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A cylindrical buoy with hemispherical ends is dropped in seawater of density 1027 kg/m3, a...

A cylindrical buoy with hemispherical ends is dropped in seawater of density 1027 kg/m3, as shown in the figure. The mass of the buoy is 75.0 kg, the radius of the cylinder and the hemispherical caps is R = 0.200 m, and the length of the cylindrical center section of the buoy. is L = 0.600 m. The lower part of the buoy is weighted so that the buoy is upright in the water as shown in the figure. In calm water, how high (distance h) will the top of the buoy be above the waterline?

Step-by-Step Solution

Solution 1
Step #1 of 2

Consider the force balance to calculate the height of the buoy above the surface of water.

Here, is the force of buoyancy, is the mass and is the acceleration due to gravity.

Substitute, for .

Here, is the density of sea with respect to water, is the volume immersed of the buoy.

Substitute, for .

Rearrange equation for .

Here, R is radius of the spherical cap and L is the length of the cylindrical center section of buoy.

Substitute, for , 75.0 kg for m, 0.200 m for R and 0.600 m for

Step #2 of 2

Hence, the height of the top of the buoy is .

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