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In an immersion measurement of a woman's density, she is found to have a mass of 62.0 $\mathrm{kg}$ in air and an apparent mass of 0.0850 $\mathrm{kg}$ when completely submerged with lungsempty. (a) What mass of water does she displace? (b) What is her volume? (c) Calculate her density. (d) If her lung capacity is 1.75 $\mathrm{L}$ , is she able to float without treading water with her lungs filled with air?

(a) $m_{\text {water }}=61.915 \mathrm{kg}$(b) $V_{\text {woman }}=61.915 \times 10^{-3} \mathrm{m}^{3}$(c) $\rho$ woman $=1001.4 \mathrm{kg} \mathrm{m}^{-3}$(d) Yes, she can float without treading water with her lungs filled with air.

Physics 101 Mechanics

Chapter 11

Fluid Statics

Fluid Mechanics

University of Washington

Simon Fraser University

Hope College

McMaster University

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in this problem. We're told that in an immersion measurement of a woman's density, she's found a have a mass of 62 kilograms of air and an apparent mass of 0.85 kilograms when completely submerged with lungs empty. First, want to find what the mass of water is that she displaces. And then we want to find out, determined her volume and then her density, and then determine if her lung capacity is 1.75 leaders if she's able to afloat without treading water, water but their lungs feel what they're. So here is our, um, schematic of our woman in immersed in the water so her weight is acting down. Warranty Force Andy Support Force are acting up to keep her from sinking to the bottom. We know that the free by Diagram says that her weight must equal the weight of the water displaced, Um, plus their force in the, um, string or the support force, which is going to be her apparent mass times gravity. So this then becomes the weight of the mass of the water times grab the her parent mass times gravity, and then gravity cancels out you know her mass and her apparent mass. So the mass of the water is just the difference, which is 61.915 kilograms. So very close to her, um, her weight mass and air because people were basically have density very close to that of water. So we can figure out the volume off the water displaced because that is the, um mass of the water times divided by its density. So we know the mass of the water from here and the density of water, if it's fresh water is 1000 kilograms for keeping meter. So we get the volume of water displeased. There's 61.915 times, 10 to the minus three cubic meters. Now her density or the density. Yet her density I'm with their lungs empty, is just her mass provided by the her volume, which is the volume of the water displaced because she's completely submerged. And that is slightly greater than 1000 in his 1000 on 1.37 kilograms per mut cubic meter. So, in fact, she would sink, come to the bottom of not from this supporting force, and then we can figure out what her her density would be if she had 1.75 leaders of air in her lungs. And so, assuming that the air basically has negligible weight compared to her weight, her masses now still 62 kilograms but the volume her volume is now 63.665 cubic meters, and if we do this, we get that her density is now 973 kilogram per cubic meter, which is less than the density of water, so that she would be able to float, um in the water without treading water.

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