- #1

Twoism

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## Homework Statement

A cylinder of density RhoO, length L, and cross-section area A floats in a liquid of density RhoF with its axis perpendicular to the surface. Length h of the cylinder is submerged when the cylinder floats at rest. Suppose the cylinder is distance y above its equilibrium position. Find an expression for Fnet (in the y direction). Use what you know to cancel terms and write this expresion as simple as possible. What is the "spring constant" k? I go on to prove h=(RhoO/RhoF)L

## Homework Equations

Fnet=F(buoyant) + -(F(cylinder))

F(buoyant)=RhoF*VolumeInWater*g

F(cylinder)=RhoO*TotalVolume*g

Fnet=-ky

VolumeInWater=A(h-y)

TotalVolume=AL

h=(RhoO/RhoF)L

k= Spring constant

## The Attempt at a Solution

I get to a point where the equation goes as follows

-ky=Ag(RhoF(h-y) - (RhoO*L))

I tried substituting in h=(RhoO/RhoF)L and L=(RhoF/RhoO)h, but neither seem to make the expression "simple" like the problem states, and when I solve for k, it's just messier. Thanks for any help. Oh, and the LaTeX kept messing up, so I had skip it, sorry.