Calculating Minimum Radius for Circular Motion in a Vertical Loop

[Thereheis]

Homework Statement

A plane pilot takes his aircraft in a vertical loop. If the plane is moving at a speed of 700km/h at the lowest point of the loop:
a) Determine the minimum radius of the circle so the pilots acceleration does not exceed 6 g's
b) What is the pilot's effective weight at the bottom of the loop if her mass is 60.0kg?

Homework Equations

Fc=mv^2/r
Ac=v^2/r

The Attempt at a Solution

I have a free body diagram with force centripetal going up towards center, and the normal force going up as well. I also have mg going down, but i feel like I am missing something and I am confused about how to setup the EFy=? EFx=? or EF=?

I think I got a) with 6(9.81)=(194)^2/r
"R= 639m

 

[LowlyPion]

When the plane is at the lowest part of the loop the downward force on the pilot is already 1g. If he is not to experience greater than 6g the centripetal acceleration shouldn't be greater than 5g right?

 

[Thereheis]

Thanks Pion :). So therefore the radius is actually larger. I'm still confused about the free body diagram because I feel like i am missing a variable and don't know how to set it up.

 

[rl.bhat]

Apply the conservation of energy and find the relation between velocity at the bottom, velocity at the top and distance between top to bottom.
At the top, v^2/R - g = 6g.
Can you proceed now?