Radius of a curvature for specific force on a seat in a jet

[54stickers]

The question is:

What is the minimum radius of curvature of a jet, pulling out of a vertical dive at a speed of v, if the force on the pilot's seat is 7 times his weight?



The way I thought to answer this is just to say that, 7 mg, the net force on the seat will be equal to the angular acceleration. This does not assume that the 7mg force is just a normal force on the seat, but the Normal added to mg is a total of 7mg. Leaving a normal of 8mg

so that

7mg = (mv^2)/r

then

r = (v^2)/ 7g

The answer to the question according to the answer sheet is that 7 mg is going to be the normal force, and that the angular acceleration that creates a 7 mg normal force is going to be that of 6mg so:

N - mg = (mv^2)/r

7mg - mg = (mv^2)/r

then

r = (v^2)/6g

My question is which one is correct?
based on the wording of the question I don't think that it is okay to assume that the 7 mg is a only a normal. Am I okay to say this?

Thanks!

 

[Doc Al]

My question is which one is correct?
based on the wording of the question I don't think that it is okay to assume that the 7 mg is a only a normal. Am I okay to say this?

The answer sheet is correct. The force on the seat is the normal force. (The weight of the pilot acts on the pilot, not the seat.)