What part of the pine cube will be submerged in water, density of pine 400kg / m3, water 1000kg / m3?

ρс = 400 kg / m3.

ρw = 1000 kg / m3.

Vп / V -?

Two forces act on a body immersed in water: the force of gravity Ft, directed vertically downward, and the buoyancy force of Archimedes Farkh, directed vertically upward.

Ft = Farch.

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

We express the mass of a cube m by the formula: m = ρс * V, where ρс is the density of the pine, V is the volume of the cube.

Fт = ρс * V * g.

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

ρс * V * g = ρw * g * Vp.

Vп / V = ​​ρс / ρв.

Vp / V = ​​400 kg / m3 / 1000 kg / m3 = 2/5.

Answer: 2/5 of the volume of the cube will be under water Vp / V = ​​2/5.