Anderson Video - What Fraction of Iceberg is Underwater

Professor Anderson
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>> All right. Let's talk about icebergs. And, let's ask the following question. What fraction of the iceberg is underneath the water level? [ Writing On Board ] Okay. We all know what an iceberg looks like. Right? We're not going to draw a complicated iceberg because we're in physics. Assume a rectangular iceberg. Okay? There is our iceberg. Some of it sticking up, some of it sticking below. We don't know how much, but let's see if we can figure it out. The whole volume of this thing, we will call that the volume of the ice. The fraction that is beneath, we'll call that the volume of the water, because that's how much water the iceberg displaces. What we know is that if it's floating there, the buoyant force up has to equal the gravitational force down on the ice. Right? Gravity's pulling down on the ice, just like pulling down on everything else. The buoyant force pushing it back up has to be equal to that. The whole thing's at rest. It's not bobbing up and down, and so we know that the buoyant force has to be equal to mg. But, the buoyant force is the weight of the displaced fluid. So, it's the density of the water times the volume of the water times gravity. All right. Density times volume down here. That gets us a mass. Multiply that by gravity. We get force. What about this guy? This is the total mass of the ice. Gravity is pulling down on all of the ice, and so we have to have the mass of the ice which is the volume of the ice. We're going to use capital V for volume. The volume of the ice times the density of the ice and then we're multiplying by gravity. G's cancel out on both sides, and we can write this volume of the ice over volume of the water. Actually, we want the fraction beneath. Let's do it the other way. The fraction beneath, f, is going to be the volume of what's underneath divided by the total volume. And, if I look at this equation, if I divide by V ice, then I get rho ice times g. And then, I have to divide by rho w times g. The g's cancel out, and we get density of the ice over the density of the water. And, those things you can look up. For cold sea water, the density of the water is about 1030 kilograms per cubic meter. And, the density of ice is 917 kilograms per cubic meter. And, those numbers are pretty close to each other, and so this fraction is .89. 89% of that iceberg is, in fact, under water. Okay. And, you've probably seen the pictures of icebergs, right? They show you the ocean, and then they show you this iceberg. And then, the ocean continues. And then, when you back out with your camera and you look underwater, it looks something like that. Okay. Maybe not exactly to scale, but pretty close. This is what an iceberg looks like when it's floating around there in the ocean. And, this is of course, the big problem, right, and this is what sunk the Titanic was it wasn't the iceberg that's sticking up above the water that was the problem. It's all the stuff underneath the water, right? You can see these and steer away from them, but if the bottom of your boat hits the stuff underneath, it can poke a hole in your boat, sink your ship. Okay. [ Music ]
>> All right. Let's talk about icebergs. And, let's ask the following question. What fraction of the iceberg is underneath the water level? [ Writing On Board ] Okay. We all know what an iceberg looks like. Right? We're not going to draw a complicated iceberg because we're in physics. Assume a rectangular iceberg. Okay? There is our iceberg. Some of it sticking up, some of it sticking below. We don't know how much, but let's see if we can figure it out. The whole volume of this thing, we will call that the volume of the ice. The fraction that is beneath, we'll call that the volume of the water, because that's how much water the iceberg displaces. What we know is that if it's floating there, the buoyant force up has to equal the gravitational force down on the ice. Right? Gravity's pulling down on the ice, just like pulling down on everything else. The buoyant force pushing it back up has to be equal to that. The whole thing's at rest. It's not bobbing up and down, and so we know that the buoyant force has to be equal to mg. But, the buoyant force is the weight of the displaced fluid. So, it's the density of the water times the volume of the water times gravity. All right. Density times volume down here. That gets us a mass. Multiply that by gravity. We get force. What about this guy? This is the total mass of the ice. Gravity is pulling down on all of the ice, and so we have to have the mass of the ice which is the volume of the ice. We're going to use capital V for volume. The volume of the ice times the density of the ice and then we're multiplying by gravity. G's cancel out on both sides, and we can write this volume of the ice over volume of the water. Actually, we want the fraction beneath. Let's do it the other way. The fraction beneath, f, is going to be the volume of what's underneath divided by the total volume. And, if I look at this equation, if I divide by V ice, then I get rho ice times g. And then, I have to divide by rho w times g. The g's cancel out, and we get density of the ice over the density of the water. And, those things you can look up. For cold sea water, the density of the water is about 1030 kilograms per cubic meter. And, the density of ice is 917 kilograms per cubic meter. And, those numbers are pretty close to each other, and so this fraction is .89. 89% of that iceberg is, in fact, under water. Okay. And, you've probably seen the pictures of icebergs, right? They show you the ocean, and then they show you this iceberg. And then, the ocean continues. And then, when you back out with your camera and you look underwater, it looks something like that. Okay. Maybe not exactly to scale, but pretty close. This is what an iceberg looks like when it's floating around there in the ocean. And, this is of course, the big problem, right, and this is what sunk the Titanic was it wasn't the iceberg that's sticking up above the water that was the problem. It's all the stuff underneath the water, right? You can see these and steer away from them, but if the bottom of your boat hits the stuff underneath, it can poke a hole in your boat, sink your ship. Okay. [ Music ]