The $12-ft-$long $($into page$)$ log $($modeled as a cylinder with a diameter of $3$ ft $)$ separates two bodies of water. The water on the left side rises just to the top surface of the log $($a depth of $3$ ft whereas the water on the right rises exactly to the center of the log $(1\mathrm{.}5$ ft$).$

a$.$ Draw a free body diagram of the cylinder representing any forces due

to the water as a combination of resultant forces that could be used to solve

the problem, not as distributed loads and not as a single resultant force. $($It

may help to draw the distributed loads due to the water first, and then replace

them with concentrated forces to represent the distributed loads.$)$

b$.$ Draw the shape of the water that is displaced by the log$,$ i$.$e$.,$ the

volume of water that is displaced that provides any buoyant force on the log$.$

c$.$ Is any frictional force required between the log and the ground? If so$,$

what is the minimum coefficient of friction between the log and the ground? If

not, why?

d$.$ What is the minimum weight of the log$?$