# Fluid Mechanics

Consider an object with height h, mass M, and uniform cross sectional area A floating upright in a liquid with density p.

a.) Calculate the vertical distance from the surface of the liquid to the bottom of the floating object at equilibrium.

b.) A downward force of magnitude F is applied to the top of the object. At the new equilibrium position, how much farther below the surface of the liquid is the bottom of the object than it was in part (a)? (The assumption that F is small enough for some of the liquid to remain above the surface of the liquid should be made)

c) The result from part b should show that if the force is suddenly removed, the object will oscillate up and down in simple harmonic motion. Calculate the period of this motion, in terms of the density p of the liquid and the mass M and cross-sectional area A of the object.

d.) A 1,500 kg cylindrical can buoy floats vertically in seawater (density 1.03 x 10^3 kg/m^3). The diameter of the buoy is 0.800m. Calculate the additional distance the buoy will sink when a 100 kg man stands on top.

e.) Calculate the period of the resulting vertical simple harmonic motion when the man dives off

f.) Calculate the period of oscillation of an ice cube 4.00 cm on a side floating in water with a density of 1.00 x 10^3 kg/m^3 if it is pushed down and released.

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#### Solution Summary

This solution looks at the bouyance, harmonic motion and period of objects in a fluid.