Pine timber (density 400 kg / m3) of rectangular shape, the length of which is 2.0 m, is able to hold a load

Pine timber (density 400 kg / m3) of rectangular shape, the length of which is 2.0 m, is able to hold a load weighing 60 kg on the water, determine the area of the base of the timber, the density of water is 1000 kg / m3, the coefficient is taken equal to 10 N / kg.

Max. cargo weight:
Р = Fa – Fт.
P – max. weight (P = m * g, m is the mass of the load (m = 60 kg), g is the acceleration of gravity (g = 10 m / s ^ 2)).
Fa – the strength of Archimedes; Fa = ρw * g * V, ρw is the density of water (ρ = 1000 kg / m ^ 3), V is the volume of the bar.
Ft is the force of gravity; Fт = m * g, m is the mass of the timber (m = ρс * V, ρс is the density of pine (ρс = 400 kg / m ^ 3)).
m * g = ρв * g * V – ρс * V * g = V * (ρв – ρс).
V = m / (ρв – ρс) = 60 / (1000 – 400) = 0.1 m ^ 3.
S = V / h, h – bar length (h = 2 m).
S = 0.1 / 2 = 0.05 m ^ 2.
Answer: The base area is 0.05 m ^ 2.