A 80 kg pilot flies a plane in a loop. At the top of the loop, where the plane is completely upside-down the pilot feels no forces from the seat or the seat belts. (The pilot is “weightless.”) If the plane’s speed is 150 m/s, what is the radius of the loop?

2296 m

Explanation:

Since the pilot is flying in a loop (circular motion), there is centripetal force acting on him.

The centripetal force at any point during the motion is the result of the combined action of the force of gravity () and the normal reaction (). However, here we are told that when the plane is upside-down, the pilot feels weightless: this means that the normal reaction is zero,

N = 0

So the gravitational force entirely provides the centripetal force, so we can write:

where

m = 80 kg is the mass of the pilot

is the acceleration due to gravity

v = 150 m/s is the speed of the pilot

r is the radius of the loop

And solving for r, we can find the radius of the loop:

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y