A pilot of mass 65 kg in a jet aircraft makes a complete vertical circle in mid-air. The vertical circle has a radius of 1.70 km at a constant speed of 215 m/s. Determine the force of the seat on the pilot at (a) the bottom of the loop and (b) the top of the loop. (Note that at the top of the loop, the aircraft is upside down.)

Okay, i know that first i will have to use 1700m as my radius.
Also, i know the equations i will have to work with (uniform circular motion
Centripetal Force= mass times velocity squared, all over radius.)
But, am i looking for the Fn (Normal Force) ..
and ifso,
Centripetal force will equal force of gravity plus the normal force in both situations, so how will the situations differ? like, is there something i'm missing?
Please explain, thanks :)

To determine the force of the seat on the pilot at the bottom and top of the loop, you are correct in using the equation for centripetal force:

Centripetal force = (mass x velocity^2) / radius

In this case, the centripetal force will be equal to the sum of the force of gravity (mg) and the normal force (Fn) acting on the pilot. Since the aircraft is making a vertical loop, the pilot will experience a varying normal force at different points of the loop.

(a) At the bottom of the loop:
The normal force will be directed upward and will help balance the force of gravity acting on the pilot. So, the equation can be written as:

Centripetal force = force of gravity + normal force

(mass x velocity^2) / radius = mg + Fn

Solving for Fn, we can rewrite the equation as:

Fn = (mass x velocity^2) / radius - mg

Substituting the given values, we have:
mass = 65 kg
velocity = 215 m/s
radius = 1700 m
g = 9.8 m/s^2

Fn = (65 kg x (215 m/s)^2) / 1700 m - (65 kg x 9.8 m/s^2)

(b) At the top of the loop:
The normal force will be directed downward, opposing the force of gravity. Rewriting the equation, we have:

Centripetal force = force of gravity - normal force

(mass x velocity^2) / radius = mg - Fn

Solving for Fn, we can rewrite the equation as:

Fn = mg - (mass x velocity^2) / radius

Substituting the given values, we have:
mass = 65 kg
velocity = 215 m/s
radius = 1700 m
g = 9.8 m/s^2

Fn = (65 kg x 9.8 m/s^2) - (65 kg x (215 m/s)^2) / 1700 m

In summary, the calculations for the force of the seat on the pilot will differ at the bottom and top of the loop due to the direction of the normal force. At the bottom of the loop, the normal force will be added to the force of gravity, while at the top of the loop, the normal force will be subtracted from the force of gravity. This is because the normal force acts in the opposite direction to counterbalance the forces at different points of the loop.

42