The Ostankino tower rests on the foundation with 10 supports. The mass of the tower is 82,000 tons.

univerkov | August 22, 2021 | education

The Ostankino tower rests on the foundation with 10 supports. The mass of the tower is 82,000 tons. The pressure produced by the tower on the foundation is 6800 kPa. What is the base area of each of the tower supports?

N = 10.

g = 10 m / s2.

m = 82000 t = 82 * 10 ^ 6 kg.

P = 6800 kPa = 68 * 10 ^ 5 Pa.

S1 -?

The pressure of the Ostankino tower on the foundation P is expressed by the formula: P = F / S, where F is the force with which the tower acts on the foundation, S is the area of contact between the tower and the foundation.

S = F / P.

The tower presses on the foundation with its weight F, the value of which is expressed by the formula: F = m * g, where m is the mass of the tower, g is the acceleration of gravity.

Since the tower is supported by N supports, and the area of each support is S1, then the total area S, on which the Ostankino tower weighs, is expressed by the formula S = N * S1.

N * S1 = m * g / P.

The area of one support S1 will be determined by the formula: S1 = m * g / P * N.

S1 = 82 * 10 ^ 6 kg * 10 m / s2 / 68 * 10 ^ 5 Pa * 10 = 12 m2.

Answer: The base area of the support is S1 = 12 m2.

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