What is the correct radius of the plane's loop?

[IGeekbot]

A pilot goes into a loop...

A 75 kg pilot goes into a loop. At the top of the loop, where the plane is completely upside down for an instant, the pilot hangs freely in the seat and does not push against the seat belt. The airspeed indicator reads 120m/s. What is the radius of the planes loop?


I did Ac=v^2/r

substitute 9.8 for ac and 120 for v, so...

9.8=120^2/r

and when you do that, the radius is 1469.39 m.


My friend disagrees and says the loop should only be 19.36 meters. He used F=ma, then put that into the equation, to get 19.36.


Can someone say who did it right?

 

[Galileo]

First of all. Which answer is more plausible. Surely I don't see an airplane make a loop with a radius of 19.36 meters.

But more rigorously. The gravitational force on the pilot equals the centrifugal force, since he doesn't push against the seat. So you're right.

 

[IGeekbot]

Thank you, and yes, I had thought of the airplane making a 19m loop. Not going to happen.

 

[Zlex]

You could still use F = ma, I don't know why you would, but you'd just you'd have to use it properly.

$$F = ma$$
$$F = \frac{mv^2}{R}$$
$$mg = \frac{mv^2}{R}$$
$$g = \frac{v^2}{R}$$
$$9.8 = \frac{120^2}{R}$$
...