A rectangular barge 5 m long and 3 m wide sagged by 50 cm after loading.

A rectangular barge 5 m long and 3 m wide sagged by 50 cm after loading. Determine the weight of the cargo received by the barge.

l = 5 m.

a = 3 m.

h = 50 cm = 0.5 m.

g = 10 m / s2.

ρ = 1000 kg / m3.

m -?

The force P, with which the cargo presses on the barge, is balanced by the force of Archimedes Farch: P = Farch.

We express the weight of the load P by the formula: P = m * g, where m is the mass of the load, 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 = l * a * h.

Farch = ρ * g * l * a * h.

m * g = ρ * g * l * a * h.

m = ρ * l * a * h.

m = 1000 kg / m3 * 5 m * 3 m * 0.5 m = 7500 kg.

Answer: a cargo weighing m = 7500 kg was loaded onto the barge.