You're in line at a cafeteria. You pass a stainless-steel cart that presents several stacks of plates. You take a plate off the top of one stack. The other plates in the stack rise from below just far enough to present the next plate at the same height as the one you just took.

Underneath each stack of plates is a spring whose tension is adjusted to keep the top plate level with the top of the cart. Once the adjustment is made, the top plate will always be level with the top of the cart, no mater how many plates are in the stack.

Those cafeteria plate dispensers cleverly exploit a general property of springs: if you put twice as much force on a spring, it compresses, or stretches, twice as far. If you put 20 plates on the stack, their weight compresses the spring just twice as far as the weight of ten plates.

This property of springs was discovered about 300 years ago by the English physicist Robert Hooke. Hooke wrote, "as the tension, so the force." Robert Hooke noticed this principle at work in all kinds of devices that rely on springy materials: spring scales, bows, watches, and the vibrating parts of musical instruments.

We now know that this relationship, called Hooke's Law, is a result of forces between atoms in solid material. If two atoms in a metal are pulled apart, they pull on each other. If you separate the atoms more, the force between them increases, in exact proportion. This is true as long as you don't upll the atoms too far.

Because of this pervasive relationship between atoms, just about all springs compress or stretch twice as far if you load them with twice the force. And because of that, cafeteria plate dispensers keep the top plate level with the top cart, no matter how many plates are in the stack.