Recent MCATs have included several questions about simple machines — devices that alter the strength of the input force and the distance through which force is applied. You should be familiar with the force multiplication concept, and somewhat familiar with some of the machines that use it.

The basic concept is this: you can change force, but you can’t get something for nothing, i.e., energy is not created or destroyed by any of these machines. The energy of a force is, more properly stated, the work done by that force; it follows that the work done by an input force is the same as that done on the object that is being moved (unless there’s friction, in which case energy is lost; we’ll neglect friction for the rest of this discussion). As work = force x distance x cos(theta), if we increase force we have to decrease distance equivalently, and vice versa. (For this discussion we’ll consider forces that do work in the direction in which they are applied, i.e., cos(theta) = 1, and W = Fd.) The amount by which force is increased by a system, and therefore distance decreased, is the force multiplier.

Because of the fixed relationship between force and distance, it is often easier to consider distance (which we can see) than force, and then work backwards. For example, if you can see that the thing you’re moving travels, say, three times farther than the force that moves it, then the force on the object is three times less than the input; if you can see that it travels only a quarter as far, then the force exerted on it is four times as great, and so on.

The simple machines (and other devices with force multipliers) follow, including all six classic simple machines (even those that aren’t likely to appear in the test; I note which these are). Do not memorize these; instead, be moderately familiar with them, especially the more common ones.

• Pulley: A single pulley or a system thereof is not necessarily a simple machine, but it can be. For MCAT-style pulley systems, output force is input force multiplied by the number of ropes that are effectively pulling on the object to be moved; equivalently, by the number of ropes that must (not just might) shorten in order for the resistance to move. Another hint: if none of the pulleys is free to move, then the force multiplier is 1: force and distance remain the same. Of course, if the force multiplier is not 1, i.e., you get greater force on the object than you put in, you will get less distance by an equivalent factor. Appears on the MCAT.
• Inclined plane: the force multiplier (relative to straight lifting) is the sine of the angle of the plane with the horizontal. Distance is divided by the same factor. Consider the problem another way: If you push a block up an incline, you push along the hypotenuse, but lift only the amount of its height; the ratio of these two is sin(theta) Because distance is less than what you input, force must be greater by the same factor — the force multiplier. Common on the MCAT.
• Lever: the force multiplier is the ratio of distance from fulcrum to object, to distance from fulcrum to applied force. (The "fulcrum" of a lever is its pivot point.) Look at the picture to make sure you know whether distance goes up or down (hence force down or up). This treatment works even when the force and the object are on the same side of the fulcrum. I saw a lever — a claw hammer pulling a nail — and a question about its force multiplier and another about its fulcrum, on the August 2004 MCAT, so you can’t ignore this one.
• Hydraulic jack: not usually considered to be a simple machine like the aforementioned, but effectively the same. Force multiplier is the ratio of the areas of the tops of the two pistons. Recall that force changes, not pressure — pressure is the same (at the same height) everywhere in a body of liquid. Assuming that the change in height is negligible, it also doesn’t matter what liquid is used. Appears on the MCAT.
• Wedge: similar to an inclined plane; the force multiplier is length divided by width; distance is divided by the same factor. Unlikely on the MCAT.
• Wheel and axle: the force multiplier is ratio of radii of the wheel and the axle. To figure whether to divide or multiply the two, look at the picture to see whether the distance the object travels is greater or less than the distance over which the force is applied; that will tell you whether the force is decreased or increased, respectively. Unlikely on the MCAT.
• Gears (technically not a separate type of simple machine, but they work the same as the others): the force multiplier is the ratio of the numbers of teeth on the two wheels. Again, look at the picture to see which increases, force or distance. Unlikely on the MCAT.
• Screw: an inclined plane wrapped around a rod. Unlikely on the MCAT. For completeness: the force multiplier is 2 x pi x radius x (turns/unit length). Don’t worry about this one at all.

It is possible to combine two or more of the types: for example, a cam is an inclined plane combined with a wheel and axle. But don’t worry: such a problem is very unlikely to appear on the MCAT, and if it did it would necessarily be a very simple setup.