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Let's say we were to take a
little excursion to the moon.

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And so here we are
sitting on the surface

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of the moon-- that's the
surface of the moon right there.

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And with us to our excursion to
the moon we brought two things.

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We brought ourself
a concrete brick.

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So that's my brick
right over there,

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although it's orange-- we'll say
it's an orange concrete brick.

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And I also bought a
bird feather with us.

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So this is the bird feather.

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And then my question
to you is, if I

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were to hold both the
brick and the bird feather

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at the same time, and I were
to let go of both of them

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at the same time and ask
you, which one of them

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would hit the surface of the
moon first, what would you say?

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Well, if you based it on
your experience on Earth--

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on Earth if you were to
take a break and a feather,

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a brick would just
go straight down.

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A brick would just
immediately fall to the Earth,

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and it would do
it quite quickly.

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It would accelerate
quite quickly.

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While a feather would
kind of float around.

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If you had a feather on Earth,
it would just float around.

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It would go that way,
then it would go that way,

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and it would slowly make
its way down to the ground.

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So on Earth, at least
in the presence of air,

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it looks like the brick
will hit the ground first.

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But what would
happen at the moon?

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And what's interesting about the
moon is we have no atmosphere.

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We have no air to
provide resistance

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for either the brick
or the feather.

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So what do you think
is going to happen?

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So your first temptation
would say, well,

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let's just use the
universal law of gravity.

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So what is the force of
gravity on the brick?

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Well, you could
calculate that out.

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The force of
gravity on the brick

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is going to be equal to big G
times the mass of the moon--

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I'll say that's m
for mass and then

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the subscript is lowercase
m for moon-- the mass

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of the moon times the
mass of the brick divided

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by the distance
between the brick

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and the center of
the moon squared.

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Fair enough.

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That's the force on the brick.

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What's going to be the force
due to gravity on the feather?

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Or another way to
think about it,

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the weight of the
feather on the moon?

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We'll do the same calculation.

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The force on the
feather is going

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to be equal to big G times
the mass of the moon times

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the mass of the feather
divided by the distance

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between the center
of this feather

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and the center of
the moon squared.

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That's the distance,
and then we square it.

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So if you look at both
of these expressions,

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they both have
this quantity right

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over here-- G times the
mass of the moon divided

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by the distance
between this height

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and the center of
the moon squared.

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So they both have this
exact expression on it.

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So let's replace
that expression.

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Let's just call that
the gravitational field

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on the moon.

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So if you apply this
number by any mass,

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it will tell you the weight
of that object on the moon,

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or the gravitational
force acting downward

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on that object on the moon.

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So this is the gravitational
field of the moon.

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So I'll just call it g sub m.

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And all it is, is all of
these quantities combined.

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So if we simplify
that way, the force

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on the brick due to
the moon is going

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to be equal to that lowercase
g on the moon-- normally

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we use this lowercase g for
the gravitational constant

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on Earth, or the
gravitational field on Earth,

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or sometimes the acceleration
of gravity on Earth,

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but now we're
referring to the moon.

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That's what this lowercase
subscript m is doing for us.

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So it's equal to that times
the mass of the brick.

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For the case of the feather,
the force on the feather

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is equal to all
of this business.

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So that's the g sub m times
the mass of the feather.

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So we're going to assume,
which is a reasonable thing

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to assume, that the
mass of the brick

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is greater than the
mass of the feather.

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What's going to be
their relative forces?

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Well, here you have a greater
mass times the same quantity.

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Here you have a smaller mass
times the same quantity.

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So if the mass of
the brick is greater

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than the mass of the feather,
it's completely reasonable

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to say that the force
of gravity on the brick

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is going to be greater
than the force of gravity

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on the feather.

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So if you do all
this, and everything

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we've done to this point
is correct, you might say,

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hey, there's going to be
more force due to gravity

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on the brick, and that's
why the brick will

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be accelerated
down more quickly.

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But what you need to
remember is that there

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is more gravitational
force on this brick.

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But it also has greater mass.

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And we remember the
larger something's mass

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is, the less acceleration it'll
experience for a given force.

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So what really determines how
quickly either of these things

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will fall is their
accelerations.

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And let's figure out
their accelerations.

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I'll do this in a neutral color.

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We know that force is equal
to mass times acceleration.

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So if we want to figure out
the acceleration of the brick--

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or we could write
it the other way.

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If we divide both
sides by mass, we

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get acceleration is equal
to force divided by mass.

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And acceleration is
a vector quantity,

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and force is also
a vector quantity.

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And in this situation, we're
not using any actual value.

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But if I were using
actual values,

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I would use negative numbers for
downwards and positive values

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for upwards.

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But we're not using
any signs here.

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But you could assume that
the direction is implicitly

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being given.

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So what's the
acceleration of the brick?

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That's a lowercase
b I was writing.

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The acceleration of
the brick is going

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to be equal to the force
applied to the brick divided

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by the mass of the brick.

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But the force applied to
the brick, we already know,

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is this business
right over here.

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It is little g on the moon,
the gravitational field

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on the moon, times
the mass of the brick,

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and we're dividing that
by the mass of the brick.

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So the acceleration on
the brick on the moon--

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the acceleration that the
brick will experience--

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is the same thing as that
gravitational field expression.

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It is g sub m.

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This is how quickly it would
accelerate on the moon.

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Now let's do the same
thing for the feather.

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I think you see
where this is going.

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The acceleration
of the feather is

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going to be the force
on the feather divided

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by the mass of the feather.

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The force on the
feather is g sub m--

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g with the subscript m--
times the mass of the feather,

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and then we're
going to divide that

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by the mass of the feather.

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And so, once again,
its acceleration

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is going to be
the same quantity.

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So they are both going to
accelerate at the same rate

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downwards, which
tells us that they'll

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both hit the ground
at the same rate.

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They'll both accelerate from
the same point at the same time,

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and they'll both have
the same velocity

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when they hit the ground.

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And they'll both hit it
at the exact same time,

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despite one having
a larger mass.

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So the reality is, because
it has a larger mass,

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it has a larger gravitational
attraction to the moon.

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But because of its
mass, that attraction

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gives it the same acceleration
as something with a smaller

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mass.

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So any mass at the same level
on the surface of the moon

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would experience the
same acceleration.

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So now the quite
natural question

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is, wait, Sal, if that's true
on the moon it should also

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be true on Earth.

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And it would be true on Earth.

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If you did this
exact same experiment

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and you evacuated all
the air from the room,

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so that you didn't
have air resistance,

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and you took a
brick and a feather

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and let them go
at the same time,

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they will both hit the ground
at the exact same time, which

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is a little unintuitive,
to imagine a feather just

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plummeting the same
way a brick would.

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But it would if you
evacuated all the air.

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And so the reason why
we see this over here,

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and I think you get the
sense because I already

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talked about
evacuating the air, is

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that the difference between
the brick and the feather

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is all due to air resistance.

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If you took the same brick,
or if you took something

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that had the same
mass as the brick,

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and you were to flatten it out
so it has more air resistance--

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but let's say it has the same
mass, let's say this thing

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and this thing have
the same mass--

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00:09:03,350 --> 00:09:04,770
this thing would
fall slower than

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that because it'll have
more air resistance.

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It has more air to collide
into, to provide resistance

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00:09:11,470 --> 00:09:13,180
as it falls.

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00:09:13,180 --> 00:09:15,900
And if you took a feather and
if you compacted it really,

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00:09:15,900 --> 00:09:18,400
really, really, really, really,
really small-- the same mass

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00:09:18,400 --> 00:09:21,370
as a feather, but you made
it so small that it could

202
00:09:21,370 --> 00:09:25,340
cut through the air-- you'll see
that it will drop a lot faster.

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00:09:25,340 --> 00:09:28,980
So the real difference between
how things fall on Earth--

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00:09:28,980 --> 00:09:30,960
if you had no air,
they would all

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00:09:30,960 --> 00:09:33,220
fall at the exact same rate.

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00:09:33,220 --> 00:09:36,464
It's only because of air that
they fall at different rates.

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00:09:36,464 --> 00:09:37,630
And the air does two things.

208
00:09:37,630 --> 00:09:39,280
For constant
pressure-- so if you

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00:09:39,280 --> 00:09:41,210
have two objects that
have the same shape,

210
00:09:41,210 --> 00:09:44,430
the object that is heavier,
that has more weight,

211
00:09:44,430 --> 00:09:46,910
will fall faster
because it'll overcome--

212
00:09:46,910 --> 00:09:49,930
it'll be able to provide more
net force against the air

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00:09:49,930 --> 00:09:50,560
pressure.

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00:09:50,560 --> 00:09:52,540
If you have something
that has the same weight,

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00:09:52,540 --> 00:09:54,430
the object that is
more aerodynamic

216
00:09:54,430 --> 00:09:56,520
will fall faster-- the
one that cuts through,

217
00:09:56,520 --> 00:09:58,670
the one that has the
least air resistance.

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00:09:58,670 --> 00:10:00,140
And as a little
experiment that you

219
00:10:00,140 --> 00:10:04,900
can try in the comfort of
your own room right now,

220
00:10:04,900 --> 00:10:10,490
take a book like this.

221
00:10:10,490 --> 00:10:11,452
And you could drop it.

222
00:10:11,452 --> 00:10:13,410
And then you could take
another piece of paper,

223
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or even a little postcard or
something, and you drop it.

224
00:10:15,989 --> 00:10:17,530
And you'll see, of
course, a postcard

225
00:10:17,530 --> 00:10:19,980
will fall much slower
than this book.

226
00:10:19,980 --> 00:10:23,730
But what you do is put the
postcard on top of the book

227
00:10:23,730 --> 00:10:25,830
so that the book is
essentially breaking

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00:10:25,830 --> 00:10:28,110
all of the air resistance
for the postcard.

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00:10:28,110 --> 00:10:30,812
And what you'll see is, if
you put it on top of the book

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and you were to
drop it, you'll see

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00:10:32,270 --> 00:00:00,000
that they fall at
the exact same rate.