The cabinet weighing 90 kg stands on four legs, each of which has a square footprint.

The cabinet weighing 90 kg stands on four legs, each of which has a square footprint. What is the side of this square if the cabinet exerts a pressure of 250 kPa?

m = 90 kg.

g = 9.8 m / s ^ 2.

P = 250 kPa = 250,000 Pa.

a -?

Cabinet pressure P is determined by the formula: P = F / S, where F is the force with which the cabinet presses on the surface, S is the area on which this force acts.

The cabinet acts on the surface with its weight: F = m * g.

The cabinet has 4 legs, so the area S of contact between the cabinet and the surface will be determined by the formula: S = 4 * S1, where S1 is the area of one leg.

Since the leg is in the shape of a square, then S1 = a ^ 2, where a is the side of the square.

P = m * g / 4 * a ^ 2.

a = √ (m * g / 4 * P).

a = √ (90 kg * 9.8 m / s ^ 2/4 * 250,000 Pa) = 0.03 m.

Answer: the side of the square of the cabinet leg is a = 0.03 m.