4: After an hour, the monkey finally regains consciousness to find himself afloa

Question

4: After an hour, the monkey finally regains consciousness to find himself afloat in the North Sea. Luckily, some kind soul made sure that he was stored within an oil drum. Assuming: The oil drum floats in such a way that one circular end is always directly up. The total mass of monkey+drum is 200 kilograms. The drum has a cross-sectional area of 0.4 m2, and the North Sea is level.

a: What is the buoyant force on the barrel as a function of depth?

b: What is the draft (the distance from the surface to the deepest point of the barrel at equilibrium) of the barrel?

c: Write out the equation of motion for the drum.

Explanation / Answer

A)
The buoyant force is equal to the weight of the water that is displaced.
That is equal to the volume of the drum that is submerged times the density of water times g.
The volume of the drum that is submerged is equal to:
V = 0.4*d where d is the depth

The density of water is 1000 kg / m^3
So, the expression for buoyant force is:
F = 0.4*d*1000*g = 400g*d

B)
At equilibrium, Mg = F,
So 200g = 400g*d
d = 200/400
d = 0.5 m

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