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Anderson Video - Melting Ice and Water Level

Professor Anderson
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>> Let's go to this problem. Cup of water with ice floating in it. So, here's our ice cubes. Here's our water level. And this is a big cup of water. Okay. Cup of water with ice floating in it. And now, let's ask you the following question. As the ice melts, the water level does what? Rises, falls, or stays the same. Three different options, here. What do you guys think? Who has a thought about this one? Steve. Somebody hand the mic back to Steve. >> Steve, can you move over this way? >> Good guy, Steve. Steve. As that ice melts, the water level is going to do something. Is it going to rise, is it going to fall, is it going to stay the same? >> Steve thinks it's going to rise. >> Steve thinks it's going to rise. >> Yeah. >> I love it when people refer to themselves in the third person. Doctor Anderson likes with Steve is saying. All right. Steve, you said it's going to rise. >> Yes. >> Why? >> Well, those ice cubes are essentially water in a solid state. So, I feel like when they melt it'll got back to water, so it'll add on to the amount that's already in there. >> Okay. Yeah. I mean, certainly, some of that ice is up above the water level. Right. So, if I take those water molecules and I throw them into the water, seems like it should rise. Yeah. Absolutely. Let's think about it from the terms the we were talking about, earlier, with these buoyant forces. And let's think about one ice cube. Okay. One ice cube is going to have mg down on it. It's going to have some buoyant force up on it. Okay. And the buoyant force b is equal to the weight of the displaced fluid. So, for one ice cube, we're talking about that amount that's under the water. That's the displaced fluid. And so, we know what that is. That is rho of water times the volume underneath, times g. All right. But that has to be equal to mg if it's floating. Where this m is the mass of the ice. So, what can I say, here? Rho H2O times that volume that's underneath, is that equal to the mass of the ice? The g's of course, cancel out. So, what do you think, Steve? If I took all that mass of ice and I melted it and I turned it into water, would it fill that volume that is underneath the water? The portion of the ice that's underneath the water, if I melted all that, would it just fill that volume? >> So, if you melt the whole ice cube, would it fill that little spot that you have depth? >> Yes. >> Doesn't look like it would. >> It doesn't look like it would. But we have to remember, that the density of ice is less than the density of water. And so, when you take ice and you melt it, it in fact, gets a little more dense. And it in fact, just fills that volume, right there. >> Cool. >> Okay. This is in fact, true. And if that's true, then the answer is right there. The water level, in fact, stays exactly the same. Why? Because all the ice that you melt exactly fills that volume that's underneath the water. Kind of cool, right? Now, this doesn't work, of course, if your ice is stacked all the way to the bottom and it's elevated way above. They do have to be floating. Okay. That's one little caveat to this problem.