• gif education science math mathematics archimedes levers teded •

The mathematician Archimedes once said, “Give me a place to stand, and I shall move the Earth." As it turns out, he was describing the fundamental principle behind the lever.

The lever is balanced when the product of the effort force and the length of the effort arm equals the product of the resistance force and the length of the resistance arm. This relies on one of the basic laws of physics, which states that work measured in joules is equal to force applied over a distance.

A lever can’t reduce the amount of work needed to lift something,but it does give you a trade-off.Increase the distance and you can apply less force. Rather than trying to lift an object directly, the lever makes the job easier by dispersing its weight across the entire length of the effort and resistance arms. So if your friend weighs twice as much as you, you’d need to sit twice as far from the center as him in order to lift him. By the same token, his little sister, whose weight is only a quarter of yours, could lift you by sitting four times as far as you.

With a big enough lever, you can lift some pretty heavy things. A person weighing 150 pounds, or 68 kilograms, could use a lever just 3.7 meters long to balance a smart car, or a ten meter lever to lift a 2.5 ton stone block, like the ones used to build the Pyramids. If you wanted to lift the Eiffel Tower, your lever would have to be a bit longer, about 40.6 kilometers.

The Earth weighs 6 x 10^24 kilograms, and the Moon that’s about 384,400 kilometers away would make a great fulcrum. So all you’d need to lift the Earth is a lever with a length of about a quadrillion light years, 1.5 billion times the distance to the Andromeda Galaxy.

And of course a place to stand so you can use it.

• levers

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