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Problem 33 Medium Difficulty

A slab of ice floats on a freshwater lake. What minimum
volume must the slab have for a $45.0 \mathrm{~kg}$ woman to be able to stand on it without getting her feet wet?

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Video Transcript

Okay, So in this problem, we must use the documents Bring simple. Because we have a slab off ice and we have a woman standing. Let's put the woman this box. So we have the ice floating on water, and we must know what should be the volume off the ice. So the system is a liberal in the in. The woman don't get his feet wet. So let's think about First of all, we know that we have the weight off the woman and the weight off this level off ice. And this isn't a Cleveland because we have, um, buoyant force. And here, so as described, this system using the documents principle. Let's see, we know that buoyant force is going to be cool. The weight boots. I'm sorry. That's put again going to be equal. You wait off the ice, plus the weight off. Do you warmer? Okay, so these buoyant force is going to be cool. We know. Actually, we know that this buoyant force, using the documents principle going to be equal did density off the water times the fordham off the ice times the gravity deceleration and this should be equal. You mess off the woman times gravity deceleration plus the mess off the ice times Gravity deceleration so we can cross all the G's in here and simply fire system to just density off water times TV equal, massive, warmer plus a mess of the ice. But the problem here is that we do not have the mess off the ice, but we can describe the mess of the ice. It's that's what's what is the mass of the ice can be described bors. Density of the ice times his volume. So let's simplify this equation. We have them that volume off the ice, the multiplies, the density off the water, miners density off the ice is going to be equal the mass of the warmer. Therefore, the volume that we want to calculate is just the mess of the woman divided by Did that city off the water. Miners density off the ice. So now that we simplify our system, we can calculate this. So the last safety woman is 45 kilograms divided by 1000 which is the mess, which is the density of the water minus four, actually, no. Sorry. Density off the ice is 920 kilograms meters Q beaks. So calculating this, we discover that the volume off the ice should be cool. 0.562 meters. Q Bix. Okay, so that's the final answer to this problem. Thanks for watching.

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