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(II) Archimedes' principle can be used not only to determine the specific gravity of a solid using a known liquid (Example 10 of "Fluids"); the reverse can be done as well. (a) As an example, a $3.80-$ kg aluminum ball has an apparent mass of 2.10 $\mathrm{kg}$ when submerged in a particular liquid: calculate the density of the liquid. (b) Derive a formula for determining the density of a liquid using this procedure.

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(a) 1210 $\mathrm{kg} / \mathrm{m}^{3}$(b) $\rho_{l i q u i d}=\left(\frac{m_{o b j e c t}-m_{l i q u i d}}{m_{o b j e c t}}\right) \rho_{o b j e c t}$

Physics 101 Mechanics

Chapter 13

Fluids

Fluid Mechanics

Cornell University

Rutgers, The State University of New Jersey

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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(II) Archimedes' prin…

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Archimedes' principle…

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A straightforward method o…

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According to Archimedes&#x…

so we want to find the density of the liquid. We know that the actual mass, uh minus the apparent mass is gonna be equal to the change in mass. And this will be equal to the density of the liquid times of loss volume of the ball. Rather, this would be equal to the density of the liquid of the liquid times the mass of the ball divided by the density of the ball work. In this case, the density the ball is made out of the ball is completely made out of aluminum. So this will be the master of the board of divided by the density of aluminum. So we can say that the density of the liquid would be equal to the change in mass times the density of aluminum divided by the mass of the ball and we can actually solve. So this will be 3.80 minus 2.10 kilograms. Uh, times 2700 kilograms per cubic meter, and then this will be divided by the mass of the ball being 3.80 kilograms. And we find that the density of the liquid is going to be equal to 1000 210 kilograms per cubic meter. So this would be our answer for a party and then for part B. When they want us to generalize the formula, we can simply just say that the density of any liquid is going to be equal to the mass of the object, minus the apparent mass of the object divided by the density rather divided by the mass of the object multiplied by the density of the object. And this would be the general formula if we wanted to find the density of any unknown liquid. That is the end of the solution. Thank you for watching.

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