A cabinet weighing 100 kg stands on four legs, each of which has a square footprint.

A cabinet weighing 100 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 150 kPa on the floor?

m = 100 kg.

g = 10 m / s2.

n = 4.

P = 150 kPa = 150,000 Pa.

but – ?

The pressure of the force P is the ratio of the force F to the area S on which this force acts: P = F / S.

The cabinet presses on the floor by the force of its weight F, the value of which is found by the formula: F = m * g, where m is the cabinet’s mass, g is the acceleration of gravity.

The area of ​​action of the weight of the cabinet S is expressed by the formula: S = n * S1, where n is the number of legs, S1 is the area of ​​one leg.

Since the leg has the shape of a square, we express its area by the formula S1 = a ^ 2.

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

a = √ (m * g / n * P).

a = √ (100 kg * 10 m / s2 / 4 * 150,000 Pa) = 0.04 m = 4 cm.

Answer: the side of the square of the cabinet leg is a = 0.04 m = 4 cm.