Question

A rectangular barge 7 m long and 2 m wide floats in fresh water. How much will the barge sink when loaded with 600 kg of sand? Show all calculations leading to an answer.

Answer 1

You must apply Archimides' principle.

The barge will sink until the sum of the forces on it equals zero.

The two forces are the weight of the barge (with sand) and the buoyancy force, the force exerted by the liquid (fresh water) on the barge.

Then, weight of the barge with sand = m*g = 600 kg * g

Buoyancy force = density of the fluid * Volume of displaced fulid * g

Then, m*g = density of the fulid * Volume of displaced fluid * g

m*g = df * Vf * g

m = df*Vf => Vf = m/df = 600 kg / 1 000 kg/m^3 = 0.6 m^3

The volume of the displaced fluid equals the volume of the portion of the barge sinked, wich is the area of the rectangular base times the depth to which it sinked>

7m*2m*H = 0.6 m^3 => H = 0.6 m^3 /[14 m^2] = 0.043 m = 4.3 cm

Answer: 4.3 cm