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  • A famous Ancient Greek once said,

  • "Give me a place to stand, and I shall move the Earth."

  • But this wasn't some wizard claiming to perform impossible feats.

  • It was the mathematician Archimedes

  • describing the fundamental principle behind the lever.

  • The idea of a person moving such a huge mass on their own

  • might sound like magic,

  • but chances are you've seen it in your everyday life.

  • One of the best examples is something you might recognize

  • from a childhood playground:

  • a teeter-totter, or seesaw.

  • Let's say you and a friend decide to hop on.

  • If you both weigh about the same,

  • you can totter back and forth pretty easily.

  • But what happens if your friend weighs more?

  • Suddenly, you're stuck up in the air.

  • Fortunately, you probably know what to do.

  • Just move back on the seesaw, and down you go.

  • This may seem simple and intuitive,

  • but what you're actually doing is using a lever to lift a weight

  • that would otherwise be too heavy.

  • This lever is one type of what we call simple machines,

  • basic devices that reduce the amount of energy required for a task

  • by cleverly applying the basic laws of physics.

  • Let's take a look at how it works.

  • Every lever consists of three main components:

  • the effort arm, the resistance arm, and the fulcrum.

  • In this case, your weight is the effort force,

  • while your friend's weight provides the resistance force.

  • What Archimedes learned was that there is an important relationship

  • between the magnitudes of these forces and their distances from the fulcrum.

  • 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.

  • Seesaws may be fun, but the implications and possible uses of levers

  • get much more impressive than that.

  • 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.

  • And what about Archimedes' famous boast?

  • Sure, it's hypothetically possible.

  • 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.

  • So for such a simple machine,

  • the lever is capable of some pretty amazing things.

  • And the basic elements of levers and other simple machines

  • are found all around us in the various instruments and tools

  • that we, and even some other animals, use to increase our chances of survival,

  • or just make our lives easier.

  • After all, it's the mathematical principles behind these devices

  • that make the world go round.

A famous Ancient Greek once said,

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【TED-Ed】The mighty mathematics of the lever - Andy Peterson and Zack Patterson

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    monica999   に公開 2014 年 11 月 19 日
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