Name: 【TED-Ed】The mighty mathematics of the lever - Andy Peterson and Zack Patterson
Uploaded: 2014-11-19T05:24:06.000Z
Duration: 4 min 46 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

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

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

describing the fundamental principle behind the lever.

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

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

One of the best examples is something you might recognize

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

you can totter back and forth pretty easily.

But what happens if your  friend weighs more?

Fortunately, you probably know what to do.

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

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

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.

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 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,

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

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,

and the Moon that's about  384,400 kilometers away

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.

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,

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