- [Instructor] Beach balls float on water,
icebergs float on water, certain things float on water,
whereas others, like a steel ball, sinks.
Why? Why do certain things float and certain things sink?
And also, if you consider the things that are floating,
sometimes, most of the object is above the water,
like the beach ball, but when it comes to the iceberg,
look, most of the object is submerged below the water.
So what controls how much of that object is above
and how much of it is submerged?
Now, you probably know the answer
has something to do with density, but why density?
Why does density matter?
What is the deeper reason behind this?
That's what we wanna figure out in this video,
so let's begin.
So, let's start by submerging an object inside a fluid.
Let's consider water to be our fluid,
and let's submerge a cubicle object.
A cube because it's a nice shape. Easier to analyze, okay?
We know that the water is going to start pushing
on this cube in all the directions perpendicular
to the surface.
And if we calculate that force per area,
we call that as the pressure.
Now, the important thing
is that the pressure increases with depth.
So, let's see how that affects the cube.
First, let's consider the horizontal forces.
For example, consider the forces on the left
and the right side of the cube.
The forces would look somewhat like this.
Look, the pressure is increasing with the depth,
but notice the forces pretty much cancel out.
And the same thing is gonna happen
with the front and back surface of the cube as well,
so all the horizontal forces cancel out.
But what about the top and the bottom surface?
Well, let's see.
The pressure on the top is smaller
than the pressure from the bottom.
And because the surface area is exactly the same
on both the top and the bottom,
the forces from the bottom will be larger
than the force from the top.
And therefore, now the forces don't cancel out.
Instead, there is a net force acting upwards.
And that net force that's acting upwards
is what we call the buoyant force.
This is the force that tends to make things float.
It tends to make things buoyant.
That's what the b stands for over here.
And so, notice where does the buoyant force come from?
It ultimately comes from the fact that as you go deeper,
the pressure increases.
That is where it all comes from.
Now, although we did this analysis for a cube,
this would be true for any object of any arbitrary shape.
Even if you take some kind of a rock,
which has some random shape,
the fact is the pressure from the top
is smaller than the pressure from the bottom.
And so, when you look at all the forces,
eventually, there will be a net force acting upward,
the buoyant force.
Now comes the big question,
because of this buoyant force, how do we know
whether this object is going to float or sink?
Well, it depends upon the weight of this object.
If the weight of this object
is smaller than the buoyant force,
well, then the buoyant force wins.
The net force will now be upwards,
and as a result, the object will accelerate upwards,
making it float.
On the other hand, if the weight of the object is larger
than the buoyant force, then the weight wins
and therefore, the object will accelerate down,
in other words, the object will sink,
which means all we need to do
is figure out what the buoyant force is.
If we can do that, we can predict
whether an object is going to float or sink.
But how do we figure out what the buoyant force
is going to be, especially when the objects
have irregular shapes like this?
Well, here's a way to think about it.
Imagine that instead of having a rock,
if I had a styrofoam over here,
but of exactly the same shape
and volume submerged in the same liquid, in the same fluid,
the question to think about is,
would the buoyant force now be the same as before
or would it be different?
Why don't you pause the video and think about this?
All right, at first, it might feel like,
"Hey, I have a different substance altogether,
so the buoyant force must be different, obviously."
But think about it,
the buoyant force, where does it come from?
It comes from the pressure differences, isn't it?
And what does pressure depend on?
Well, the pressure only depends upon the depth.
And so if you have the exact same shape as before,
then all the forces will be exactly the same, and therefore,
the pressure would be exactly the same as before,
and therefore, the buoyant force
would be exactly the same as before.
So, this is the key insight.
This means that the buoyant force
has nothing to do with what material you have submerged.
All that matters is the shape of the material.
If the shape remains the same,
then regardless of what material it is,
the buoyant force should be the same.
Okay, the buoyant force does not depend upon the material,
how can we use that insight?
Well, now, in this exact same shape,
let's fill water. (laughs)
Well, the buoyant force is gonna be the same as before,
but this time, we know that this particular piece
of water is in equilibrium because, remember,
this is just water.
It's static. It's not moving at all.
This piece of water is neither sinking nor it's floating.
It's not accelerating upwards, which means it's static.
And therefore, this means this piece of water
is in equilibrium.
So, the weight of this piece of water
must be exactly equal
to the buoyant force.
And there we have it.
We have figured out what the buoyant force must be.
For this particular shape,
it doesn't matter what you put inside this,
the buoyant force should equal the weight
of this fluid.
In other words, when you fill this object,
when you fill this space with some object,
that fluid got displaced somewhere,
and the weight of that fluid that got displaced literally
is the buoyant force.
Isn't it amazing?
Long story short, the buoyant force acting on any object
will always equal the weight of the fluid that it displaces.
And this is what we call the Archimedes' principle.
So now let's see if we can use this insight
to figure out when will an object float
and when it'll sink, okay?
So, we know that if the weight of the object
is larger than the buoyant force, in other words,
larger than the weight of the fluid it displaces,
the object is going to sink.
So this is a sinking case, but when will this happen?
When will the object have more weight compared to the fluid
that it's displacing?
Well, what is weight?
Weight is just mass times gravity.
So we can plug mg over here.
This represents the mass of the object,
and this represents the mass of the fluid
that got displaced.
But we know that mass is the density times volume.
So we can replace masses
with density of the object times the volume of the object,
and the density of the fluid displaced
times the volume of the fluid displaced.
But here's the key thing,
the volume of the fluid displaced is exactly the same
as the volume of the object, right?
And therefore, these things cancel out,
and look what the condition becomes.
The condition for sinking
is the density of the object should be larger
than the density of the fluid it's submerged in.
When that happens, the object will sink.
But can we now understand why?
Well, because if the density of the object
is larger than that of the fluid,
then the weight of the object
will be larger than the weight of the fluid
that it displaces when it's completely submerged.
And as a result, its weight wins.
Its weight will be larger than the buoyant force
and that's why it ends up sinking.
And this is why a steel ball sinks in water
because it has a higher density than water.
But what if an object has a lower density
than the fluid it's submerged in?
Well, then its weight would be lower
than the weight of the fluid that it displaces,
and therefore, the buoyant force will be larger
and the whole object will accelerate up.
In other words, this is the condition for flotation.
This is the reason why beach balls
and icebergs float in water
because they have a density that's smaller than water.
And now, look, we have the complete equation
for the buoyant force.
The buoyant force is the weight of the fluid displaced,
which is the density of the fluid times the volume times g.
And so this is the expression for the buoyant force.
And again, this helps us see
why it's the density that matters
because, look, the weight of the displaced fluid
will have the exact same volume
as the weight of the submerged object.
The volumes cancel out,
and that's why it's eventually the density that decides
whether something's going to sink or float.
So it all comes from the Archimedes' principle,
which eventually comes from the pressure differences.
Amazing, right?
But now, let's think about what's going to happen
to this object.
We know it's going to start accelerating up,
but when will it stop?
Well, let's see.
As long as the whole thing is submerged inside,
the buoyant force stays the same.
But now, as it starts coming above the surface,
it starts displacing lesser fluid.
Can you see that?
It now only displaces this much amount of the fluid,
and therefore, the buoyant force will become smaller.
But as long as it's still larger than the weight,
the object continues accelerating upwards,
and eventually, at some point,
the weight of the fluid displaced
will exactly match the weight of the object,
and that's when equilibrium is reached
and the object pretty much stops at that point.
So look, for an object to float,
it needs to be submerged enough so that the weight
of the fluid displaced exactly equals the object's weight.
Does that make sense?
Now, consider the beach ball.
It has a very low density, so the amount of water needed
to match the weight of the beach ball is very little.
So only a small portion needs to be submerged
because by then, the weight of the water
that has been displaced already equals the weight
of the entire beach ball
because the beach ball has a much smaller density compared
to the water.
That's the whole idea.
On the other hand, if you consider an iceberg,
it has a density very, very close to that of water.
And so now, to displace the water equal to its weight,
you need to submerge a lot more.
Pretty much the entire thing needs to be submerged
because its density is very, very close to that of water.
It's still less, that's why it's floating,
but it's very close to that of water.
So, higher the density of the object,
more it needs to be submerged
so that it can be in equilibrium.
So, if you put it all together,
we can say that when the density of an object
is smaller than density of the fluid, it will be floating.
And the amount of the objects submerged depends
on how small the density is.
If the density of the object is very tiny compared
to the density of the fluid,
it'll be submerged just a little bit.
On the other hand, if the density is very close
to the density of the fluid, but still smaller,
it needs to be smaller for it to be floating,
but if it's close enough, then most of it will be submerged.
On the other hand, if the density of the object is higher
than the density of the fluid itself,
then the object will sink.
And by the way, in all the examples,
we have taken water as our fluid,
but this would work for any fluid, okay?
For example, air is also a fluid,
so it can also put a buoyant force.
But since air has a very low density compared
to everyday objects, we don't usually notice it.
But if you consider a helium balloon, its density,
helium density is smaller than that of the air.
And now, as a result of that, helium tends to float,
and that's why helium balloons tend to rise up.
But now is an interesting question,
what if the density of the object exactly equals the density
of the fluid?
What happens then?
Well, now, if you completely submerge it,
it will neither float nor sink.
We call this the neutral buoyancy.
That object will just stay at that particular depth,
and that's exactly how submarines
can stay at a particular depth.
They do that by changing their average density.
If they want to sink,
they will increase their average density
by allowing water to flood their tanks.
On the other hand,
if it now needs to come towards the surface of the water,
then it'll decrease its average density.
It does so by now using compressed air
to force the water out.
And by carefully balancing the amount of water
and air inside its tanks,
it can also make sure that its density exactly equals out
of the surrounding water, maintaining neutral buoyancy,
and in which case, it'll stay at a particular depth.
That's amazing, right?
Now, instead of submarine, imagine you were wearing a suit
which could also maintain neutral buoyancy in water.
Then you would be, just like the submarine,
stay at a particular location in water,
not going down nor going up.
In other words, you would kind of feel weightless,
which means now you can train
for the weightless environments that you would face
in the space stations.
And that's exactly
what the NASA's Neutral Buoyancy Lab does.
It's a giant swimming pool inside
which astronauts can maintain neutral buoyancy
and train for the weightless environment.
It's not perfect, but it's way better
and more realistic than training on the ground, for example.