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功是如何工作的?

How does work...work? - Peter Bohacek

在物理学中
In Physics,
功和功率的概念帮助我们理解
the concepts of work and power help us understand
并解释许多发生在我们宇宙中的事
and explain lots of things in our universe.
让我们先从功开始
Let’s start with work.
我们输入系统的能量叫正功
Positive work is the energy we put into a system,
然后输出来的能量叫做负功
and negative work is energy that is transferred out.
假想正功就像你存入银行的钱
Think of positive work as money being added to your bank account,
那么负功就是你从银行里拿出的钱
and negative work as money taken out.
在公制(度量衡的一种,还有英制和美制)中
In the metric system,
功和能量是用焦耳来测量的
work and energy are measured in Joules.
举个例子,让我们拿出一个漂亮的,老旧的机械式落地大摆钟
As an example, let’s take a beautiful, old, mechanical grandfather clock.
让我们把能量转换到钟里
We transfer energy into the clock
当我们转动曲柄
when we turn the crank
去提升钟里的重金属圆筒
to raise the heavy metal cylinders inside the clock.
当我们这样做时,我们在做正功
When we do this, we are doing positive work,
增加钟里的能量
adding energy to the clock,
能量被储存为重力势能
and that energy is stored as gravitational potential energy.
我们可以计算出所做的功的总量 等于我们施加力的大小乘上
We can calculate the amount of work done by multiplying the force we apply
力作用的距离所得的乘积。
times the distance over which we apply the force.
为了提升金属圆筒
To raise the metal cylinders,
我们需要施加一个和它们重量相等的力
we need to apply a force equal to their weight.
换言之,等于作用在圆筒上
That is, equal to the force of gravity
向下拉的的重力
pulling downward on the cylinders.
这些圆筒重300牛
These cylinders weight 300 Newtons,
这还是很重的
which is pretty heavy,
相当于一个小孩的体重
about as much as a small child,
如果我们把它们抬升0.5米的高度
and if we lift them 1/2 meter,
那么我们做的300牛的力
then we do 300 Newtons
乘以0.5米
times 1/2 meter
就得出150焦耳的功
or 150 Joules of work.
功率是指能量的转化效率
Power is the rate at which energy is transferred.
当我们谈到效率
When we say rate,
我们是在讨论在单位时间内
we mean the amount of energy transferred
能量转化的总量
per unit of time.
在公制里,功率是用
In the metric system, power is measured in
焦耳每秒来衡量的,
Joules per second,
或者是瓦特
or Watts.
瓦特这个术语来源于詹姆斯·瓦特
The term Watt goes back to James Watt,
他提出了马力的概念
who came up with the concept of horsepower
去衡量功率值
to measure the amount of power
一只役马(专门工作的马)所产生的
produced by a typical work horse.
詹姆斯·瓦特是工业蒸汽机的制造者
James Watt was a producer of industrial steam engines,
他希望他的潜在客户
and he wanted his potential customers
能够在
to be able to make comparisons
他的蒸汽机和常见的??作一个比较
between his steam engines and a familiar quanity,
他们从一匹役马所能得到的能量
the power they could get from a working horse.
这是一个非常实用的想法
It was such a useful idea
所以公制的功率单位 ,瓦特
that the metric system unit for power, the Watt,
是以詹姆斯·瓦特的名字命名的
is named after James Watt.
跟着瓦特的步伐
Following in James Watt’s footsteps,
让我们来比较所需的能量
let’s compare the amount of power it takes
去运行这落地钟
to run this grandfather clock
和我们所需的能量去点亮
to the power we’d need to run
一个明亮的100瓦的灯泡
a bright, 100-Watt light bulb.
我们可以测量一个人
We can measure the power a person uses
去给钟上发条所耗费的功率
to wind the clock
通过他们所做的功除以
by dividing the amount of work they did
他们花费的时间。
by the time it took them to do it.
如果花费1分钟,即60s
If it takes 1 minute, or 60 seconds,
去举起这个重量
to lift the weights,
那么他们做功150焦耳
then they are doing 150 Joules
除以60s
divided by 60 seconds,
即做功是2.5焦耳每秒
or 2.5 Joules per second of work.
他们增加钟的能量
They are adding energy to the clock
以2.5瓦特的速率。
in the rate of 2.5 Watts.
你将需要以同样效率的40倍
You would need about 40 times as much
去点亮一个100瓦明亮的灯泡
to run a bright, 100-Watt light bulb.
在我们让时钟运行之前
Before we let the clock run,
能量被储存着
the energy is stored
以重力势能形式存在圆筒中
as gravitational potential energy of the cylinders.
就像你的银行账户
It’s like your bank account
存的款。
when you have just deposited money.
但如果我们让钟运行
But if we let the clock run,
圆筒慢慢下降
the cylinders slowly move downward.
能量不断离开钟
Energy is leaving the clock.
事实上,当圆筒到达底部
In fact, when the cylinders get to the bottom,
我们输入的所有能量都已离去
all the energy that we put in will have left.
所以这口钟消耗了多少能量呢?
So how much power does the clock use?
即能量以每秒多少焦耳离开时钟
That is, how many Joules of energy per second leave the clock
假设需要5天使圆筒回到原来的位置
if it takes 5 days for the cylinders to return to their original position?
我们可以算出
We can figure this out
因为我们已经知道我们提升圆筒时
because we already know how much work we did
做了多少功:
when we lifted the cylinders:
150焦耳
150 Joules.
但是这一次,需要花费5天时间,而不是一分钟
But this time, it took 5 days rather than a minute.
5天是5乘以24
Five days is 5 times 24
乘以60
times 60
再乘以60
times 60 again
即432000秒
or 432,000 seconds.
所以我们把所做的功除以时间
So we divide the work done by the time
得出答案约0.00035焦耳每秒
and find the answer of about 0.00035 Joules per second,
或者说约0.35毫瓦
or about 0.35 milliwatts.
这是一个很小的功率
That’s a tiny amount of power.
这个钟使用的能量如此少
This clock uses so little power
你可以运行将近300000口钟
that you could run almost 300,000 clocks
相同的能量来运行一个100瓦的灯泡
using the same power it takes to run one 100-Watt light bulb.
没错,你可以用那么多的能量运行一个中等城市里
That’s right, you could run a clock in every house
每户家庭的一口钟
in a medium sized city with that much power.
这是相当惊人的结论
That’s a pretty amazing conclusion
它是用功和功率的知识算出来的
and it took knowledge of work and power to figure it out.

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https://www.youtube.com/watch?v=u6y2RPQw7E0

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