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If your body has a density of $995 \mathrm{kg} / \mathrm{m}^{3},$ what fraction of you will be submerged when floating gently in: (a) Freshwater? (b) Salt water, which has a density of 1027 $\mathrm{kg} / \mathrm{m}^{3} ?$

(a) $f=99.5 \%$(b) $f^{\prime}=96.9 \%$

Physics 101 Mechanics

Chapter 11

Fluid Statics

Fluid Mechanics

Cornell University

University of Washington

Hope College

University of Sheffield

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west that if your body has a density of 995 kilogram per cubic meter, what fraction of you will be submerged, floating gently in fresh water and then also in salt water, which we assume as a density of 1027 kilograms per cubic meter. So I've drawn a little schematic of ah person here floating in water. So we have the weight of the person on that must be equal to the buoyancy force if they're floating in equilibrium. So we have the weight of the person is mg. The buoyancy force is the volume submerged times the density of the fluid, which will be either salt water, freshwater times, gravity. Then we can figure out that, um, if the massive the masses, the volume of the total volume of the person, times the density of that person and then we substitute that in the here and cancel out the G's, then we have the diary. Was the volume submerged times the density of the fluid so the you can solve for the volumes of marriage? That's the value of the total volume times the density of the person provided by the density of fluid and so give the fluid is fresh water. That's 1000 kilograms per cubic meter and we can see that then if we pick this racial, that 0.995 So we have 99.5% of us is below water. Now if we use the same formula but substitute in our density of salt water, you see that we now only 96.9% of us is below water. So we folk better in salt water, as would expect because it dancer.

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