When the Tucurui Dam was constructed in northern Brazil, the lake that was
created covered a large forest of valuable hardwood trees. It was found that
even after 15 years underwater the trees were perfectly preserved and
underwater logging was started. During the logging process a tree is selected,
trimmed, and anchored with ropes to prevent it from shooting to the surface
like a missile when cut. Assume that a typical large tree can be approximated
as a truncated cone with a base diameter of \(8 \mathrm{ft},\) a top diameter of
\(2 \mathrm{ft}\), and a height of \(100 \mathrm{ft}\). Determine the resultant
vertical force that the ropes must resist when the completely submerged tree
is cut. The specific gravity of the wood is approximately 0.6.