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Carnegie Mellon University

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Problem 16 Easy Difficulty

A 6.0 -cm-tall cylinder floats in water with its axis perpendicular to the surface. The length of the cylinder above water is
2.0 $\mathrm{cm}$. What is the cylinder's mass density?

Answer

$667 \mathrm{kg} / \mathrm{m}^{3}$

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Video Transcript

the system is in static equilibrium. We know that the 1,000,000,000 see forces equaling the gravitational force for the cylinder. And so the buoyancy force would be equaling the density of the water times of bowling, with the water displaced multiplied by G Equalling MGI. And so we can then say that then this would be Equalling the density of the cylinder multiplied by the volume of the cylinder multiplied by G. And that's simply getting the mass so we can then see the density of water multiplied by the volume of the water would be equaling the density of the cylinder multiplied by the volume of the cylinder. Of course, G cancels out, and we find that then the density of the cylinder would be equal in the density of water multiplied by the volume of water divided by the volume of the cylinder. And so we can say that then the density of the cylinder would be equaling two 1000 kilograms per cubic meter multiplied by the area times the height 0.40 meters, divided by some area multiplied by Queen 060 meters, the total length. And so this is giving us then approximately 670 kilograms. Kirk. Cubic meter. So this would be the density of the cylinder. So we can say, Of course, the density of the cylinder is less than the density of water. And this is, of course, expected. The sunder floats. That is the end of the solution. Thank you for watching.

Carnegie Mellon University
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