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An ore sample weighs 17.50 $\mathrm{N}$ in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.20 $\mathrm{N}$ . Find the total volume and the density of the sample.

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(a) 6.43 \times 10^{-4} m^{3}(b) 2.78 \times 10^{3} k g / m^{3}$

Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

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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okay. And this problem, what the tension reads is the difference between the gravitational force and the buoyant force. Basically, the bigger the buoyant force is, the lighter on the sample of war is going to appear. So we're given that the force of tension is 11.2 and the force of gravity is 17.5. So we know is well that the buoyant force is given by the density of water, time's gravitational acceleration, times the volume of the object. So if we want to know the volume of the object, it's simply, um actually, let's let's include all the algebra here. So we have ro water times G times we object is equal to 17.5 oh, minus 11 points you. And so all together, the object which is our or sample, is equal to 17.5 minus 11.2, divided by 9.8, which is the gravitational acceleration and divided as well by the density of water, which is tend to the three kilograms per meter cubed. So that's the volume of our object. One of the density of the air sample. Ro sample will be equal. Tio the mass of the sample divided by the volume of the sample, which I had previously called the object. So I'm using objects and sample interchangeably here. So if we know the mass than we can determine the density simply by dividing by the volume that we've calculated previously and to get the mass, we simply divide its way, which is f grab um I G. So this is equal to 17.5 over 9.8. That gives us the mass of the object and we to write us well by the volume of the object.

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