The area of a raft made of square pine beams is 4 m2, thickness 30 cm. What is the maximum weight

The area of a raft made of square pine beams is 4 m2, thickness 30 cm.What is the maximum weight of cargo that the raft can hold? The density of pine is 500 kg / m3 and water is 1000 kg / m3

S = 4 m2.

d = 30 cm = 0.3 m.

g = 10 m / s2.

ρс = 500 kg / m3.

ρw = 1000 kg / m3.

mg -?

The condition of equilibrium in water will be equality of the gravity Ft, which acts on the raft with a load, and the buoyancy force of Archimedes Farch, which acts on the raft completely immersed in water: Ft = Farch.

Ft = (mg + mp) * g, where mg is the mass of the cargo, mp is the mass of the raft.

mп = Vп * ρс = S * d * ρс.

Farch = ρw * g * V, where ρw is the density of water, g is the acceleration of gravity, V is the volume of the submerged part of the body in the liquid.

Farch = ρw * g * S * d.

(mg + mp) * g = ρw * g * S * d.

mg + mp = ρw * S * d.

mg = ρw * S * d – mp = ρw * S * d – S * d * ρс = S * d * (ρw – ρс).

mg = 4 m2 * 0.3 m * (1000 kg / m3 – 500 kg / m3) = 600 kg.

Answer: the raft can withstand a load of mass mg = 600 kg.