Crater Lake in Oregon has a curiosity known as the ?Old man of the Lake? shown in the picture below. First noted in 1896 by geologist Joseph Diller, the floating tree stump is 9 meters long(30 ft) with a diameter of 61 cm (2 ft). In its equilibrium position, it extends 1.2 m (4 ft) above the surface. One explanation for the mysterious ?old man? is that before it began freely roaming the lake part of it became water logged while the other part remained dry.

PROBLEM II. Model the "Old Man" as a cylinder with cross-sectional area A and a total submerged depth H. The upper section with specific gravity S has a height h, and the lower section with specific gravity S has a height h. The specific weight of the lake water is YHO. Assume that in its equilibrium position, H = h. D S S h h H B. What is an expression for the total weight of the log?