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

槓桿中的強力數學 - 安迪·彼得森和扎克‧帕特森

譯者: 葉 Yah 宇倫 審譯者: 瑞文Eleven 林Lim

A famous Ancient Greek once said,

一位著名的古希臘人曾經說過

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

給我一個支點，我可以移動地球

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

但這不是那些巫師口中 不可能的壯舉

It was the mathematician Archimedes

他就是數學家阿基米德

describing the fundamental principle behind the lever.

描述槓桿原理背後的基本原則

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

一個人要獨自移動 如此龐大的物體的概念

might sound like magic,

聽起來就像魔術一樣

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

但你可能早就在日常生活中見過它

One of the best examples is something you might recognize

但其中一個最好的例子， 你可能曾經見過

from a childhood playground:

在兒童遊樂場

a teeter-totter, or seesaw.

一個蹺蹺板

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

比方說，你和你的朋友決定要玩

If you both weigh about the same,

如果你們的體重差不多

you can totter back and forth pretty easily.

你們可以很容易上下擺動

But what happens if your friend weighs more?

但是如果你的朋友比你更重， 會發生什麼事?

Suddenly, you're stuck up in the air.

突然間，你會無法移動， 像卡在空氣中一樣

Fortunately, you probably know what to do.

幸運的是，你應該知道要怎麼做

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

就只是向後退，就可以繼續移動了

This may seem simple and intuitive,

這可能看起來非常簡單且直觀

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

但實際上，你正運用槓桿來舉起重物

that would otherwise be too heavy.

否則物體過重你就舉不起來

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

這是我們稱為槓桿的簡單機器

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

透過巧妙運用基礎的物理定律

by cleverly applying the basic laws of physics.

來減少完成一件事情所需要的力量

Let's take a look at how it works.

讓我們看看它是如何運作的吧

Every lever consists of three main components:

每個槓桿由三個主要元件所組成

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

施力臂、抗力臂與支點

In this case, your weight is the effort force,

在這個例子中， 你的體重就是施力的力量

while your friend's weight provides the resistance force.

而你朋友的體重則提供抗力

What Archimedes learned was that there is an important relationship

阿基米德自此習得

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

有關力及它們與支點的距離(力臂) 的重要的關係

The lever is balanced when

當槓桿平衡的時候

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

施力大小與施力臂長度的乘積

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

會等於抗力大小 與抗力臂長度的乘積

This relies on one of the basic laws of physics,

這基於一個物理學基本定律

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

施力作功(單位為焦耳) 等於力乘上距離

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

槓桿降低不了 舉起某物所需的能量

but it does give you a trade-off.

但它確實給你一個取捨的機會

Increase the distance and you can apply less force.

增加距離，就可以 用較少的力去達到目標

Rather than trying to lift an object directly,

而不是試圖直接抬起對象

the lever makes the job easier by dispersing its weight

槓桿透過施力臂與阻力臂的長度

across the entire length of the effort and resistance arms.

來分散重量使目的更容易達成

So if your friend weighs twice as much as you,

所以，如果朋友的體重是你的兩倍

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

你必須坐在距中心距離是他的兩倍處， 才有辦法舉起他

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

同理，如果他的小妹體重 只有你的四分之一

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

只要小妹距離是你的四倍遠， 也有辦法舉起你

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

蹺蹺板可能是有趣的， 但其中涉及到槓桿的可能用途

get much more impressive than that.

比這更令人印象深刻

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

如果你有一個夠大的槓桿， 就可以抬起非常重的東西

A person weighing 150 pounds, or 68 kilograms,

一個體重150磅(68公斤重)的人

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

可以利用一支3.7公尺的槓桿 來與一輛車保持平衡

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

或用十公尺長的槓桿 來舉起2.5公噸的石塊

like the ones used to build the Pyramids.

就像製造金字塔一樣

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

如果你想要舉起埃菲爾鐵塔 你會需要一個有點長的槓桿

about 40.6 kilometers.

大約40.6公里

And what about Archimedes' famous boast?

那阿基米德著名的大話呢?

Sure, it's hypothetically possible.

當然，它是可能的

The Earth weighs 6 x 10^24 kilograms,

地球的體量 6 x 10 ^24 公斤，

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

而月球大約是384400公里遠

would make a great fulcrum.

剛好可作為一個好用的支點

So all you'd need to lift the Earth

因此，如果你需要舉起地球

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

需要一個大約 千萬億光年長的槓桿

1.5 billion times the distance to the Andromeda Galaxy.

距離仙女座星系大約1.5億倍的長度

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

剛然還有一個站的地方，然後 你就可以使用它了ˊ

So for such a simple machine,

因此，對於這樣一個簡單的機器

the lever is capable of some pretty amazing things.

槓桿能做到一些 非常了不起的事情

And the basic elements of levers and other simple machines

與槓桿等簡單機械的基本要素

are found all around us in the various instruments and tools

就存在於我們 四周的儀器與工具

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

我們，甚至其他動物利用它 來增加我們的生存機會

or just make our lives easier.

或讓我們生活更便利

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

畢竟，這些設備背後的數學原理

that make the world go round.

它們讓世界運轉