The mighty mathematics of the lever - Andy Peterson and Zack Patterson

奇妙的杠杆的数学原理 - 安迪 彼得森 , 扎克 派德森

翻译人员: Qin Yu 校对人员: Qiwen Lu

A famous Ancient Greek once said,

一个有名的古希腊人曾说：

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

”给我一个支点，我可以撬动地球。“

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

这可不是哪个巫师在吹他的通天大法

It was the mathematician Archimedes

这是数学家阿基米德

describing the fundamental principle behind the lever.

对杠杆的基本原理的描述

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

一个人能撬动这么大的质量

might sound like magic,

可能听起来不可思议

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

但其实你很可能在日常生活中已经看到过了

One of the best examples is something you might recognize

其中一个最好的例子你在儿童游乐园

from a childhood playground:

就可能看出来

a teeter-totter, or seesaw.

那就是跷跷板

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

假如你和你朋友想要玩跷跷板

If you both weigh about the same,

如果你倆儿一样重

you can totter back and forth pretty easily.

你就可以上上下下自如运动

But what happens if your friend weighs more?

但如果你朋友比你重呢？

Suddenly, you're stuck up in the air.

那你只能一直停在上面

Fortunately, you probably know what to do.

幸好，你估计知道怎么做

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

只需要向后移一点，你就下来了

This may seem simple and intuitive,

这看上去好像简单到你生下来就会

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

但是你实际上已经在使用杠杆

that would otherwise be too heavy.

举起平时举不起的重物了

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

杠杆是我们所称的简单机械的一种

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

他们都巧妙的运用了基本物理原理

by cleverly applying the basic laws of physics.

减少了完成任务所需的能量

Let's take a look at how it works.

让我们来看看这背后的原理

Every lever consists of three main components:

每一个杠杆都主要由三部分组成

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

动力臂，阻力臂和支点

In this case, your weight is the effort force,

在跷跷板的例子中，你的重力是动力

while your friend's weight provides the resistance force.

你朋友的重力是阻力

What Archimedes learned was that there is an important relationship

阿基米德发现，力的大小

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

与到支点的距离之间有着重要的关系

The lever is balanced when

杠杆的平衡条件是：

the product of the effort force and the length of the effort arm

动力与动力臂的乘积

equals the product of the resistance force and the length of the resistance arm.

与阻力和阻力臂的乘积相等

This relies on one of the basic laws of physics,

原因是一条基本物理原理，即

which states that work measured in joules is equal to force applied over a distance.

以焦耳计量的功等于力与力的作用距离的乘积

A lever can't reduce the amount of work needed to lift something,

杠杆不能减少提起重物所需的功

but it does give you a trade-off.

但是你可以拿距离换力，即

Increase the distance and you can apply less force.

增加做功距离，减小作用力

Rather than trying to lift an object directly,

无须直接把重物举起来

the lever makes the job easier by dispersing its weight

杠杆可以把重量分散到整个力臂上，

across the entire length of the effort and resistance arms.

从而降低了工作难度

So if your friend weighs twice as much as you,

所以如果你朋友是你的两倍体重

you'd need to sit twice as far from the center as him in order to lift him.

你需要坐到离支点两倍远的距离才能把他翘起来

By the same token, his little sister, whose weight is only a quarter of yours,

同样的，他那个只有你四分之一重的小妹妹

could lift you by sitting four times as far as you.

也可以坐到四倍距离处把你翘起来

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

有趣的跷跷板背后隐藏的是深刻的

get much more impressive than that.

杠杆的原理和可能用途

With a big enough lever, you can lift some pretty heavy things.

你可以用一个足够大的杠杆举起很重的东西

A person weighing 150 pounds, or 68 kilograms,

一个150磅（68千克）重的人可以用一根仅仅3.7米长的杠杆

could use a lever just 3.7 meters long to balance a smart car,

举起一辆小轿车

or a ten meter lever to lift a 2.5 ton stone block,

或者用10米长的杠杆举起一块2.5吨的石块

like the ones used to build the Pyramids.

跟建金字塔的那些差不多

If you wanted to lift the Eiffel Tower, your lever would have to be a bit longer,

如果你想举起埃菲尔铁塔，你的杠杆恐怕得长一点

about 40.6 kilometers.

大概40.6公里长

And what about Archimedes' famous boast?

那阿基米德的那个著名牛皮呢？

Sure, it's hypothetically possible.

当然，理论上是有可能的

The Earth weighs 6 x 10^24 kilograms,

地球重6乘以10的24次方千克

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

而离距地球384400公里的月亮

would make a great fulcrum.

刚好成为一个支点

So all you'd need to lift the Earth

所以要举起地球，你只需

is a lever with a length of about a quadrillion light years,

一根一千万亿光年长的杠杆便可

1.5 billion times the distance to the Andromeda Galaxy.

等于到仙女座星系距离的一百五十万倍

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

当然了，你还需要一个站的地方

So for such a simple machine,

所以别看它只是个简单机械，

the lever is capable of some pretty amazing things.

杠杆可是能做很多神奇的事情呢

And the basic elements of levers and other simple machines

而杠杆等简单机械里的基本元素

are found all around us in the various instruments and tools

也可见于生活中的各种器械和工具中

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

人类和其他动物用它们来求生存

or just make our lives easier.

或求便捷

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

说到底，是这些工具背后的数学原理

that make the world go round.

支配着这大千世界