Posted by Jason on .
A boat is constructed in the shape of a rectangular cube. The base of the boat is 2m by 3m and the side of the boat is 2m high. The boat has a total mass of 4500kg. Hint-The density of the water is 1000kg/m^3.
a. What is the buoyant force on the boat? Explain answer.
b. Calculate the length of the side of the boat sticking out of the water.
c. What is the pressure on the bottom of the boat? Calculate this in two different ways and compare answer.
a) buoyant force equal total mass, assuming the boat floats.
b) From Archimedes principle, the total mass equals the mass of liquid displaced by the boat, so
if h=height immersed, then
2*3*h*1000 kg = 4500 kg.
Solve for h, and then subtract from 2 m to get the height out of water.
Pressure = buoyant force / area of bottom
Hydrostatic pressure at depth h
= h*1000 kg/m^2
The values obtained by both methods should be equal.