Centripetal Force: 80kg Pilot in Jet at 305m/s

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An 80 kg pilot experiences centripetal force while performing a loop in a jet at a speed of 305 m/s and a loop radius of 1.9 km. The pilot's angular velocity (omega) was calculated to be 0.1605 rad/s. The attempt to find the apparent weight at the bottom of the loop involved using the formula for centripetal acceleration (Acp), but the initial calculation of Acp was incorrect. The correct approach combines gravitational force (mg) with the centripetal acceleration to determine the total force felt by the pilot. Accurate calculations are crucial for determining the apparent weight experienced during the maneuver.
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Homework Statement



An 80 kg pilot, makes a loop the loop in a jet, the jet maintains a constant speed of 305 m/s and the radius of the loop is 1.900km. What is the apparent weiht that the pilot feels( Force) at the bottom of the loop the loop.

Homework Equations


Acp=w^2/r
w=(v/r)
F= ma or F= mg


The Attempt at a Solution


First I solved for omega w=0.1605, then I solved for Acp=0.0000136
the Force the pilot feels at the bottom of the loop would be
mg+ Acp or is this wrong?
 
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I figured out what I was doing wrong, I calculated the Acp wrong.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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