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(II) A cube of side length 10.0 $\mathrm{cm}$ and made of unknownmaterial floats at the surface between water and oil. The oilhas a density of 810 $\mathrm{kg} / \mathrm{m}^{3} .$ If the cube floats so that it is72$\%$ in the water and 28$\%$ in the oil, what is the mass of the cube and what is the buoyant force on the cube?

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0.95 $\mathrm{kg}$

Physics 101 Mechanics

Chapter 13

Fluids

Fluid Mechanics

University of Washington

Simon Fraser University

University of Sheffield

Lectures

03:45

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

09:49

A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases and plasmas. Fluids display properties such as flow, pressure, and tension, which can be described with a fluid model. For example, liquids form a surface which exerts a force on other objects in contact with it, and is the basis for the forces of capillarity and cohesion. Fluids are a continuum (or "continuous" in some sense) which means that they cannot be strictly separated into separate pieces. However, there are theoretical limits to the divisibility of fluids. Fluids are in contrast to solids, which are able to sustain a shear stress with no tendency to continue deforming.

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So we want the mass on the cube and the buoyant force of the Cube. So we can say that mg the the weight would be equal to the brilliant force of the oil plus the brilliant force of the water. And this would be equal to the density of the oil times the volume of the oil times gravity plus the density of the water times the volume of the water, times gravity. And we can say that and G will then equal the density of oil times l squared times point to a L Times G plus the density of water times l squared times 0.7 to L Times G uh, jeez, we're gonna cancel out, and we find that the mass is simply going to be equal to El Cubed times 0.28 times the density of oil Ah, plus 0.72 times the density of water. And so this is going to be equal to 0.1 meter cubes and then the density of oil would be 810 kilograms per cubic meter. And then I'll be plus 0.72 times tend to the third. So, uh, the density of water would be 1000 kilograms per cubic meter. And the density of boy would be 810 kilograms per cubic meter. And we find that the mass is gonna be 8100.947 kilograms. So this would be the first answer. And then the second answer, they want the brilliant force. So the brilliant force would simply be equal to the, uh, mass times the gravity because this is in translational equilibrium. So this would be equal to 0.9447 times 9.8, and we find that the brilliant force is gonna be equal to 9.3 Newtons. My apologies. Nine approximately 93 Newtons. I'm sorry. I'm reading that around 0.947 times 9.8 a bit less than 9.8. My apologies. 9.3 Uh, right. I thought that was 10 for some reason. So the mass would be 0.947 kilograms on. That would be ah, We would be able to find that by taking the sum of the forces in the wind direction and equating thesame the brilliant force toothy, uh, weight of the object of the of the liquids to find the bully and force. It would simply be equal to the mass times the gravity. And this is what we used to, of course, find the mass in the first place. That is the end of the solution. Thank you for watching.

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