The word machine comes from a Greek word meaning to help make things easier. Archimedes developed the law of the lever with his Treatise on the Balance, and Hero of Alexandria analyzed five simple machines: the lever, pulley, wheel, wedge and screw. Guidobaldo del Monte showed in 1577 that all five of Hero's machines could be deduced from the principle of the lever. The modern list has six simple machines: the lever, the wheel and axle, the pulley, the inclined plane, the wedge and the screw, although some engineers call gears the seventh simple machine. Most of them were in common use for centuries before Leonardo da Vinci's time, but he experimented with them and improved them.

A force is any push or pull. In science, each time a person pushes or pulls an object and moves it, that person does work, whereas pushing against a wall that does not move is not work in the physics sense, even though it is tiring. Work is force times distance. Force is measured in newtons, distance in meters, and work in joules, so a force of 8 newtons that lifts a ball 2 meters does 16 joules of work. Simple machines make work easier, but they do not decrease the amount of work you have to do. Although a simple machine cannot change the amount of work, it can change the force you apply and the distance over which you apply it. A simple machine has no internal source of energy, and no machine can output more energy than was put into it. In the ideal case, the work put into a simple machine equals the work it puts out.

A lever is a bar that turns around a pivot point called the fulcrum, and there are three classes of levers, set by where the effort, the load and the fulcrum are placed. In a first-class lever the fulcrum is between the load and the effort, in a second-class lever the load is between the fulcrum and the effort, and in a third-class lever the effort is between the load and the fulcrum, so the effort must be greater than the load. A lever is in balance when effort times its arm length equals load times its arm length. The ideal mechanical advantage of a lever is the length of the effort arm divided by the length of the resistance arm. A machine can have a mechanical advantage greater than 1 or even less than 1: a shovel is a lever with a mechanical advantage less than one, because its input lever arm is shorter than its output lever arm. A lever has high efficiency because it has low internal resistance, so its work out is almost equal to its work in, and a rigid lever can come close to an ideal machine, since very little work is lost.

A wheel and axle is a kind of lever, and its ideal mechanical advantage is the ratio of the lever arms, the wheel radius over the axle radius. A wheel and axle can move a load farther than a lever can, since the travel is limited only by the rope or cable that can be wrapped around the wheel or axle, and any crank-operated device is an example of one. A pulley is a wheel that a rope goes over. A single fixed pulley has an ideal mechanical advantage of 1, but lets you redirect the force so you can stand clear of the load, while with a suspended pulley, two ropes share the load, so the ideal mechanical advantage is 2. For a pulley system, count the ropes holding up the load, and to raise a load 1 meter you must pull N meters of rope, where N is the number of supporting ropes. A pulley may be relatively inefficient because it has considerably more internal friction.

A ramp is an inclined plane, and pushing an object up a ramp takes less force than lifting it straight up. The more gradual a ramp's slope, the greater its mechanical advantage, but the load must move farther, and rollers used with an inclined plane can raise its efficiency by reducing friction. Ramps were probably used when the ancient Egyptians built the pyramids, to move large blocks of stone to the top. An inclined plane and a wedge are two forms of the same simple machine, and a wedge is made of two inclined planes put back to back. When an inclined plane is used the load moves, but when a wedge is used the load stays still and the machine moves. With a wedge, the smaller the angle at the thin end, the less force is needed to drive it a given distance, although for a wedge the ideal mechanical advantage has little meaning, because friction is usually large in practice.

A screw is essentially a long incline wrapped around a shaft, which is to say an inclined plane wrapped around a cylinder, and it turns a twisting motion into movement forward or backward. When a screw is turned once, it advances by the distance between adjacent screw threads. A screw helps to hold things together, but for a screw the ideal mechanical advantage has little meaning, because there is typically a lot of friction, and wood screws lose a considerable amount of energy to friction and to pushing material aside. A wedge pushes things apart or cuts them, and a machine can trade a large force over a short distance for a small force over a large distance, which is useful for getting more speed. Ask a grown-up to help with sharp or heavy tools.

Friction is a force that resists the motion of two objects sliding past one another. It always acts in the direction opposite to movement, and its strength depends on the type of surfaces in contact and how hard they are pressed together. In real machines, friction turns some of the work put in into wasted heat. The ideal mechanical advantage is that of a perfect machine with no loss of useful work to friction between moving parts. The efficiency of a machine is its output work divided by its input work, usually shown as a percent, and the efficiency of real machines is always under 100 percent, because friction and air resistance turn some work into unavailable heat. Mechanical advantage tells how many times a machine multiplies the force you put in.

Words to know

• fulcrum: the pivot point
• friction: resists sliding motion
• efficiency: output over input
• deduced: worked out logically
• radius: center to edge