[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:01.84,Default,,0000,0000,0000,,- [Instructor] Beach balls float on water,
Dialogue: 0,0:00:01.84,0:00:04.51,Default,,0000,0000,0000,,icebergs float on water,\Ncertain things float on water,
Dialogue: 0,0:00:04.51,0:00:07.34,Default,,0000,0000,0000,,whereas others, like a steel ball, sinks.
Dialogue: 0,0:00:07.34,0:00:10.41,Default,,0000,0000,0000,,Why? Why do certain things\Nfloat and certain things sink?
Dialogue: 0,0:00:10.41,0:00:12.11,Default,,0000,0000,0000,,And also, if you consider\Nthe things that are floating,
Dialogue: 0,0:00:12.11,0:00:14.74,Default,,0000,0000,0000,,sometimes, most of the\Nobject is above the water,
Dialogue: 0,0:00:14.74,0:00:17.35,Default,,0000,0000,0000,,like the beach ball, but\Nwhen it comes to the iceberg,
Dialogue: 0,0:00:17.35,0:00:20.30,Default,,0000,0000,0000,,look, most of the object is\Nsubmerged below the water.
Dialogue: 0,0:00:20.30,0:00:23.08,Default,,0000,0000,0000,,So what controls how much\Nof that object is above
Dialogue: 0,0:00:23.08,0:00:24.86,Default,,0000,0000,0000,,and how much of it is submerged?
Dialogue: 0,0:00:24.86,0:00:26.19,Default,,0000,0000,0000,,Now, you probably know the answer
Dialogue: 0,0:00:26.19,0:00:29.55,Default,,0000,0000,0000,,has something to do with\Ndensity, but why density?
Dialogue: 0,0:00:29.55,0:00:31.14,Default,,0000,0000,0000,,Why does density matter?
Dialogue: 0,0:00:31.14,0:00:33.01,Default,,0000,0000,0000,,What is the deeper reason behind this?
Dialogue: 0,0:00:33.01,0:00:35.04,Default,,0000,0000,0000,,That's what we wanna\Nfigure out in this video,
Dialogue: 0,0:00:35.04,0:00:35.87,Default,,0000,0000,0000,,so let's begin.
Dialogue: 0,0:00:35.87,0:00:38.24,Default,,0000,0000,0000,,So, let's start by submerging\Nan object inside a fluid.
Dialogue: 0,0:00:38.24,0:00:40.23,Default,,0000,0000,0000,,Let's consider water to be our fluid,
Dialogue: 0,0:00:40.23,0:00:42.16,Default,,0000,0000,0000,,and let's submerge a cubicle object.
Dialogue: 0,0:00:42.16,0:00:45.61,Default,,0000,0000,0000,,A cube because it's a nice\Nshape. Easier to analyze, okay?
Dialogue: 0,0:00:45.61,0:00:47.99,Default,,0000,0000,0000,,We know that the water\Nis going to start pushing
Dialogue: 0,0:00:47.99,0:00:50.60,Default,,0000,0000,0000,,on this cube in all the\Ndirections perpendicular
Dialogue: 0,0:00:50.60,0:00:51.62,Default,,0000,0000,0000,,to the surface.
Dialogue: 0,0:00:51.62,0:00:53.49,Default,,0000,0000,0000,,And if we calculate that force per area,
Dialogue: 0,0:00:53.49,0:00:55.11,Default,,0000,0000,0000,,we call that as the pressure.
Dialogue: 0,0:00:55.11,0:00:56.06,Default,,0000,0000,0000,,Now, the important thing
Dialogue: 0,0:00:56.06,0:00:58.73,Default,,0000,0000,0000,,is that the pressure increases with depth.
Dialogue: 0,0:00:58.73,0:01:01.34,Default,,0000,0000,0000,,So, let's see how that affects the cube.
Dialogue: 0,0:01:01.34,0:01:02.92,Default,,0000,0000,0000,,First, let's consider\Nthe horizontal forces.
Dialogue: 0,0:01:02.92,0:01:04.59,Default,,0000,0000,0000,,For example, consider\Nthe forces on the left
Dialogue: 0,0:01:04.59,0:01:06.12,Default,,0000,0000,0000,,and the right side of the cube.
Dialogue: 0,0:01:06.12,0:01:07.75,Default,,0000,0000,0000,,The forces would look somewhat like this.
Dialogue: 0,0:01:07.75,0:01:10.68,Default,,0000,0000,0000,,Look, the pressure is\Nincreasing with the depth,
Dialogue: 0,0:01:10.68,0:01:14.24,Default,,0000,0000,0000,,but notice the forces\Npretty much cancel out.
Dialogue: 0,0:01:14.24,0:01:15.09,Default,,0000,0000,0000,,And the same thing is gonna happen
Dialogue: 0,0:01:15.09,0:01:17.32,Default,,0000,0000,0000,,with the front and back\Nsurface of the cube as well,
Dialogue: 0,0:01:17.32,0:01:19.74,Default,,0000,0000,0000,,so all the horizontal forces cancel out.
Dialogue: 0,0:01:19.74,0:01:22.24,Default,,0000,0000,0000,,But what about the top\Nand the bottom surface?
Dialogue: 0,0:01:22.24,0:01:23.24,Default,,0000,0000,0000,,Well, let's see.
Dialogue: 0,0:01:23.24,0:01:25.11,Default,,0000,0000,0000,,The pressure on the top is smaller
Dialogue: 0,0:01:25.11,0:01:27.75,Default,,0000,0000,0000,,than the pressure from the bottom.
Dialogue: 0,0:01:27.75,0:01:31.09,Default,,0000,0000,0000,,And because the surface\Narea is exactly the same
Dialogue: 0,0:01:31.09,0:01:32.99,Default,,0000,0000,0000,,on both the top and the bottom,
Dialogue: 0,0:01:32.99,0:01:36.18,Default,,0000,0000,0000,,the forces from the bottom will be larger
Dialogue: 0,0:01:36.18,0:01:38.68,Default,,0000,0000,0000,,than the force from the top.
Dialogue: 0,0:01:38.68,0:01:41.08,Default,,0000,0000,0000,,And therefore, now the\Nforces don't cancel out.
Dialogue: 0,0:01:41.08,0:01:45.57,Default,,0000,0000,0000,,Instead, there is a net\Nforce acting upwards.
Dialogue: 0,0:01:45.57,0:01:48.24,Default,,0000,0000,0000,,And that net force that's acting upwards
Dialogue: 0,0:01:48.24,0:01:50.99,Default,,0000,0000,0000,,is what we call the buoyant force.
Dialogue: 0,0:01:50.99,0:01:55.35,Default,,0000,0000,0000,,This is the force that\Ntends to make things float.
Dialogue: 0,0:01:55.35,0:01:57.93,Default,,0000,0000,0000,,It tends to make things buoyant.
Dialogue: 0,0:01:57.93,0:01:59.98,Default,,0000,0000,0000,,That's what the b stands for over here.
Dialogue: 0,0:01:59.98,0:02:02.76,Default,,0000,0000,0000,,And so, notice where does\Nthe buoyant force come from?
Dialogue: 0,0:02:02.76,0:02:06.75,Default,,0000,0000,0000,,It ultimately comes from the\Nfact that as you go deeper,
Dialogue: 0,0:02:06.75,0:02:09.04,Default,,0000,0000,0000,,the pressure increases.
Dialogue: 0,0:02:09.04,0:02:11.61,Default,,0000,0000,0000,,That is where it all comes from.
Dialogue: 0,0:02:11.61,0:02:13.84,Default,,0000,0000,0000,,Now, although we did\Nthis analysis for a cube,
Dialogue: 0,0:02:13.84,0:02:17.50,Default,,0000,0000,0000,,this would be true for any\Nobject of any arbitrary shape.
Dialogue: 0,0:02:17.50,0:02:18.99,Default,,0000,0000,0000,,Even if you take some kind of a rock,
Dialogue: 0,0:02:18.99,0:02:20.74,Default,,0000,0000,0000,,which has some random shape,
Dialogue: 0,0:02:20.74,0:02:22.78,Default,,0000,0000,0000,,the fact is the pressure from the top
Dialogue: 0,0:02:22.78,0:02:25.29,Default,,0000,0000,0000,,is smaller than the\Npressure from the bottom.
Dialogue: 0,0:02:25.29,0:02:26.92,Default,,0000,0000,0000,,And so, when you look at all the forces,
Dialogue: 0,0:02:26.92,0:02:30.50,Default,,0000,0000,0000,,eventually, there will be\Na net force acting upward,
Dialogue: 0,0:02:30.50,0:02:32.35,Default,,0000,0000,0000,,the buoyant force.
Dialogue: 0,0:02:32.35,0:02:33.74,Default,,0000,0000,0000,,Now comes the big question,
Dialogue: 0,0:02:33.74,0:02:35.100,Default,,0000,0000,0000,,because of this buoyant\Nforce, how do we know
Dialogue: 0,0:02:35.100,0:02:38.60,Default,,0000,0000,0000,,whether this object is\Ngoing to float or sink?
Dialogue: 0,0:02:38.60,0:02:42.40,Default,,0000,0000,0000,,Well, it depends upon the\Nweight of this object.
Dialogue: 0,0:02:42.40,0:02:44.74,Default,,0000,0000,0000,,If the weight of this object
Dialogue: 0,0:02:44.74,0:02:47.90,Default,,0000,0000,0000,,is smaller than the buoyant force,
Dialogue: 0,0:02:47.90,0:02:49.74,Default,,0000,0000,0000,,well, then the buoyant force wins.
Dialogue: 0,0:02:49.74,0:02:51.78,Default,,0000,0000,0000,,The net force will now be upwards,
Dialogue: 0,0:02:51.78,0:02:54.61,Default,,0000,0000,0000,,and as a result, the object\Nwill accelerate upwards,
Dialogue: 0,0:02:54.61,0:02:56.83,Default,,0000,0000,0000,,making it float.
Dialogue: 0,0:02:56.83,0:03:01.10,Default,,0000,0000,0000,,On the other hand, if the\Nweight of the object is larger
Dialogue: 0,0:03:01.10,0:03:04.24,Default,,0000,0000,0000,,than the buoyant force,\Nthen the weight wins
Dialogue: 0,0:03:04.24,0:03:06.66,Default,,0000,0000,0000,,and therefore, the object\Nwill accelerate down,
Dialogue: 0,0:03:06.66,0:03:09.42,Default,,0000,0000,0000,,in other words, the object will sink,
Dialogue: 0,0:03:09.42,0:03:10.67,Default,,0000,0000,0000,,which means all we need to do
Dialogue: 0,0:03:10.67,0:03:12.75,Default,,0000,0000,0000,,is figure out what the buoyant force is.
Dialogue: 0,0:03:12.75,0:03:14.32,Default,,0000,0000,0000,,If we can do that, we can predict
Dialogue: 0,0:03:14.32,0:03:16.76,Default,,0000,0000,0000,,whether an object is\Ngoing to float or sink.
Dialogue: 0,0:03:16.76,0:03:18.79,Default,,0000,0000,0000,,But how do we figure out\Nwhat the buoyant force
Dialogue: 0,0:03:18.79,0:03:21.50,Default,,0000,0000,0000,,is going to be, especially\Nwhen the objects
Dialogue: 0,0:03:21.50,0:03:23.34,Default,,0000,0000,0000,,have irregular shapes like this?
Dialogue: 0,0:03:23.34,0:03:25.29,Default,,0000,0000,0000,,Well, here's a way to think about it.
Dialogue: 0,0:03:25.29,0:03:28.23,Default,,0000,0000,0000,,Imagine that instead of having a rock,
Dialogue: 0,0:03:28.23,0:03:30.49,Default,,0000,0000,0000,,if I had a styrofoam over here,
Dialogue: 0,0:03:30.49,0:03:32.74,Default,,0000,0000,0000,,but of exactly the same shape
Dialogue: 0,0:03:32.74,0:03:36.67,Default,,0000,0000,0000,,and volume submerged in the\Nsame liquid, in the same fluid,
Dialogue: 0,0:03:36.67,0:03:38.81,Default,,0000,0000,0000,,the question to think about is,
Dialogue: 0,0:03:38.81,0:03:41.71,Default,,0000,0000,0000,,would the buoyant force\Nnow be the same as before
Dialogue: 0,0:03:41.71,0:03:43.29,Default,,0000,0000,0000,,or would it be different?
Dialogue: 0,0:03:43.29,0:03:45.85,Default,,0000,0000,0000,,Why don't you pause the\Nvideo and think about this?
Dialogue: 0,0:03:45.85,0:03:47.50,Default,,0000,0000,0000,,All right, at first, it might feel like,
Dialogue: 0,0:03:47.50,0:03:49.50,Default,,0000,0000,0000,,"Hey, I have a different\Nsubstance altogether,
Dialogue: 0,0:03:49.50,0:03:51.99,Default,,0000,0000,0000,,so the buoyant force must\Nbe different, obviously."
Dialogue: 0,0:03:51.99,0:03:53.02,Default,,0000,0000,0000,,But think about it,
Dialogue: 0,0:03:53.02,0:03:54.38,Default,,0000,0000,0000,,the buoyant force,\Nwhere does it come from?
Dialogue: 0,0:03:54.38,0:03:57.09,Default,,0000,0000,0000,,It comes from the pressure\Ndifferences, isn't it?
Dialogue: 0,0:03:57.09,0:03:58.84,Default,,0000,0000,0000,,And what does pressure depend on?
Dialogue: 0,0:03:58.84,0:04:02.88,Default,,0000,0000,0000,,Well, the pressure only\Ndepends upon the depth.
Dialogue: 0,0:04:02.88,0:04:06.03,Default,,0000,0000,0000,,And so if you have the\Nexact same shape as before,
Dialogue: 0,0:04:06.03,0:04:09.28,Default,,0000,0000,0000,,then all the forces will be\Nexactly the same, and therefore,
Dialogue: 0,0:04:09.28,0:04:11.94,Default,,0000,0000,0000,,the pressure would be\Nexactly the same as before,
Dialogue: 0,0:04:11.94,0:04:13.90,Default,,0000,0000,0000,,and therefore, the buoyant force
Dialogue: 0,0:04:13.90,0:04:16.14,Default,,0000,0000,0000,,would be exactly the same as before.
Dialogue: 0,0:04:16.14,0:04:17.68,Default,,0000,0000,0000,,So, this is the key insight.
Dialogue: 0,0:04:17.68,0:04:19.18,Default,,0000,0000,0000,,This means that the buoyant force
Dialogue: 0,0:04:19.18,0:04:22.06,Default,,0000,0000,0000,,has nothing to do with what\Nmaterial you have submerged.
Dialogue: 0,0:04:22.06,0:04:25.88,Default,,0000,0000,0000,,All that matters is the\Nshape of the material.
Dialogue: 0,0:04:25.88,0:04:27.25,Default,,0000,0000,0000,,If the shape remains the same,
Dialogue: 0,0:04:27.25,0:04:29.11,Default,,0000,0000,0000,,then regardless of what material it is,
Dialogue: 0,0:04:29.11,0:04:31.49,Default,,0000,0000,0000,,the buoyant force should be the same.
Dialogue: 0,0:04:31.49,0:04:34.60,Default,,0000,0000,0000,,Okay, the buoyant force does\Nnot depend upon the material,
Dialogue: 0,0:04:34.60,0:04:36.49,Default,,0000,0000,0000,,how can we use that insight?
Dialogue: 0,0:04:36.49,0:04:40.14,Default,,0000,0000,0000,,Well, now, in this exact same shape,
Dialogue: 0,0:04:40.14,0:04:44.56,Default,,0000,0000,0000,,let's fill water. (laughs)
Dialogue: 0,0:04:44.56,0:04:46.73,Default,,0000,0000,0000,,Well, the buoyant force is\Ngonna be the same as before,
Dialogue: 0,0:04:46.73,0:04:50.79,Default,,0000,0000,0000,,but this time, we know\Nthat this particular piece
Dialogue: 0,0:04:50.79,0:04:54.16,Default,,0000,0000,0000,,of water is in equilibrium\Nbecause, remember,
Dialogue: 0,0:04:54.16,0:04:55.34,Default,,0000,0000,0000,,this is just water.
Dialogue: 0,0:04:55.34,0:04:57.50,Default,,0000,0000,0000,,It's static. It's not moving at all.
Dialogue: 0,0:04:57.50,0:05:00.13,Default,,0000,0000,0000,,This piece of water is neither\Nsinking nor it's floating.
Dialogue: 0,0:05:00.13,0:05:02.94,Default,,0000,0000,0000,,It's not accelerating upwards,\Nwhich means it's static.
Dialogue: 0,0:05:02.94,0:05:05.60,Default,,0000,0000,0000,,And therefore, this\Nmeans this piece of water
Dialogue: 0,0:05:05.60,0:05:07.33,Default,,0000,0000,0000,,is in equilibrium.
Dialogue: 0,0:05:07.33,0:05:10.29,Default,,0000,0000,0000,,So, the weight of this piece of water
Dialogue: 0,0:05:10.29,0:05:13.29,Default,,0000,0000,0000,,must be exactly equal
Dialogue: 0,0:05:13.29,0:05:15.24,Default,,0000,0000,0000,,to the buoyant force.
Dialogue: 0,0:05:15.24,0:05:16.36,Default,,0000,0000,0000,,And there we have it.
Dialogue: 0,0:05:16.36,0:05:20.35,Default,,0000,0000,0000,,We have figured out what\Nthe buoyant force must be.
Dialogue: 0,0:05:20.35,0:05:21.85,Default,,0000,0000,0000,,For this particular shape,
Dialogue: 0,0:05:21.85,0:05:23.86,Default,,0000,0000,0000,,it doesn't matter what\Nyou put inside this,
Dialogue: 0,0:05:23.86,0:05:26.88,Default,,0000,0000,0000,,the buoyant force should equal the weight
Dialogue: 0,0:05:26.88,0:05:29.74,Default,,0000,0000,0000,,of this fluid.
Dialogue: 0,0:05:29.74,0:05:32.49,Default,,0000,0000,0000,,In other words, when you fill this object,
Dialogue: 0,0:05:32.49,0:05:35.76,Default,,0000,0000,0000,,when you fill this space with some object,
Dialogue: 0,0:05:35.76,0:05:39.27,Default,,0000,0000,0000,,that fluid got displaced somewhere,
Dialogue: 0,0:05:39.27,0:05:43.100,Default,,0000,0000,0000,,and the weight of that fluid\Nthat got displaced literally
Dialogue: 0,0:05:43.100,0:05:46.60,Default,,0000,0000,0000,,is the buoyant force.
Dialogue: 0,0:05:46.60,0:05:47.92,Default,,0000,0000,0000,,Isn't it amazing?
Dialogue: 0,0:05:47.92,0:05:50.85,Default,,0000,0000,0000,,Long story short, the buoyant\Nforce acting on any object
Dialogue: 0,0:05:50.85,0:05:55.41,Default,,0000,0000,0000,,will always equal the weight\Nof the fluid that it displaces.
Dialogue: 0,0:05:55.41,0:05:59.56,Default,,0000,0000,0000,,And this is what we call\Nthe Archimedes' principle.
Dialogue: 0,0:05:59.56,0:06:01.59,Default,,0000,0000,0000,,So now let's see if we\Ncan use this insight
Dialogue: 0,0:06:01.59,0:06:03.56,Default,,0000,0000,0000,,to figure out when will an object float
Dialogue: 0,0:06:03.56,0:06:05.60,Default,,0000,0000,0000,,and when it'll sink, okay?
Dialogue: 0,0:06:05.60,0:06:07.57,Default,,0000,0000,0000,,So, we know that if the\Nweight of the object
Dialogue: 0,0:06:07.57,0:06:10.33,Default,,0000,0000,0000,,is larger than the buoyant\Nforce, in other words,
Dialogue: 0,0:06:10.33,0:06:12.99,Default,,0000,0000,0000,,larger than the weight of\Nthe fluid it displaces,
Dialogue: 0,0:06:12.99,0:06:14.74,Default,,0000,0000,0000,,the object is going to sink.
Dialogue: 0,0:06:14.74,0:06:17.50,Default,,0000,0000,0000,,So this is a sinking case,\Nbut when will this happen?
Dialogue: 0,0:06:17.50,0:06:20.24,Default,,0000,0000,0000,,When will the object have more\Nweight compared to the fluid
Dialogue: 0,0:06:20.24,0:06:21.49,Default,,0000,0000,0000,,that it's displacing?
Dialogue: 0,0:06:21.49,0:06:22.99,Default,,0000,0000,0000,,Well, what is weight?
Dialogue: 0,0:06:22.99,0:06:24.68,Default,,0000,0000,0000,,Weight is just mass times gravity.
Dialogue: 0,0:06:24.68,0:06:26.84,Default,,0000,0000,0000,,So we can plug mg over here.
Dialogue: 0,0:06:26.84,0:06:28.32,Default,,0000,0000,0000,,This represents the mass of the object,
Dialogue: 0,0:06:28.32,0:06:30.64,Default,,0000,0000,0000,,and this represents the mass of the fluid
Dialogue: 0,0:06:30.64,0:06:31.99,Default,,0000,0000,0000,,that got displaced.
Dialogue: 0,0:06:31.99,0:06:35.56,Default,,0000,0000,0000,,But we know that mass is\Nthe density times volume.
Dialogue: 0,0:06:35.56,0:06:36.64,Default,,0000,0000,0000,,So we can replace masses
Dialogue: 0,0:06:36.64,0:06:39.80,Default,,0000,0000,0000,,with density of the object\Ntimes the volume of the object,
Dialogue: 0,0:06:39.80,0:06:41.81,Default,,0000,0000,0000,,and the density of the fluid displaced
Dialogue: 0,0:06:41.81,0:06:43.60,Default,,0000,0000,0000,,times the volume of the fluid displaced.
Dialogue: 0,0:06:43.60,0:06:45.23,Default,,0000,0000,0000,,But here's the key thing,
Dialogue: 0,0:06:45.23,0:06:48.37,Default,,0000,0000,0000,,the volume of the fluid\Ndisplaced is exactly the same
Dialogue: 0,0:06:48.37,0:06:51.06,Default,,0000,0000,0000,,as the volume of the object, right?
Dialogue: 0,0:06:51.06,0:06:53.24,Default,,0000,0000,0000,,And therefore, these things cancel out,
Dialogue: 0,0:06:53.24,0:06:55.88,Default,,0000,0000,0000,,and look what the condition becomes.
Dialogue: 0,0:06:55.88,0:06:56.89,Default,,0000,0000,0000,,The condition for sinking
Dialogue: 0,0:06:56.89,0:06:59.58,Default,,0000,0000,0000,,is the density of the\Nobject should be larger
Dialogue: 0,0:06:59.58,0:07:01.40,Default,,0000,0000,0000,,than the density of the\Nfluid it's submerged in.
Dialogue: 0,0:07:01.40,0:07:04.81,Default,,0000,0000,0000,,When that happens, the object will sink.
Dialogue: 0,0:07:04.81,0:07:06.100,Default,,0000,0000,0000,,But can we now understand why?
Dialogue: 0,0:07:06.100,0:07:08.66,Default,,0000,0000,0000,,Well, because if the density of the object
Dialogue: 0,0:07:08.66,0:07:10.58,Default,,0000,0000,0000,,is larger than that of the fluid,
Dialogue: 0,0:07:10.58,0:07:12.58,Default,,0000,0000,0000,,then the weight of the object
Dialogue: 0,0:07:12.58,0:07:14.89,Default,,0000,0000,0000,,will be larger than\Nthe weight of the fluid
Dialogue: 0,0:07:14.89,0:07:17.73,Default,,0000,0000,0000,,that it displaces when\Nit's completely submerged.
Dialogue: 0,0:07:17.73,0:07:19.92,Default,,0000,0000,0000,,And as a result, its weight wins.
Dialogue: 0,0:07:19.92,0:07:21.87,Default,,0000,0000,0000,,Its weight will be larger\Nthan the buoyant force
Dialogue: 0,0:07:21.87,0:07:24.57,Default,,0000,0000,0000,,and that's why it ends up sinking.
Dialogue: 0,0:07:24.57,0:07:26.54,Default,,0000,0000,0000,,And this is why a steel\Nball sinks in water
Dialogue: 0,0:07:26.54,0:07:29.50,Default,,0000,0000,0000,,because it has a higher\Ndensity than water.
Dialogue: 0,0:07:29.50,0:07:31.38,Default,,0000,0000,0000,,But what if an object has a lower density
Dialogue: 0,0:07:31.38,0:07:33.01,Default,,0000,0000,0000,,than the fluid it's submerged in?
Dialogue: 0,0:07:33.01,0:07:35.64,Default,,0000,0000,0000,,Well, then its weight would be lower
Dialogue: 0,0:07:35.64,0:07:38.10,Default,,0000,0000,0000,,than the weight of the\Nfluid that it displaces,
Dialogue: 0,0:07:38.10,0:07:39.74,Default,,0000,0000,0000,,and therefore, the buoyant\Nforce will be larger
Dialogue: 0,0:07:39.74,0:07:41.07,Default,,0000,0000,0000,,and the whole object will accelerate up.
Dialogue: 0,0:07:41.07,0:07:44.16,Default,,0000,0000,0000,,In other words, this is the\Ncondition for flotation.
Dialogue: 0,0:07:44.16,0:07:45.81,Default,,0000,0000,0000,,This is the reason why beach balls
Dialogue: 0,0:07:45.81,0:07:47.51,Default,,0000,0000,0000,,and icebergs float in water
Dialogue: 0,0:07:47.51,0:07:50.74,Default,,0000,0000,0000,,because they have a density\Nthat's smaller than water.
Dialogue: 0,0:07:50.74,0:07:52.20,Default,,0000,0000,0000,,And now, look, we have\Nthe complete equation
Dialogue: 0,0:07:52.20,0:07:53.35,Default,,0000,0000,0000,,for the buoyant force.
Dialogue: 0,0:07:53.35,0:07:55.58,Default,,0000,0000,0000,,The buoyant force is the\Nweight of the fluid displaced,
Dialogue: 0,0:07:55.58,0:07:59.89,Default,,0000,0000,0000,,which is the density of the\Nfluid times the volume times g.
Dialogue: 0,0:07:59.89,0:08:02.23,Default,,0000,0000,0000,,And so this is the expression\Nfor the buoyant force.
Dialogue: 0,0:08:02.23,0:08:03.35,Default,,0000,0000,0000,,And again, this helps us see
Dialogue: 0,0:08:03.35,0:08:04.100,Default,,0000,0000,0000,,why it's the density that matters
Dialogue: 0,0:08:04.100,0:08:06.48,Default,,0000,0000,0000,,because, look, the weight\Nof the displaced fluid
Dialogue: 0,0:08:06.48,0:08:08.49,Default,,0000,0000,0000,,will have the exact same volume
Dialogue: 0,0:08:08.49,0:08:10.60,Default,,0000,0000,0000,,as the weight of the submerged object.
Dialogue: 0,0:08:10.60,0:08:11.74,Default,,0000,0000,0000,,The volumes cancel out,
Dialogue: 0,0:08:11.74,0:08:14.24,Default,,0000,0000,0000,,and that's why it's eventually\Nthe density that decides
Dialogue: 0,0:08:14.24,0:08:16.10,Default,,0000,0000,0000,,whether something's\Ngoing to sink or float.
Dialogue: 0,0:08:16.10,0:08:18.40,Default,,0000,0000,0000,,So it all comes from the\NArchimedes' principle,
Dialogue: 0,0:08:18.40,0:08:21.78,Default,,0000,0000,0000,,which eventually comes from\Nthe pressure differences.
Dialogue: 0,0:08:21.78,0:08:22.65,Default,,0000,0000,0000,,Amazing, right?
Dialogue: 0,0:08:22.65,0:08:24.24,Default,,0000,0000,0000,,But now, let's think about\Nwhat's going to happen
Dialogue: 0,0:08:24.24,0:08:25.25,Default,,0000,0000,0000,,to this object.
Dialogue: 0,0:08:25.25,0:08:27.67,Default,,0000,0000,0000,,We know it's going to\Nstart accelerating up,
Dialogue: 0,0:08:27.67,0:08:29.49,Default,,0000,0000,0000,,but when will it stop?
Dialogue: 0,0:08:29.49,0:08:30.36,Default,,0000,0000,0000,,Well, let's see.
Dialogue: 0,0:08:30.36,0:08:32.74,Default,,0000,0000,0000,,As long as the whole\Nthing is submerged inside,
Dialogue: 0,0:08:32.74,0:08:34.81,Default,,0000,0000,0000,,the buoyant force stays the same.
Dialogue: 0,0:08:34.81,0:08:38.94,Default,,0000,0000,0000,,But now, as it starts\Ncoming above the surface,
Dialogue: 0,0:08:38.94,0:08:42.46,Default,,0000,0000,0000,,it starts displacing lesser fluid.
Dialogue: 0,0:08:42.46,0:08:43.41,Default,,0000,0000,0000,,Can you see that?
Dialogue: 0,0:08:43.41,0:08:46.17,Default,,0000,0000,0000,,It now only displaces this\Nmuch amount of the fluid,
Dialogue: 0,0:08:46.17,0:08:49.49,Default,,0000,0000,0000,,and therefore, the buoyant\Nforce will become smaller.
Dialogue: 0,0:08:49.49,0:08:51.61,Default,,0000,0000,0000,,But as long as it's still\Nlarger than the weight,
Dialogue: 0,0:08:51.61,0:08:55.20,Default,,0000,0000,0000,,the object continues accelerating upwards,
Dialogue: 0,0:08:55.20,0:08:57.48,Default,,0000,0000,0000,,and eventually, at some point,
Dialogue: 0,0:08:57.48,0:08:59.04,Default,,0000,0000,0000,,the weight of the fluid displaced
Dialogue: 0,0:08:59.04,0:09:02.43,Default,,0000,0000,0000,,will exactly match the\Nweight of the object,
Dialogue: 0,0:09:02.43,0:09:04.30,Default,,0000,0000,0000,,and that's when equilibrium is reached
Dialogue: 0,0:09:04.30,0:09:06.60,Default,,0000,0000,0000,,and the object pretty\Nmuch stops at that point.
Dialogue: 0,0:09:06.60,0:09:08.50,Default,,0000,0000,0000,,So look, for an object to float,
Dialogue: 0,0:09:08.50,0:09:11.09,Default,,0000,0000,0000,,it needs to be submerged\Nenough so that the weight
Dialogue: 0,0:09:11.09,0:09:15.22,Default,,0000,0000,0000,,of the fluid displaced exactly\Nequals the object's weight.
Dialogue: 0,0:09:15.22,0:09:16.25,Default,,0000,0000,0000,,Does that make sense?
Dialogue: 0,0:09:16.25,0:09:17.35,Default,,0000,0000,0000,,Now, consider the beach ball.
Dialogue: 0,0:09:17.35,0:09:21.75,Default,,0000,0000,0000,,It has a very low density,\Nso the amount of water needed
Dialogue: 0,0:09:21.75,0:09:25.25,Default,,0000,0000,0000,,to match the weight of the\Nbeach ball is very little.
Dialogue: 0,0:09:25.25,0:09:27.50,Default,,0000,0000,0000,,So only a small portion\Nneeds to be submerged
Dialogue: 0,0:09:27.50,0:09:29.24,Default,,0000,0000,0000,,because by then, the weight of the water
Dialogue: 0,0:09:29.24,0:09:32.49,Default,,0000,0000,0000,,that has been displaced\Nalready equals the weight
Dialogue: 0,0:09:32.49,0:09:33.99,Default,,0000,0000,0000,,of the entire beach ball
Dialogue: 0,0:09:33.99,0:09:37.67,Default,,0000,0000,0000,,because the beach ball has a\Nmuch smaller density compared
Dialogue: 0,0:09:37.67,0:09:38.54,Default,,0000,0000,0000,,to the water.
Dialogue: 0,0:09:38.54,0:09:39.84,Default,,0000,0000,0000,,That's the whole idea.
Dialogue: 0,0:09:39.84,0:09:42.24,Default,,0000,0000,0000,,On the other hand, if\Nyou consider an iceberg,
Dialogue: 0,0:09:42.24,0:09:46.65,Default,,0000,0000,0000,,it has a density very, very\Nclose to that of water.
Dialogue: 0,0:09:46.65,0:09:49.74,Default,,0000,0000,0000,,And so now, to displace the\Nwater equal to its weight,
Dialogue: 0,0:09:49.74,0:09:52.83,Default,,0000,0000,0000,,you need to submerge a lot more.
Dialogue: 0,0:09:52.83,0:09:55.50,Default,,0000,0000,0000,,Pretty much the entire\Nthing needs to be submerged
Dialogue: 0,0:09:55.50,0:09:58.66,Default,,0000,0000,0000,,because its density is very,\Nvery close to that of water.
Dialogue: 0,0:09:58.66,0:10:00.35,Default,,0000,0000,0000,,It's still less, that's why it's floating,
Dialogue: 0,0:10:00.35,0:10:01.94,Default,,0000,0000,0000,,but it's very close to that of water.
Dialogue: 0,0:10:01.94,0:10:04.48,Default,,0000,0000,0000,,So, higher the density of the object,
Dialogue: 0,0:10:04.48,0:10:06.84,Default,,0000,0000,0000,,more it needs to be submerged
Dialogue: 0,0:10:06.84,0:10:09.24,Default,,0000,0000,0000,,so that it can be in equilibrium.
Dialogue: 0,0:10:09.24,0:10:10.74,Default,,0000,0000,0000,,So, if you put it all together,
Dialogue: 0,0:10:10.74,0:10:12.41,Default,,0000,0000,0000,,we can say that when\Nthe density of an object
Dialogue: 0,0:10:12.41,0:10:15.59,Default,,0000,0000,0000,,is smaller than density of the\Nfluid, it will be floating.
Dialogue: 0,0:10:15.59,0:10:17.64,Default,,0000,0000,0000,,And the amount of the\Nobjects submerged depends
Dialogue: 0,0:10:17.64,0:10:19.50,Default,,0000,0000,0000,,on how small the density is.
Dialogue: 0,0:10:19.50,0:10:21.11,Default,,0000,0000,0000,,If the density of the\Nobject is very tiny compared
Dialogue: 0,0:10:21.11,0:10:22.53,Default,,0000,0000,0000,,to the density of the fluid,
Dialogue: 0,0:10:22.53,0:10:23.74,Default,,0000,0000,0000,,it'll be submerged just a little bit.
Dialogue: 0,0:10:23.74,0:10:25.66,Default,,0000,0000,0000,,On the other hand, if\Nthe density is very close
Dialogue: 0,0:10:25.66,0:10:27.22,Default,,0000,0000,0000,,to the density of the\Nfluid, but still smaller,
Dialogue: 0,0:10:27.22,0:10:29.04,Default,,0000,0000,0000,,it needs to be smaller\Nfor it to be floating,
Dialogue: 0,0:10:29.04,0:10:31.74,Default,,0000,0000,0000,,but if it's close enough, then\Nmost of it will be submerged.
Dialogue: 0,0:10:31.74,0:10:34.50,Default,,0000,0000,0000,,On the other hand, if the\Ndensity of the object is higher
Dialogue: 0,0:10:34.50,0:10:35.85,Default,,0000,0000,0000,,than the density of the fluid itself,
Dialogue: 0,0:10:35.85,0:10:37.24,Default,,0000,0000,0000,,then the object will sink.
Dialogue: 0,0:10:37.24,0:10:38.74,Default,,0000,0000,0000,,And by the way, in all the examples,
Dialogue: 0,0:10:38.74,0:10:40.24,Default,,0000,0000,0000,,we have taken water as our fluid,
Dialogue: 0,0:10:40.24,0:10:42.65,Default,,0000,0000,0000,,but this would work for any fluid, okay?
Dialogue: 0,0:10:42.65,0:10:44.15,Default,,0000,0000,0000,,For example, air is also a fluid,
Dialogue: 0,0:10:44.15,0:10:46.12,Default,,0000,0000,0000,,so it can also put a buoyant force.
Dialogue: 0,0:10:46.12,0:10:48.25,Default,,0000,0000,0000,,But since air has a very\Nlow density compared
Dialogue: 0,0:10:48.25,0:10:50.82,Default,,0000,0000,0000,,to everyday objects, we\Ndon't usually notice it.
Dialogue: 0,0:10:50.82,0:10:53.74,Default,,0000,0000,0000,,But if you consider a\Nhelium balloon, its density,
Dialogue: 0,0:10:53.74,0:10:56.14,Default,,0000,0000,0000,,helium density is smaller\Nthan that of the air.
Dialogue: 0,0:10:56.14,0:10:58.99,Default,,0000,0000,0000,,And now, as a result of\Nthat, helium tends to float,
Dialogue: 0,0:10:58.99,0:11:01.50,Default,,0000,0000,0000,,and that's why helium\Nballoons tend to rise up.
Dialogue: 0,0:11:01.50,0:11:03.11,Default,,0000,0000,0000,,But now is an interesting question,
Dialogue: 0,0:11:03.11,0:11:06.43,Default,,0000,0000,0000,,what if the density of the\Nobject exactly equals the density
Dialogue: 0,0:11:06.43,0:11:07.30,Default,,0000,0000,0000,,of the fluid?
Dialogue: 0,0:11:07.30,0:11:08.25,Default,,0000,0000,0000,,What happens then?
Dialogue: 0,0:11:08.25,0:11:10.24,Default,,0000,0000,0000,,Well, now, if you completely submerge it,
Dialogue: 0,0:11:10.24,0:11:13.60,Default,,0000,0000,0000,,it will neither float nor sink.
Dialogue: 0,0:11:13.60,0:11:16.34,Default,,0000,0000,0000,,We call this the neutral buoyancy.
Dialogue: 0,0:11:16.34,0:11:20.49,Default,,0000,0000,0000,,That object will just stay\Nat that particular depth,
Dialogue: 0,0:11:20.49,0:11:22.62,Default,,0000,0000,0000,,and that's exactly how submarines
Dialogue: 0,0:11:22.62,0:11:24.74,Default,,0000,0000,0000,,can stay at a particular depth.
Dialogue: 0,0:11:24.74,0:11:28.34,Default,,0000,0000,0000,,They do that by changing\Ntheir average density.
Dialogue: 0,0:11:28.34,0:11:29.85,Default,,0000,0000,0000,,If they want to sink,
Dialogue: 0,0:11:29.85,0:11:31.84,Default,,0000,0000,0000,,they will increase their average density
Dialogue: 0,0:11:31.84,0:11:36.23,Default,,0000,0000,0000,,by allowing water to flood their tanks.
Dialogue: 0,0:11:36.23,0:11:37.06,Default,,0000,0000,0000,,On the other hand,
Dialogue: 0,0:11:37.06,0:11:40.49,Default,,0000,0000,0000,,if it now needs to come towards\Nthe surface of the water,
Dialogue: 0,0:11:40.49,0:11:42.49,Default,,0000,0000,0000,,then it'll decrease its average density.
Dialogue: 0,0:11:42.49,0:11:44.100,Default,,0000,0000,0000,,It does so by now using compressed air
Dialogue: 0,0:11:44.100,0:11:47.23,Default,,0000,0000,0000,,to force the water out.
Dialogue: 0,0:11:47.23,0:11:49.61,Default,,0000,0000,0000,,And by carefully balancing\Nthe amount of water
Dialogue: 0,0:11:49.61,0:11:51.42,Default,,0000,0000,0000,,and air inside its tanks,
Dialogue: 0,0:11:51.42,0:11:54.74,Default,,0000,0000,0000,,it can also make sure that\Nits density exactly equals out
Dialogue: 0,0:11:54.74,0:11:57.74,Default,,0000,0000,0000,,of the surrounding water,\Nmaintaining neutral buoyancy,
Dialogue: 0,0:11:57.74,0:12:00.49,Default,,0000,0000,0000,,and in which case, it'll\Nstay at a particular depth.
Dialogue: 0,0:12:00.49,0:12:02.12,Default,,0000,0000,0000,,That's amazing, right?
Dialogue: 0,0:12:02.12,0:12:04.90,Default,,0000,0000,0000,,Now, instead of submarine,\Nimagine you were wearing a suit
Dialogue: 0,0:12:04.90,0:12:07.84,Default,,0000,0000,0000,,which could also maintain\Nneutral buoyancy in water.
Dialogue: 0,0:12:07.84,0:12:10.18,Default,,0000,0000,0000,,Then you would be, just\Nlike the submarine,
Dialogue: 0,0:12:10.18,0:12:12.48,Default,,0000,0000,0000,,stay at a particular location in water,
Dialogue: 0,0:12:12.48,0:12:14.90,Default,,0000,0000,0000,,not going down nor going up.
Dialogue: 0,0:12:14.90,0:12:18.50,Default,,0000,0000,0000,,In other words, you would\Nkind of feel weightless,
Dialogue: 0,0:12:18.50,0:12:20.11,Default,,0000,0000,0000,,which means now you can train
Dialogue: 0,0:12:20.11,0:12:22.49,Default,,0000,0000,0000,,for the weightless environments\Nthat you would face
Dialogue: 0,0:12:22.49,0:12:23.83,Default,,0000,0000,0000,,in the space stations.
Dialogue: 0,0:12:23.83,0:12:24.100,Default,,0000,0000,0000,,And that's exactly
Dialogue: 0,0:12:24.100,0:12:28.61,Default,,0000,0000,0000,,what the NASA's Neutral Buoyancy Lab does.
Dialogue: 0,0:12:28.61,0:12:30.59,Default,,0000,0000,0000,,It's a giant swimming pool inside
Dialogue: 0,0:12:30.59,0:12:33.60,Default,,0000,0000,0000,,which astronauts can\Nmaintain neutral buoyancy
Dialogue: 0,0:12:33.60,0:12:34.87,Default,,0000,0000,0000,,and train for the weightless environment.
Dialogue: 0,0:12:34.87,0:12:37.18,Default,,0000,0000,0000,,It's not perfect, but it's way better
Dialogue: 0,0:12:37.18,0:12:40.32,Default,,0000,0000,0000,,and more realistic than training\Non the ground, for example.