# Problem: A solid aluminum cylinder of length L, radius r and density pal is suspended vertically from a thin wire and slowly lowered into a still lake. Let z denote the depth of the bottom of the cylinder. (When z &lt; 0 no portion of the cylinder is submerged in water. Note that  z is assumed here to increase downwards.) Assume that both the mass of the wire and the density of air are negligibly small. Let pω denote the density of water. What is the tension T in the wire a) for z &lt; 0? b) for 0 &lt; z &lt; L? c) for z &gt; L? d) Plot T(z).

###### Problem Details

A solid aluminum cylinder of length L, radius r and density pal is suspended vertically from a thin wire and slowly lowered into a still lake. Let z denote the depth of the bottom of the cylinder. (When z < 0 no portion of the cylinder is submerged in water. Note that  z is assumed here to increase downwards.) Assume that both the mass of the wire and the density of air are negligibly small. Let pω denote the density of water. What is the tension T in the wire

a) for z < 0?
b) for 0 < z < L?
c) for z > L?
d) Plot T(z).