The traditional "simple machines" -- inclined plane,lever, pulley, gear, and screw -- all work the same way. Each consists of an input and an output. At the input we exert a force f on something (a handle, in the cartoon). When the handle moves a distance D, we have given the system energy f x D. At the output side, another handle moves a distance d, and exerts a force F. If the machine is well lubricated, so that no energy is converted into other forms, the output energy F x d is equal to the input energy f x D. The distances D and d can be very different sizes (this is determined by how the input and output are connected inside the machine), and then F and f are also very different. Note that the machine is not "labor saving": we put in just as much energy as we get out. But a lever does make it possible to move a very large rock (a very small distance), while a fan lets us exert a small force that moves air a large distance, by a small motion of the wrist.

Here are some examples:

The inclined plane we already met in the unit Balanced Forces, and the energy analysis was given in the unit Force and Energy. We exert a force to make the cart move up the plane, and the energy we put in is f x D. The outcome is that the cart is lifted a height H, which implies that we can calculate the energy added a different way: W x H. Because the distance D is larger than the height H, the force f is less than the weight W of the cart.

A screw is just an inclined plane that has been rolled up.

A set of pulleys are another way to transform forces. Here's the Farmer family again. still trying to get the tractor out of the mud. Now there is a pulley wheel on the front of the tractor, and the rope runs around the wheel and to a stump. This will enable the family to pull twice as hard!
*One way to see this is to note that the family is pulling on one end of the rope, and the stump is pulling on the other end (because the rope is pulling on the stump) in the same direction. Both of these forces are balanced by the force of the tractor on the rope.
*Here's another way: suppose the tractor moves a small distance. Then the pullers move back twice as far, because the part of the rope between the stump and the tractor will be shorter by the two segments colored blue. Then the force on the tractor times the distance it moves can be equated to the force at the end of the rope times how far it moves: the pullers exert half the force for twice the distance.

Extending either argument, you can see that the force ratio will get larger and larger the more times the rope passes back and forth. This arrangement multiplies the force by three.

Gears on a bicycle complicate the story but don't change it. In one gear, you have to push the pedals really hard, but they turn slowly; in another gear, it is easier to turn the pedals but you have to pedal really fast. In low gear you have to make more turns of the pedals than in high gear, to go the same distance. The result is that it takes the same amount of energy.

Check the box when you are done:   

Discussion of the unit on simple machines