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Archimedes' principle can be used to calculate the density of a fluid as well as that of a solid. Suppose a chunk of iron with a mass of 390.0 g in air is found to have an apparent mass of 350.5 g when completely submerged in an unknown liquid. (a) What mass of fluid does the iron displace? (b) What is the volume of iron, using its density as given in Table 11.1 (c) Calculate the fluid's density and identify it.

(a) $m_{\text {liquid }}=0.0395 \mathrm{kg}=39.5 \mathrm{g}$(b) $V_{\mathrm{iron}}=5.00 \times 10^{-5} \mathrm{m}^{3}$(c) $\rho_{\text {liguid }}=790 \mathrm{kg} \mathrm{m}^{-3} .$ The unknown liquid is ethvl alcohol.

Physics 101 Mechanics

Chapter 11

Fluid Statics

Fluid Mechanics

Cornell University

University of Washington

Simon Fraser University

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So for party, we're going to use our committee's principal mother for our all parts were using our committee's principal and so we can see that the mass of the of the fluid displaced would be equaling the map. The rather we can say the actual mass of the iron minus the apparent mass of the iron. And this would be equaling 390 point zero grams minus 350 0.5 grams. And so we find that the mass of the fluid displaced would be equaling 39.50 grams. So this would be our answer for part A for part B. Then we want to find the volume. And so we can say that the density has been equal to the mass divided by the volume and here we can see that, then the volume of iron would be equaling the mass of the iron divided by the density of iron. This is gonna be equal to that act. The actual mass of the iron 390.0 grams, divided by the density of iron which we know to be 7.8 grams per cubic centimeter. This is equaling 50 cubic centimeters. And so we then know that for part C, um, from the front part A. We know that the average density of the fluid would be equal to the mass of the fluid displaced divided by the volume of the fluid. Here, the volume of the fluid would simply be equal to the volume of the iron. And so this would be equaling 39.50 grams, divided by the volume of the fluid displaced, which is equaling the volume of the iron submerged. And so this would be 50 39.50 grams, divided by 50 cubic centers. And so the density, the average density of the fluid would be equaling 0.79 grams per cubic centimeter. And we can say that from table 11 1 This fluid is gonna be fo alcohol, so this would be the average density of the fluid and identifying the fluid. We see that this fluid is indeed ethyl alcohol from table 11 1 That is the end of the solution. Thank you for one

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