During the manufacture of the raft, 25 pine logs were tied. Determine the weight of the cargo

During the manufacture of the raft, 25 pine logs were tied. Determine the weight of the cargo that can be placed on the raft if the volume of each log is 0.8 m³, the density of water is 1000 kg / m³, the density of pine is 650 kg / m³.

V1 = 0.8 m3.

g = 9.8 m / s2.

ρд = 650 kg / m3.

ρw = 1000 kg / m3.

P -?

mg -?

Two forces act on the raft: gravity Ft, directed vertically downward, and buoyant force of Archimedes Farch, directed vertically upward.

The force of gravity is determined by the formula: Ft = m * g, where m is the mass of the raft, g is the acceleration of gravity.

m = V * ρд.

V = n * V1.

m = n * V1 * ρд.

Ft = n * V1 * ρd * g.

The buoyancy force of Archimedes Farch is determined by the formula: Farch = ρw * 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.

Farch = ρv * g * n * V1.

The weight of the cargo P, which can be placed on the raft, is expressed by the formula: P = Farch – Ft = ρw * g * n * V1 – n * V1 * ρd * g = g * n * V1 * (ρw – ρd).

P = 9.8 m / s2 * 25 * 0.8 m3 * (1000 kg / m3 – 650 kg / m3) = 68600 N.

P = mg * g.

mg = P / g.

mg = 68600 N / 9.8 m / s2 = 7000 kg.

Answer: the raft can withstand a load weighing P = 68600 N or weighing mg = 7000 kg.