89% of that iceberg is, in fact, under water. And, those numbers are pretty close to each other, and so this fraction is. And, the density of ice is 917 kilograms per cubic meter. For cold sea water, the density of the water is about 1030 kilograms per cubic meter. The g's cancel out, and we get density of the ice over the density of the water. And then, I have to divide by rho w times g. And, if I look at this equation, if I divide by V ice, then I get rho ice times g. The fraction beneath, f, is going to be the volume of what's underneath divided by the total volume. G's cancel out on both sides, and we can write this volume of the ice over volume of the water. The volume of the ice times the density of the ice and then we're multiplying by gravity. 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. What about this guy? This is the total mass of the ice. So, it's the density of the water times the volume of the water times gravity. But, the buoyant force is the weight of the displaced fluid. It's not bobbing up and down, and so we know that the buoyant force has to be equal to mg. The buoyant force pushing it back up has to be equal to that. Right? Gravity's pulling down on the ice, just like pulling down on everything else. What we know is that if it's floating there, the buoyant force up has to equal the gravitational force down on 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. The whole volume of this thing, we will call that the volume of the ice. We don't know how much, but let's see if we can figure it out. Some of it sticking up, some of it sticking below. Right? We're not going to draw a complicated iceberg because we're in physics. What fraction of the iceberg is underneath the water level? Okay.

Iceberg underwater