the concepts of work and power help us understand

「功」 (work) 與「功率」 (power) 幫我們了解

and explain lots of things in our universe.

並解釋宇宙的許多現象

Let's start with work.

我們先從功談起

Positive work is the energy we put into a system,

正向的功是指投入系統的能量

and negative work is energy that is transferred out.

負向的功是指系統放出的能量

Think of positive work as money being added to your bank account,

正功相當於在銀行存錢

and negative work as money taken out.

負功相當於把錢領出來

In the metric system,

在公制系統

work and energy are measured in Joules.

功和能量的單位是焦耳 (Joule)

As an example, let's take a beautiful, old, mechanical grandfather clock.

以優美的機械式老爺鐘為例

We transfer energy into the clock

我們把能量傳進時鐘裡

when we turn the crank

是靠旋轉曲柄

to raise the heavy metal cylinders inside the clock.

抬高裡面的金屬重錘

When we do this, we are doing positive work,

如此我們做了正功

adding energy to the clock,

把能量加到時鐘裡

and that energy is stored as gravitational potential energy.

能量以重力位能的形式儲存

We can calculate the amount of work done by multiplying the force we apply

要計算做的功，可將所施的力

times the distance we over which we apply the force.

乘以施力的距離

To raise the metal cylinders,

要把金屬重錘抬高

we need to apply a force equal to their weight.

所施的力，等於其重量

That is, equal to the force of gravity

也就是重力

pulling downward on the cylinders.

往下拉金屬重錘的力

These cylinders weight 300 Newtons,

金屬重錘的重量為 300 牛頓

which is pretty heavy,

蠻重的

about as much as a small child,

相當於一個小孩的重量

and if we lift them 1/2 meter,

如果我們抬高 1/2 公尺

then we do 300 Newtons

我們就做了 300 牛頓

times 1/2 meter

乘以 1/2 公尺

or 150 Joules of work.

等於 150 焦耳的功

Power is the rate at which energy is transferred.

功率 (power) 是指能量傳遞的速率

When we say rate,

當我們說速率的時候

we mean the amount of energy transferred

我們指的是

per unit of time.

單位時間內，傳送的能量

In the metric system, power is measured in

功率的公制單位為

Joules per second,

每秒的焦耳數

or Watts.

也就是「瓦特」 (Watt)

The term Watt goes back to James Watt,

這個名詞來自詹姆斯瓦特 (James Watt)

who came up with the concept of horsepower

他提出了「馬力」的想法

to measure the amount of power

要度量功率

produced by a typical work horse.

可採用一般工作馬匹為基準

James Watt was a producer of industrial steam engines,

瓦特是工業用蒸汽機的製造商

and he wanted his potential customers

他希望潛在客戶

to be able to make comparisons

能夠比較

between his steam engines and a familiar quanity,

他的蒸汽機，及大家熟悉的度量…

the power they could get from a working horse.

也就是工作馬匹的力量

It was such a useful idea

這是個有用的想法

that the metric system unit for power, the Watt,

所以公制的功率單位－瓦特

is named after James Watt.

就是以他為名

Following in James Watt's footsteps,

追隨瓦特的腳步

let's compare the amount of power it takes

我們來比較一下

to run this grandfather clock

讓老爺鐘運作

to the power we'd need to run

的功率以及

a bright, 100-Watt light bulb.

讓 100 瓦燈泡發亮的功率

We can measure the power a person uses

要算出

to wind the clock

幫老爺鐘上發條的功率

by dividing the amount of work they did

只要把所做的功

by the time it took them to do it.

除以所花的時間

If it takes 1 minute, or 60 seconds,

如果花了 1 分鐘，也就是 60 秒

to lift the weights,

抬起重錘

then they are doing 150 Joules

把 150 焦耳的功

divided by 60 seconds,

除以 60 秒時間

or 2.5 Joules per second of work.

就得到功率，每秒 2.5 焦耳

They are adding energy to the clock

將能量加進時鐘的功率

in the rate of 2.5 Watts.

是 2.5 瓦特

You would need about 40 times as much

要 40 倍這樣的能量

to run a bright, 100-Watt light bulb.

才能讓 100 瓦的燈泡發亮

Before we let the clock run,

在我們讓時鐘運轉前

the energy is stored

能量以

as gravitational potential energy of the cylinders.

重力位能的形式儲存在圓柱中

It's like your bank account

相當於把錢

when you have just deposited money.

存入銀行

But if we let the clock run,

如果我們讓時鐘開始運轉

the cylinders slowly move downward.

圓柱就會緩緩下降

Energy is leaving the clock.

能量開始從時鐘流失

In fact, when the cylinders get to the bottom,

當圓柱到達底部的時候

all the energy that we put in will have left.

所有存進去的能量都用完了

So how much power does the clock use?

時鐘所用的功率是多少？

That is, how many Joules of energy per second leave the clock

就是每秒有多少焦耳流出時鐘？

if it takes 5 days for the cylinders to return to their original position?

假設 5 天後圓柱完全降下

We can figure this out

我們可以算出功率

because we already know how much work we did

我們已知抬升圓柱時

when we lifted the cylinders:

所做的功

150 Joules.

是 150 焦耳

But this time, it took 5 days rather than a minute.

時間是 5 天，而不是 1 分鐘

Five days is 5 times 24

5 天相當於 5 乘以 24 小時

times 60

乘以 60 分鐘

times 60 again

再乘以 60 秒

or 432,000 seconds.

也就是 432,000 秒

So we divide the work done by the time

我們把所做的功除以時間

and find the answer of about 0.00035 Joules per second,

得到每秒 0.00035 焦耳

or about 0.35 milliwatts.

也就是 0.35 毫瓦

That's a tiny amount of power.

這是很小的功率

This clock uses so little power

時鐘用的功率極小

that you could run almost 300,000 clocks

表示 30 萬個時鐘運作的功率

using the same power it takes to run one 100-Watt light bulb.

等於一個 100 瓦燈泡的功率

That's right, you could run a clock in every house

沒錯，這足夠在一個中型城市裡

in a medium sized city with that much power.

讓家家戶戶的時鐘運作了

That's a pretty amazing conclusion

這是很神奇的結論

and it took knowledge of work

只要你有功和功率的知識

and power to figure it out.

就可以算得出來