Can an ice floe hold three fishermen with a total mass of 240 kg, if the area of the ice floe is 100 m2 and 25 cm thick?

mp = 240 kg.

S = 100 m2.

d = 25 cm = 0.25 m.

g = 9.8 m / s2.

ρl = 900 kg / m3.

ρw = 1000 kg / m3.

Farkh -?

Two forces act on a body in water: gravity Ft directed vertically downward, and buoyancy 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 ice floe with fishermen, g is the acceleration of gravity.

m = mr + ml.

ml = ρl * V = ρl * S * d.

Fт = (mр + ρl * S * d) * g.

Ft = (240 kg + 900 kg / m3 * 100 m2 * 0.25 m) * 9.8 m / s2 = 222852 N.

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

Farch = 900 kg / m3 * 9.8 m / s2 * 100 m2 * 0.25 m = 220500 N.

We see that Ft> Fark the ice floe will sink.

Answer: the ice floe will not withstand the fishermen.