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In the last video, we learned
that the pressure at some

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depth in a fluid is equal to the
density of the fluid times

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how deep we are in the fluid,
or how high is the column of

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fluid above us times gravity.

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Let's see if we can use that
to solve a fairly typical

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problem that you'll see in your
physics class, or even on

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an AP physics test.

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Let's say that I have a bowl.

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And in that bowl, I have
mercury, and then I also have

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this kind of inverted test
tube that I stick in the

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middle of-- this is the side
view of the bowl, and I'll

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draw everything shortly.

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Let's say my test tube looks
something like this.

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Let's say I have no air in this
test tube-- there's a

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vacuum here-- but the outside
of the bowl, this whole area

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out here, this is exposed
to the air.

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We are actually on Earth, or
actually in Paris, France, at

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sea level, because that's what
an atmosphere is defined as--

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the atmospheric pressure.

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Essentially, the way you could
think about it-- the weight of

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all of the air above us is
pushing down on the surface of

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this bowl at one atmosphere.

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An atmosphere is just the
pressure of all of the air

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above you at sea level
in Paris, France.

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And in the bowl,
I have mercury.

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Let's say that that mercury--
there's no air in here, and it

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is actually going to go up
this column a little bit.

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We're going to do the math as
far as-- one, we'll see why

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it's going up, and then we'll do
the math to figure out how

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high up does it go.

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Say the mercury goes up
some distance-- this

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is all still mercury.

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And this is actually how a
barometer works; this is

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something that measures
pressure.

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Over here at this part, above
the mercury, but still within

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our little test tube, we have
a vacuum-- there is no air.

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Vacuum is one of my favorite
words, because it has

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two u's in a row.

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We have this set up, and so my
question to you is-- how high

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is this column of mercury
going to go?

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First of all, let's just have
the intuition as to why this

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thing is going up
to begin with.

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We have all this pressure from
all of the air above us-- I

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know it's a little un-intuitive
for us, because

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we're used to all of that
pressure on our shoulders all

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of the time, so we don't really
imagine it, but there

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is literally the weight of
the atmosphere above us.

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That's going to be pushing down
on the surface of the

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mercury on the outside
of the test tube.

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Since there's no pressure here,
the mercury is going to

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go upwards here.

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This state that I've drawn is
a static state-- we have

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assumed that all the
motion has stopped.

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So let's try to solve
this problem.

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Oh, and there are a couple of
things we have to know before

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we do this problem.

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It's mercury, and we know the
specific gravity-- I'm using

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terminology, because a lot of
these problems, the hardest

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part is the terminology--
of mercury is 13.6.

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That's often a daunting
statement on a test-- you know

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how to do all the math, and all
of a sudden you go, what

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is specific gravity?

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All specific gravity is, is the
ratio of how dense that

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substance is to water.

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All that means is that
mercury is 13.6

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times as dense as water.

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Hopefully, after the last
video-- because I told you

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to-- you should have memorized
the density of water.

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It's 1,000 kilograms per meter
cubed, so the density of

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mercury-- let's write that down,
and that's the rho, or

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little p, depending on how you
want to do it-- is going to be

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equal to 13.6 times the density
of water, or times

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1,000 kilograms per
meter cubed.

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Let's go back to the problem.

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What we want to know
is how high this

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column of mercury is.

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We know that the pressure--
let's consider this point

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right here, which is essentially
the base of this

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column of mercury.

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What we're saying is the
pressure on the base of this

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column of mercury right here, or
the pressure at this point

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down, has to be the same thing
as the pressure up, because

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the mercury isn't moving--
we're in a static state.

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We learned several videos ago
that the pressure in is equal

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to the pressure out on
a liquid system.

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Essentially, I have one
atmosphere pushing down here

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on the outside of the surface,
so I must have one atmosphere

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pushing up here.

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The pressure pushing up at this
point right here-- we

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could imagine that we have
that aluminum foil there

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again, and just imagine where
the pressure is hitting-- is

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one atmosphere, so the pressure
down right here must

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be one atmosphere.

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What's creating the pressure
down right there?

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It's essentially this column
of water, or it's this

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formula, which we learned
in the last video.

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What we now know is that the
density of the mercury, times

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the height of the column of
water, times the acceleration

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of gravity on Earth-- which is
where we are-- has to equal

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one atmosphere, because it has
to offset the atmosphere

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that's pushing on the outside
and pushing up here.

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The density of mercury is this:
13.6 thousand, so 13,600

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kilogram meters per
meter cubed.

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That's the density times the
height-- we don't know what

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the height is, that's going to
be in meters-- times the

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acceleration of gravity,
which is 9.8

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meters per second squared.

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It's going to be equal
to one atmosphere.

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Now you're saying-- Sal,
this is strange.

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I've never seen this atmosphere
before-- we've

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talked a lot about it, but how
does an atmosphere relate to

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pascals or newtons?

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This is something else you
should memorize: one

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atmosphere is equal to 103,000
pascals, and that also equals

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103,000 newtons per
meter squared.

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One atmosphere is how much we're
pushing down out here.

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So it's how much we're pushing
up here, and that's going to

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be equal to the amount of
pressure at this point from

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this column of mercury.

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One atmosphere is exactly this
much, which equals 103,000

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newtons per meters squared.

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If we divide both sides by
13,609.8, we get that the

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height is equal to 103,000
newtons per meter cubed, over

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13,600 kilograms per meter cubed
times 9.8 meters per

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second squared.

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Make sure you always have the
units right-- that's the

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hardest thing about these
problems, just to know that an

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atmosphere is 103,000 pascals,
which is also the same as

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newtons per meter squared.

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Let's just do the math, so let
me type this in-- 103,000

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divided by 13,600 divided
by 9.8 equals 0.77.

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We were dealing with newtons,
so height is

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equal to 0.77 meters.

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And you should see that the
units actually work, because

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we have a meters cubed in the
denominator up here, we have a

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meters cubed in the denominator
down here, and

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then we have kilogram meters
per second squared here.

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We have newtons up here,
but what's a newton?

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A newton is a kilogram meter
squared per second, so when

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you divide you have kilogram
meters squared per second

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squared, and here you
have kilogram

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meter per second squared.

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When you do all the division of
the units, all you're left

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with is meters, so we have 0.77
meters, or roughly 77

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centimeters-- is how high this
column of mercury is.

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And you can make a barometer out
of it-- you can say, let

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me make a little notch on this
test tube, and that represents

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one atmosphere.

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You can go around and figure
out how many atmospheres

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different parts of
the globe are.

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Anyway, I've run out of time.

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See you in the next video.