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- [Instructor] Beach balls float on water,

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icebergs float on water,
certain things float on water,

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whereas others, like a steel ball, sinks.

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Why? Why do certain things
float and certain things sink?

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And also, if you consider
the things that are floating,

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sometimes, most of the
object is above the water,

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like the beach ball, but
when it comes to the iceberg,

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look, most of the object is
submerged below the water.

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So what controls how much
of that object is above

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and how much of it is submerged?

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Now, you probably know the answer

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has something to do with
density, but why density?

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Why does density matter?

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What is the deeper reason behind this?

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That's what we wanna
figure out in this video,

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so let's begin.

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So, let's start by submerging
an object inside a fluid.

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Let's consider water to be our fluid,

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and let's submerge a cubicle object.

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A cube because it's a nice
shape. Easier to analyze, okay?

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We know that the water
is going to start pushing

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on this cube in all the
directions perpendicular

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to the surface.

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And if we calculate that force per area,

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we call that as the pressure.

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Now, the important thing

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is that the pressure increases with depth.

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So, let's see how that affects the cube.

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First, let's consider
the horizontal forces.

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For example, consider
the forces on the left

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and the right side of the cube.

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The forces would look somewhat like this.

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Look, the pressure is
increasing with the depth,

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but notice the forces
pretty much cancel out.

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And the same thing is gonna happen

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with the front and back
surface of the cube as well,

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so all the horizontal forces cancel out.

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But what about the top
and the bottom surface?

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Well, let's see.

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The pressure on the top is smaller

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than the pressure from the bottom.

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And because the surface
area is exactly the same

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on both the top and the bottom,

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the forces from the bottom will be larger

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than the force from the top.

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And therefore, now the
forces don't cancel out.

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Instead, there is a net
force acting upwards.

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And that net force that's acting upwards

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is what we call the buoyant force.

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This is the force that
tends to make things float.

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It tends to make things buoyant.

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That's what the b stands for over here.

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And so, notice where does
the buoyant force come from?

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It ultimately comes from the
fact that as you go deeper,

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the pressure increases.

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That is where it all comes from.

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Now, although we did
this analysis for a cube,

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this would be true for any
object of any arbitrary shape.

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Even if you take some kind of a rock,

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which has some random shape,

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the fact is the pressure from the top

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is smaller than the
pressure from the bottom.

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And so, when you look at all the forces,

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eventually, there will be
a net force acting upward,

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the buoyant force.

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Now comes the big question,

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because of this buoyant
force, how do we know

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whether this object is
going to float or sink?

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Well, it depends upon the
weight of this object.

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If the weight of this object

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is smaller than the buoyant force,

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well, then the buoyant force wins.

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The net force will now be upwards,

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and as a result, the object
will accelerate upwards,

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making it float.

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On the other hand, if the
weight of the object is larger

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than the buoyant force,
then the weight wins

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and therefore, the object
will accelerate down,

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in other words, the object will sink,

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which means all we need to do

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is figure out what the buoyant force is.

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If we can do that, we can predict

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whether an object is
going to float or sink.

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But how do we figure out
what the buoyant force

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is going to be, especially
when the objects

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have irregular shapes like this?

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Well, here's a way to think about it.

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Imagine that instead of having a rock,

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if I had a styrofoam over here,

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but of exactly the same shape

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and volume submerged in the
same liquid, in the same fluid,

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the question to think about is,

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would the buoyant force
now be the same as before

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or would it be different?

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Why don't you pause the
video and think about this?

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All right, at first, it might feel like,

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"Hey, I have a different
substance altogether,

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so the buoyant force must
be different, obviously."

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But think about it,

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the buoyant force,
where does it come from?

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It comes from the pressure
differences, isn't it?

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And what does pressure depend on?

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Well, the pressure only
depends upon the depth.

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And so if you have the
exact same shape as before,

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then all the forces will be
exactly the same, and therefore,

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the pressure would be
exactly the same as before,

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and therefore, the buoyant force

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would be exactly the same as before.

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So, this is the key insight.

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This means that the buoyant force

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has nothing to do with what
material you have submerged.

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All that matters is the
shape of the material.

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If the shape remains the same,

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then regardless of what material it is,

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the buoyant force should be the same.

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Okay, the buoyant force does
not depend upon the material,

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how can we use that insight?

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Well, now, in this exact same shape,

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let's fill water. (laughs)

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Well, the buoyant force is
gonna be the same as before,

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but this time, we know
that this particular piece

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of water is in equilibrium
because, remember,

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this is just water.

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It's static. It's not moving at all.

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This piece of water is neither
sinking nor it's floating.

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It's not accelerating upwards,
which means it's static.

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And therefore, this
means this piece of water

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is in equilibrium.

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So, the weight of this piece of water

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must be exactly equal

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to the buoyant force.

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And there we have it.

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We have figured out what
the buoyant force must be.

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For this particular shape,

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it doesn't matter what
you put inside this,

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the buoyant force should equal the weight

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of this fluid.

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In other words, when you fill this object,

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when you fill this space with some object,

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that fluid got displaced somewhere,

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and the weight of that fluid
that got displaced literally

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is the buoyant force.

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Isn't it amazing?

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Long story short, the buoyant
force acting on any object

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will always equal the weight
of the fluid that it displaces.

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And this is what we call
the Archimedes' principle.

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So now let's see if we
can use this insight

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to figure out when will an object float

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and when it'll sink, okay?

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So, we know that if the
weight of the object

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is larger than the buoyant
force, in other words,

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larger than the weight of
the fluid it displaces,

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the object is going to sink.

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So this is a sinking case,
but when will this happen?

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When will the object have more
weight compared to the fluid

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that it's displacing?

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Well, what is weight?

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Weight is just mass times gravity.

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So we can plug mg over here.

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This represents the mass of the object,

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and this represents the mass of the fluid

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that got displaced.

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But we know that mass is
the density times volume.

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So we can replace masses

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with density of the object
times the volume of the object,

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and the density of the fluid displaced

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times the volume of the fluid displaced.

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But here's the key thing,

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the volume of the fluid
displaced is exactly the same

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as the volume of the object, right?

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And therefore, these things cancel out,

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and look what the condition becomes.

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The condition for sinking

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is the density of the
object should be larger

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than the density of the
fluid it's submerged in.

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When that happens, the object will sink.

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But can we now understand why?

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Well, because if the density of the object

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is larger than that of the fluid,

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then the weight of the object

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will be larger than
the weight of the fluid

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that it displaces when
it's completely submerged.

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And as a result, its weight wins.

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Its weight will be larger
than the buoyant force

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and that's why it ends up sinking.

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And this is why a steel
ball sinks in water

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because it has a higher
density than water.

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But what if an object has a lower density

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than the fluid it's submerged in?

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Well, then its weight would be lower

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than the weight of the
fluid that it displaces,

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and therefore, the buoyant
force will be larger

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and the whole object will accelerate up.

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In other words, this is the
condition for flotation.

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This is the reason why beach balls

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and icebergs float in water

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because they have a density
that's smaller than water.

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And now, look, we have
the complete equation

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for the buoyant force.

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The buoyant force is the
weight of the fluid displaced,

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which is the density of the
fluid times the volume times g.

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And so this is the expression
for the buoyant force.

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And again, this helps us see

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why it's the density that matters

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because, look, the weight
of the displaced fluid

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will have the exact same volume

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as the weight of the submerged object.

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The volumes cancel out,

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and that's why it's eventually
the density that decides

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whether something's
going to sink or float.

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So it all comes from the
Archimedes' principle,

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which eventually comes from
the pressure differences.

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Amazing, right?

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But now, let's think about
what's going to happen

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to this object.

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We know it's going to
start accelerating up,

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but when will it stop?

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Well, let's see.

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As long as the whole
thing is submerged inside,

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the buoyant force stays the same.

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But now, as it starts
coming above the surface,

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it starts displacing lesser fluid.

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Can you see that?

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It now only displaces this
much amount of the fluid,

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and therefore, the buoyant
force will become smaller.

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But as long as it's still
larger than the weight,

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the object continues accelerating upwards,

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and eventually, at some point,

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the weight of the fluid displaced

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will exactly match the
weight of the object,

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and that's when equilibrium is reached

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and the object pretty
much stops at that point.

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So look, for an object to float,

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it needs to be submerged
enough so that the weight

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of the fluid displaced exactly
equals the object's weight.

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Does that make sense?

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Now, consider the beach ball.

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It has a very low density,
so the amount of water needed

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to match the weight of the
beach ball is very little.

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So only a small portion
needs to be submerged

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because by then, the weight of the water

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that has been displaced
already equals the weight

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of the entire beach ball

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because the beach ball has a
much smaller density compared

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to the water.

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That's the whole idea.

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On the other hand, if
you consider an iceberg,

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it has a density very, very
close to that of water.

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And so now, to displace the
water equal to its weight,

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you need to submerge a lot more.

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Pretty much the entire
thing needs to be submerged

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because its density is very,
very close to that of water.

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It's still less, that's why it's floating,

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but it's very close to that of water.

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So, higher the density of the object,

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more it needs to be submerged

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00:10:06,836 --> 00:10:09,238
so that it can be in equilibrium.

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So, if you put it all together,

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we can say that when
the density of an object

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00:10:12,410 --> 00:10:15,588
is smaller than density of the
fluid, it will be floating.

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00:10:15,588 --> 00:10:17,641
And the amount of the
objects submerged depends

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on how small the density is.

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00:10:19,498 --> 00:10:21,113
If the density of the
object is very tiny compared

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00:10:21,113 --> 00:10:22,530
to the density of the fluid,

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00:10:22,530 --> 00:10:23,739
it'll be submerged just a little bit.

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00:10:23,739 --> 00:10:25,659
On the other hand, if
the density is very close

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to the density of the
fluid, but still smaller,

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00:10:27,223 --> 00:10:29,040
it needs to be smaller
for it to be floating,

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but if it's close enough, then
most of it will be submerged.

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On the other hand, if the
density of the object is higher

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than the density of the fluid itself,

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then the object will sink.

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And by the way, in all the examples,

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we have taken water as our fluid,

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but this would work for any fluid, okay?

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For example, air is also a fluid,

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so it can also put a buoyant force.

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00:10:46,120 --> 00:10:48,253
But since air has a very
low density compared

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to everyday objects, we
don't usually notice it.

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But if you consider a
helium balloon, its density,

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helium density is smaller
than that of the air.

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00:10:56,142 --> 00:10:58,993
And now, as a result of
that, helium tends to float,

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and that's why helium
balloons tend to rise up.

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But now is an interesting question,

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what if the density of the
object exactly equals the density

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00:11:06,428 --> 00:11:07,304
of the fluid?

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00:11:07,304 --> 00:11:08,250
What happens then?

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Well, now, if you completely submerge it,

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00:11:10,243 --> 00:11:13,598
it will neither float nor sink.

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We call this the neutral buoyancy.

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That object will just stay
at that particular depth,

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00:11:20,489 --> 00:11:22,620
and that's exactly how submarines

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00:11:22,620 --> 00:11:24,744
can stay at a particular depth.

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00:11:24,744 --> 00:11:28,340
They do that by changing
their average density.

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00:11:28,340 --> 00:11:29,848
If they want to sink,

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00:11:29,848 --> 00:11:31,845
they will increase their average density

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00:11:31,845 --> 00:11:36,231
by allowing water to flood their tanks.

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00:11:36,231 --> 00:11:37,064
On the other hand,

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if it now needs to come towards
the surface of the water,

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then it'll decrease its average density.

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00:11:42,491 --> 00:11:44,996
It does so by now using compressed air

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00:11:44,996 --> 00:11:47,231
to force the water out.

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00:11:47,231 --> 00:11:49,614
And by carefully balancing
the amount of water

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00:11:49,614 --> 00:11:51,422
and air inside its tanks,

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00:11:51,422 --> 00:11:54,740
it can also make sure that
its density exactly equals out

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00:11:54,740 --> 00:11:57,740
of the surrounding water,
maintaining neutral buoyancy,

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00:11:57,740 --> 00:12:00,493
and in which case, it'll
stay at a particular depth.

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00:12:00,493 --> 00:12:02,115
That's amazing, right?

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00:12:02,115 --> 00:12:04,901
Now, instead of submarine,
imagine you were wearing a suit

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which could also maintain
neutral buoyancy in water.

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00:12:07,843 --> 00:12:10,182
Then you would be, just
like the submarine,

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00:12:10,182 --> 00:12:12,482
stay at a particular location in water,

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00:12:12,482 --> 00:12:14,895
not going down nor going up.

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00:12:14,895 --> 00:12:18,495
In other words, you would
kind of feel weightless,

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00:12:18,495 --> 00:12:20,106
which means now you can train

316
00:12:20,106 --> 00:12:22,490
for the weightless environments
that you would face

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00:12:22,490 --> 00:12:23,828
in the space stations.

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00:12:23,828 --> 00:12:24,999
And that's exactly

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00:12:24,999 --> 00:12:28,614
what the NASA's Neutral Buoyancy Lab does.

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00:12:28,614 --> 00:12:30,593
It's a giant swimming pool inside

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00:12:30,593 --> 00:12:33,600
which astronauts can
maintain neutral buoyancy

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00:12:33,600 --> 00:12:34,872
and train for the weightless environment.

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00:12:34,872 --> 00:12:37,182
It's not perfect, but it's way better

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00:12:37,182 --> 00:12:40,323
and more realistic than training
on the ground, for example.