An object with height h , mass M , and a uniform cross-sectional area A floats u

Question

An object with height h, mass M, and a uniform cross-sectional area A floats upright in a liquid with density ?.

Part A

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

Express your answer in terms of the given quantities.

Part B

A downward force with 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? (Assume that some of the object remains above the surface of the liquid.)

Express your answer in terms of the given quantities.

Part C

Your result in part B shows that if the force is suddenly removed, the object will oscillate up and down in SHM. Calculate the period of this motion in terms of the density ? of the liquid, the mass M, and cross-sectional area A of the object. Neglect the damping due to fluid friction.

Express your answer in terms of the given quantities.

Explanation / Answer

partA)

he weight of displaced water equals the weight of the object
the water is displaced by the submerged portion of the object
let x be the height of the submerged portion which is the desired answer

rho * x * A * g = M * g
canncel g and rearrange

x = M / (rho * A)
add numbers and solve

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