Apparent weight of a pilot in a loop

[adam199]

Here's a picture:

Edit: Here's a description of the problem in case the picture isn't clear. A 54-kg pilot flies a jet trainer in a half vertical loop of 1200-m radius so that the speed of the trainer
decreases at a constant rate. Knowing that the pilot’s apparent weights at Points A and C are 1680 N and 350 N, respectively, determine the force exerted on her by the seat of the trainer when the trainer
is at Point B.

The picture is of an airplane flying horizontally in the positive x, then doing a semicircular loop, so that it is flying in the negative x-direction at a height above the previous horizontal flight path. Point A is at the start of the loop, B is halfway through the loop when the plane is completely vertical, and C is right at the exit of the loop.

Relevant equations are:

a(tangential) is constant throughout the loop

F=ma and the use of normal forces and apparent weight to calculate force and acceleration

a(normal)=v^2/p (p is the radius of the loop and v is velocity)
Attempt at a solution:I wrote out a bunch of force equations for the three points of the loop:

pt A:

+->ƩF(tangential) = -R(A) = ma(tangential)
+^ƩF(normal) = -mg+N(A) = ma(normal at A)

pt B:

+^ƩF(tangential) = -R(B)-mg = ma(tangential)
+<-ƩF(normal) = N(B) = ma(normal at B)

pt C:

+<-ƩF(tangential) = -R(C) = ma(tangential)
(positive down)ƩF(normal) = mg+N(C) = ma(normal at C)

From here, I don't know how to get the force exerted by the seat on the pilot at B.

 

[adam199]

I solved it by using the apparent weights as the normal reactions at each point and using that to find the velocities and accelerations needed to solve the problem.