Circular motion jet fighter problem

[bcjochim07]

Homework Statement

A jet fighter pilot flies at mach 3 vertically down and intends to pull up in a circular maneuver before crashing in the ground. He knows that he is able to withstand an acceleration of 9g before blacking out.

a) Where does the max. acceleration occur in the maneuver?

b) What is the minimum radius that he can take?

Homework Equations

The Attempt at a Solution

I'm going to work in polar coordinates.

So the Fnet=mv^2/r = N-mgsin(theta), so the max. acceleration would occur at the bottom of the loop. That being said, I'm having a bit of a difficult time picturing which way the normal force points when the pilot is say somewhere in between his point of entering the loop and the bottom of the loop. So, when I try to draw a FBD, I get a little confused. Anway, here's what I did:

The force on the person is N, so

N=mgsin(theta)+mv^2/r = 9mg and at the bottom of the loop theta =90

then v^2/r = 9g v = 343 m/s * 3 = 1029

so r = 13.5 km --- Is this correct?

 

[bcjochim07]

I guess it's a subtle distinction between the force on the plane and the force on the person. So, in order for the plane to be moving in a circle, it's net force must also be mv^2/r, only there is no normal force. There must be a force of thrust? I guess I'm again falling into confusion about the elusive "centrifugal" and "centripetal" forces. Could someone please enlighten me? Thanks.

 

[tomcue]

In response to the content, I would say that the solution provided is correct. The maximum acceleration would occur at the bottom of the loop when the pilot is experiencing both the downward force of gravity and the centripetal force required for circular motion. The minimum radius that the pilot can take would be 13.5 km, which means that the pilot would have to pull up at a minimum of 13.5 km above the ground to avoid crashing. It is important for the pilot to know their limits and be able to withstand the 9g acceleration in order to successfully complete the maneuver without blacking out.