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A simple compass can be made by placing a small bar magnet on a cork floating in water. (a) What fraction of a plain cork will be submerged when floating in water? If the cork has a mass of 10.0 $\mathrm{g}$ and a 20.0 -g magnet is placed on it, what fraction of the cork will be submerged? (c) Will the bar magnet and cork float in ethyl alcohol?

(a) $f=0.24$(b) $f^{\prime}=0.68$(c) $f^{\prime \prime}=1.01 . \mathrm{Yes}$

0:00

Averell H.

Physics 101 Mechanics

Chapter 11

Fluid Statics

Fluid Mechanics

Cornell University

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

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So here in this problem were given that the mosque off the cock is 10 g on the mosque off the magnet. This is a magnet. Were given us 20 g on their three parts in the Croatian in the A. But we have to calculate that what fraction off a plane cork will be submerged in floating. I went floating in water so we know that the equation for the fraction some most is given by the density off the object divided by the density off the fluid. Now here the food we have the water. So the density off of water we know it is 1000 kg for me to cube on the density off the cock from the table Asper Given the book, we can calculate Toby 0.24 times 10 to the power three k g. Permit a cube. So we have the values have been back here to calculate the fraction some worst and it would be close to the density of cock which is 0.24 times 10 to the power three k g. Permit a cube divide by the injury of fluid, which is water. So it's densities 1000 times 10 to the power three k g permitted cube. So from here will get the fraction off cox almost, or we can wait after s would be called to 0.24 So this is the fraction. So most now, next will be solving the be part now in the bay, but were given that magnet off 20 g is placed on the cock and now we have to calculate the fraction of the cock that will be some most. So we'll be using the same formula. But now we don't know the density of the object, since the object is a combination off the cock on the magnet. So we'll be first calculated the density of the object. So for that, I will be calculating the volume off the cock. So density, you know, it is the ratio of moss over the volume, so we'll be calculating the density, the volume for cock. So this is for cock. So from here, volume off cock will be called to massive cock divided by the density of cock. So the mouse off the clock were given us 10 ground divided by the density of the cock. Now this density is in k g permitted you. But we will take the values in Grandpa Centimeter Cube so that this will you can this gram and gram can cancel out soon. Grandpa Centimeter Cube. The density of the cock would would be 0.24 g per centimeter cube. So from here will get the answer. That is the volume off caucus 41.6 67 centimeter cube. Similarly, we can calculate the volume off the iron basically magnet. So we do. You would be equal to the mass off the magnet, divided by the density off the magnet. So Mars off magnet were given us to any ground divided by the density off the magnet. So a density of the magnet is 7.8 gram per centimeter cube. So from here, we'll get the volume off the magnet. Asked 2.56 centimeter cube Now, next week. Uncalculated density of the object. So the density off the object that is the combination off the cock and the magnet would be close to the mask off the cock, plus the mask off the magnet divided by the volume off the cock, plus the volume off the magnet. So mass off the clock is 10 g. Also, the magnet is 20 ground divide by. We see, we have calculated as 41.67 centimeter cube. This is 41 0.67 Send a medic U plus V G. We have 2.56 centimeter cube. So from here, we'll get the density off object as 0.67 eight since eight grand person the molecule. Now we can calculate the fractions almost on. It would be called the same formula. That is the density of the object divided by the density of the feud. So density off object. We have calculated US zero point 678 Grandpa Centimeter Cube, divided by the density of water. So he'll take the values in Grandpa Centimeter Cube. So density of water and Grandpa Centimeter Cube is one. So, one Grandpa, Centimeter Cube. And here also, you know the same. That is Grandpa Centimeter Cube. So from here we'll get a fraction as 0.678 So this is the answer for the be part now. Next will be solving the C part now in the sea part, we have to tell whether the magnet and the cock will float in ethyl alcohol. Now we have to see the density off alcohol. And if its density is more than the density of the object, then it'll float. Otherwise it'll sink. So the density off the little alcohol it is zero point 79 Grandpa, Centimeter cube. And since it is greater than the density off the object, that is the magnet and the cock. So the bar and the cock will float in ethyl alcohol. So the answer is yes, it is flawed. So I hope you have understood the problem. Thank you.

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