When loading a ship with a bottom area of 1500 m², its draft increased by 40 cm.

When loading a ship with a bottom area of 1500 m², its draft increased by 40 cm. What is the weight of the cargo placed on the ship?

S = 1500 m ^ 2.

h = 40 cm = 0.4 m.

g = 9.8 m / s ^ 2.

ρ = 1000 kg / m ^ 3.

m -?

When loading the ship, the weight of the cargo P is balanced by the buoyancy force of Archimedes Farch.

P = Farch.

The weight of the body P is determined by the formula: P = m * g, where m is the mass of the body, g is the acceleration of gravity.

The buoyancy force of Archimedes is determined by the formula: Farch = ρ * g * V. Where ρ is the density of the liquid in which the body is immersed, g is the acceleration of gravity, V is the volume of the immersed part of the body in the liquid.

V = S * h.

m * g = ρ * g * S * h.

m = ρ * S * h.

m = 1000 kg / m ^ 3 * 1500 m ^ 2 * 0.4 m = 600000 kg.

Answer: m = 600,000 kg.