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What speed must a gold sphere of radius 3.00 $\mathrm{mm}$ have incastor oil for the viscous drag force to be one-fourth of the weight of the sphere? The density of gold is $19,300 \mathrm{kg} / \mathrm{m}^{3}$ and the viscosity of the oil is 0.986 $\mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}$

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Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

Sonia S.

June 20, 2022

What speed must agood sphere of radius 3mm have in caster oil

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

McMaster University

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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Okay, so in this problem, we just want to calculate the speech off the gold sphere. But the problem say's that drag force. So it's called is F D. It's going to be CO 1/4 off the weight off this fear. So it was just 14 off MGI. First of all, let's remember what he's the drag force. So the dreck force can to describe us six by it's the are V off the sphere. So this is constant. This is the radios off this fear, and this is the speed of this fear. Okay, so that is the definition off the drag force. The second finger must remember it. What is it? Weight. The weight M g. We can describe us. The volume multiply by the density of this fear that multiplies the gravitational acceleration. So we can describe this first equation here. Us. Let's see six by at our V t. Do you object? It's going to be the volume and the volume actually warned for sorry. 14 off the volume of this fear reaches for divided by three times the ragers que bix the multiplies density to move to place gravitational acceleration. So we can cross the four and here and we can cross one of the radios in the here. So we have only readers square left and we can simplify this equation to really velocity, which is what we want to calculate so that the speeds velocity off his fear is going to be equal. Our square, the multiple eyes g whole divided by 18 at the I forgot to put in here if by because it's, uh the The volume of this fear is four by divided by three. So I forgot it by we can cross here with here. Okay, so that's finally the equation that we have to calculate to this speed off this fear. So that's car Cletus. We know that the speed of this fear is going to be cool. Ah, the radius reaches three times turned to new miners three the square because we want to meters. The Raiders time is to gravity is nine point eight times the density, which is 19 0.3 times poetry. All this divided by 18 times either, which is zero point nine 86. So that's our velocity. Now. If Rick are Cledus, we have finally the result which is this speed is going to be cool. Zero point a little, nine. 59 meters per second or for simplify. You can say this is nine point 59. Same team enters first seconds and that's the final answer to this problem. Thanks for watching.

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