A pilot weighing 70 kg describes a loop with a radius of 100 m on an airplane flying at a speed of 108

A pilot weighing 70 kg describes a loop with a radius of 100 m on an airplane flying at a speed of 108 km / h. determine the pilot’s weight at the bottom of the loop.

Given:

m = 70 kilograms – pilot’s weight;

g = 9.8 m / s ^ 2 – acceleration of gravity;

v = 108 km / h = 30 m / s – aircraft speed;

R = 100 meters – radius of the loop.

It is required to determine P (Newton) – the weight of the pilot at the bottom of the loop.

Let’s find the centripetal acceleration acting on the pilot:

a = v ^ 2 / R = 30 ^ 2/100 = 900/100 = 9 m / s ^ 2.

In the lower part of the loop, the acceleration is directed towards the center of the circle described by the plane, that is, up. Then:

P = m * (g + a) = 70 * (9.8 + 9) = 70 * 18.8 = 1316 Newtons.

Answer: the weight of the pilot will be 1316 Newtons.