The aircraft must have a speed of 800 km / h for take-off. The length of the takeoff run before takeoff is 150 m.

| July 11, 2021 | education

The aircraft must have a speed of 800 km / h for take-off. The length of the takeoff run before takeoff is 150 m. What is the power of the motors during takeoff, if the weight of the aircraft is 104 N and the coefficient of friction of the landing gear wheels on the ground is 0.02.

V = 800 km / h = 222.2 m / s.

V0 = 0 m / s.

S = 150 m.

m * g = 104 N.

g = 10 m / s2.

μ = 0.02.

P -?

Let us express the power of the aircraft engines by the formula: P = A / t.

A = Ft * S.

m * a = Ft + m * g + N + Ftr, where Ft is the engine thrust force, m * g is the gravity force, N is the reaction force of the surface of the inclined plane, Ftr is the friction force.

ОХ: m * a = Fт – Fтр.

OU: 0 = – m * g + N.

Ft = m * a + Ftr.

The friction force Ffr is expressed by the formula: Ffr = μ * P = μ * m * g.

Fт = m * a + μ * m * g = m * (a + μ * g).

a = (V ^ 2 – V0 ^ 2) / 2 * S = V2 / 2 * S.

a = (222.2 m / s) ^ 2/2 * 150 m = 164.5 m / s2.

a = V / t.

t = V / a.

t = 222.2 m / s / 164.5 m / s2 = 1.35 s.

m = 104 N / 10 m / s2 = 10.4 kg.

P = m * (a + μ * g) * S / t ..

P = 10.4 kg * (164.5 m / s2 + 0.02 * 10 m / s2) * 150 m / 1.35 s = 190 320 W.

Answer: P = 190320 W.



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