allows a load to be raised by pushing it up a slope with less force than the load's weight. The price is a longer path. Levers also help. A simple machine such as a lever lets a small push or pull do a job that calls for a big force. The lever is a rigid bar turning on a fixed point, the fulcrum. A nail puller is a lever with a large mechanical advantage, meaning the ratio of the force you get out to the force you put in.

Friction can be measured as well. Starting a heavy crate takes more force than keeping it moving, since friction on a resting thing is bigger than on a moving one. For a 100-kilogram crate on a floor with a static friction coefficient of 0.45, a push of more than about 440 newtons is needed to start it. After it moves, the kinetic coefficient of 0.30 means about 290 newtons keeps it going at constant speed.

Words to know

• inertia: resisting change
• momentum: mass times velocity
• fulcrum: lever's pivot point
• projectiles: thrown objects