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(III) A long vertical hollow tube with an inner diameter of1.00 $\mathrm{cm}$ is filled with SAE 10 motor oil. A $0.900-$ cm-diameter,30.0 -cm-long 150 -g rod is dropped vertically through the oil in thetube. What is the maximum speed attained by the rod as it falls?

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0.43 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 13

Fluids

Fluid Mechanics

Cornell University

Simon Fraser University

University of Winnipeg

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 this should be the system, the diagram of the system and they're trying to find the velocity of the liquid. So we know that the force of the viscosity is going to be equal to the viscosity of the liquid times the cross sectional area times the velocity divided by the length. We know that A is going to be equal to the surface, sir, of the the surface area. So this would be two pi r times h for a cylinder. And you know that l is giving us 1/2 times one centimeter minus 10.9 centimeters. So this would give us a point 0005 meters. So at this point, we know that here this sum of forces in the UAE direction equal zero Therefore, the viscosity force the force. The viscous force would equal the force of gravity s So we can say that, uh, and talk brother the viscosity times two pi r h times V over no is going to be equal to M G. And so the would be equal to m g l divided by two pi r times, h times, ADA or the viscosity. So V is going to be equal to ah 0.15 kilograms times 9.8 meters per second squared times, 0.0 five meters and then this will be divided by two pi times 0.45 meters times 0.30 meters times 200 times 10 to the negative. Third this'll be the viscosity Newton in seconds, uh per meter squared and we find that the velocity is going to be 0.43 meters per second. This was our final answer. That is the end of the solution. Thank you for watching.

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