Name: lWDtFHDVqqk
Uploaded: 2014-12-06T14:02:25.000Z
Duration: 10 min 13 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Past continuous

To just review what I was doing on the last video before

Past simple

I ran out of time, I said that conservation of energy tells

us that the work I've put into the system or the energy that

I've put into the system-- because they're really the

same thing-- is equal to the work that I get out of the

system, or the energy that I get out of the system.

That means that the input work is equal to the output work,

or that the input force times the input distance is equal to

the output force times the output distance-- that's just

If I could just rewrite this exact equation, I could say--

the input force, and let me just divide it by this area.

The input here-- I'm pressing down this piston that's

So this input force-- times the input area.

Let's call the input 1, and call the output 2 for

Let's say I have a piston on the top here.

Let me do this in a good color-- brown is good color.

I have another piston here, and there's going to be some

The general notion is that I'm pushing on this water, the

water can't be compressed, so the water's going to push up

The input force times the input distance is going to be

equal to the output force times the output distance

right-- this is just the law of conservation of energy and

I'm rewriting this equation, so if I take the input force

and divide by the input area-- let me switch back to green--

then I multiply by the area, and then I just

You see what I did here-- I just multiplied and divided by

You can multiply and divide by any number, and these two

It's equal to the same thing on the other side, which is

F2-- I'm not good at managing my space on my whiteboard--

What's this quantity right here, this F1 divided by A1?

Force divided by area, if you haven't been familiar with it

already, and if you're just watching my videos there's no

reason for you to be, is defined as pressure.

Pressure is force in a given area, so this is pressure--

That's the area of the tube at this point, the

cross-sectional area, times this distance.

That's equal to this volume that I calculated in the

Pressure times V1 is equal to the output pressure-- force 2

divided by area 2 is the output pressure that the water

The cross sectional area, times the height at which how

much the water's being displaced upward, that is

But what do we know about these two volumes?

I went over it probably redundantly in the previous

video-- those two volumes are equal, V1 is equal to V2, so

we could just divide both sides by that equation.

You get the pressure input is equal to the pressure output,

I did all of that just to show you that this isn't a new

concept: this is just the conservation of energy.

The only new thing I did is I divided-- we have this notion

of the cross-sectional area, and we have this notion of

This actually tells us-- and you can do this example in

multiple situations, but I like to think of if we didn't

have gravity first, because gravity tends to confuse

things, but we'll introduce gravity in a video or two-- is

that when you have any external pressure onto a

liquid, onto an incompressible fluid, that pressure is

That's what we essentially just proved just using the law

of conservation of energy, and everything we know about work.

What I just said is called Pascal's principle: if any

external pressure is applied to a fluid, that pressure is

distributed throughout the fluid equally.

Another way to think about it-- we proved it with this

little drawing here-- is, let's say that I have a tube,

Let's say I'm doing this on the Space Shuttle.

It's saying that if I increase-- say I have some

Let me see if I can use that field function again-- oh no,

there must have been a hole in my drawing.

I have water throughout this whole thing, and all Pascal's

principle is telling us that if I were to apply some

pressure here, that that net pressure, that extra pressure