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A famous Ancient Greek once said,
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"Give me a place to stand, and I shall move the Earth."
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But this wasn't some wizard claiming to perform impossible feats.
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It was the mathematician Archimedes
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describing the fundamental principle behind the lever.
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The idea of a person moving such a huge mass on their own
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might sound like magic,
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but chances are you've seen it in your everyday life.
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One of the best examples is something you might recognize
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from a childhood playground:
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a teeter-totter, or seesaw.
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Let's say you and a friend decide to hop on.
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If you both weigh about the same,
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you can totter back and forth pretty easily.
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But what happens if your friend weighs more?
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Suddenly, you're stuck up in the air.
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Fortunately, you probably know what to do.
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Just move back on the seesaw, and down you go.
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This may seem simple and intuitive,
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but what you're actually doing is using a lever to lift a weight
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that would otherwise be too heavy.
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This lever is one type of what we call simple machines,
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basic devices that reduce the amount of energy required for a task
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by cleverly applying the basic laws of physics.
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Let's take a look at how it works.
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Every lever consists of three main components:
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the effort arm, the resistance arm, and the fulcrum.
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In this case, your weight is the effort force,
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while your friend's weight provides the resistance force.
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What Archimedes learned was that there is an important relationship
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between the magnitudes of these forces and their distances from the fulcrum.
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The lever is balanced when
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the product of the effort force and the length of the effort arm
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equals the product of the resistance force and the length of the resistance arm.
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This relies on one of the basic laws of physics,
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which states that work measured in joules is equal to force applied over a distance.
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A lever can't reduce the amount of work needed to lift something,
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but it does give you a trade-off.
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Increase the distance and you can apply less force.
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Rather than trying to lift an object directly,
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the lever makes the job easier by dispersing its weight
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across the entire length of the effort and resistance arms.
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So if your friend weighs twice as much as you,
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you'd need to sit twice as far from the center as him in order to lift him.
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By the same token, his little sister, whose weight is only a quarter of yours,
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could lift you by sitting four times as far as you.
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Seesaws may be fun, but the implications and possible uses of levers
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get much more impressive than that.
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With a big enough lever, you can lift some pretty heavy things.
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A person weighing 150 pounds, or 68 kilograms,
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could use a lever just 3.7 meters long to balance a smart car,
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or a ten meter lever to lift a 2.5 ton stone block,
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like the ones used to build the Pyramids.
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If you wanted to lift the Eiffel Tower, your lever would have to be a bit longer,
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about 40.6 kilometers.
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And what about Archimedes' famous boast?
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Sure, it's hypothetically possible.
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The Earth weighs 6 x 10^24 kilograms,
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and the Moon that's about 384,400 kilometers away
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would make a great fulcrum.
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So all you'd need to lift the Earth
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is a lever with a length of about a quadrillion light years,
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1.5 billion times the distance to the Andromeda Galaxy.
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And of course a place to stand so you can use it.
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So for such a simple machine,
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the lever is capable of some pretty amazing things.
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And the basic elements of levers and other simple machines
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are found all around us in the various instruments and tools
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that we, and even some other animals, use to increase our chances of survival,
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or just make our lives easier.
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After all, it's the mathematical principles behind these devices
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that make the world go round.