How many screws do you need to screw into a 100 cm3 oak bar to start sinking in water?

How many screws do you need to screw into a 100 cm3 oak bar to start sinking in water? the weight of one screw is 4 g. Consider that when the screws are screwed in, the dimensions of the bar do not change.

Vb = 100 cm3 = 0.0001 m3.

m1 = 4 g = 0.004 kg.

g = 10 m / s2.

ρд = 700 kg / m3.

ρw = 1000 kg / m3.

n -?

In order for the bar to start sinking, the force of gravity Ft, which acts on it, must be a wound by the buoyant force of Archimedes Farkh: Ft = Farch.

The force of gravity of a bar with screws Ft is expressed by the formula: Ft = (mb + msh) * g, where mb is the mass of an oak bar, msh is the mass of screws that were screwed into the bar.

mb = Vb * ρd.

msh = n * m1, where n is the number of bars, m1 is the mass of one screw.

Ft = (Vb * ρd + n * m1) * g.

Farch = ρv * Vb * g.

(Vb * ρd + n * m1) * g = ρv * Vb * g.

Vb * ρd + n * m1 = ρw * Vb.

n * m1 = ρw * Vb – Vb * ρd.

n = Vb * (ρw – ρd) / m1.

n = 0.0001 m3 * (1000 kg / m3 – 700 kg / m3) / 0.004 kg = 7.5.

Since the quantity must be an integer, then n = 8.

Answer: in order for the bar to start sinking, n = 8 screws must be screwed into it.