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• In Physics,

在物理學中

• 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

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

得到每秒 0.00035 焦耳

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

In Physics,

B1 中級 中文 TED-Ed 功率 時鐘 焦耳 能量 圓柱

# TED-Ed】工作......是如何進行的？- Peter Bohacek (【TED-Ed】How does work...work? - Peter Bohacek)

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稲葉白兎 發佈於 2021 年 01 月 14 日