# The plane makes a loop with a radius of 100 m, and moves at the same time with a linear speed, the modulus of which

The plane makes a loop with a radius of 100 m, and moves at the same time with a linear speed, the modulus of which is v = 280 km / h. Determine the pressure force modulus of the pilot weighing 80.0 kg on the seat at the top of the loop.

R = 100 m.
V = 280 km / h = 77.77 m / s.
m = 80 kg.
g = 9.8 m / s ^ 2.
N -?
Two forces act on the pilot at the top point: the force of gravity Ft directed vertically downward and the force F with which the seat presses on the pilot directed vertically downward. Under the action of these two forces, it moves with a centripetal acceleration a.
Let’s write Newton’s 2 law for the pilot: m * a = Ft + F.
F = m * a – Ft.
The force of gravity is determined by the formula: Ft = m * g, where m is the mass of the body, g is the acceleration of gravity.
F = m * a – m * g = m * (a – g).
Centripetal acceleration is determined by the formula: a = V ^ 2 / R.
The force with which the seat presses on the pilot will be expressed by the formula: F = m * (V ^ 2 / R – g).
According to Newton’s 3 law: the force F with which the seat presses on the pilot is equal to the force N with which the pilot presses on the seat, only oppositely directed.
F = N.
N = m * (V ^ 2 / R – g).
N = 80 kg * ((77.77 m / s) ^ 2/100 m – 9.8 m / s ^ 2) = 4054.5 N.
Answer: the module of the force of pressure of the pilot on the seat at the upper point of the loop N = 4054.5 N.

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