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Advertisements for a certain small car claim that it floats in water. (a) If the car's mass is 900 $\mathrm{kg}$ and its interior volume is $3.0 \mathrm{m}^{3},$ what fraction of the car is immersed when it floats? You can ignore the volume of steel and other materials. (b) Water gradually leaks in and displaces the air in the car. What fraction of the interior volume is filled with water when the car sinks?

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a) 30$\%$b) 70$\%$

Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

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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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all right in this problem, we have a car of 900 kilograms and a volume of three cubic meters, and we're told that the car floats and we want to know what fraction of the car um, get submerged below the surface when it floats. So basically, what we need is that the buoyant force is equal to the force of gravity in order for it to float. And the buoyant force will be given by the mass of water that's displaced, which were writing is rosewater times v submerged times G. And ultimately we want the fraction that submerged. So we'll divide this V sub bye v so we can cancel achieve from both sides of the equation. And, um, V sub is then simply em over and through water. And if we divide by the this's Irv, our final expression where am is the 900 kilograms density ofwater is tend to the three kilograms and V is three meters cubed. Now in part B. We're told that the car starts to fill up with water and we want to know what fraction gets filled up before it sinks and the car will will start to sing when its density is equal to, I should say technically, it when it becomes greater than the density of water that the threshold is winding down. Density matches, then steal water so we can write the density of the car with some portion filled up a CZ, its original mass plus the mass of water Come on that's filled up The car in the mouths of the water can be written as the density of water times the volume that's been filled and then we divide by the total volume of the car and said this equal tow n ce que border. So then again, we want the fraction that's filled up before it sinks. So working a divide by the at the end and using this expression on the left um, the Phil, let's take a step back. I'm sorry. I don't want to race what I have. Um, so the Phil we'll just write The numerator is goingto be ro with the minus divided by row. And then we divide by Mia's well, and so this reduces to one minus and over Roe v.

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