A jet pilot takes his aircraft in a vertical loop. If the jet is moving at a speed of 1100km/h at the lowest point of the loop:

Question

A)Determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 5.5g's
B)Calculate the 68kg pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle.
C)Calculate the 68kg pilot's effective weight (the force with which the seat pushes up on him) at the top of the circle (assume the same speed)

Answer 1

v =1100 km/h = 305.6 m/s.

a =v^2/R => R = v^2/a = (305.6)^2/5.5•9.8 = 1732 m
R > 1732 m.

The magnitude of the effective weight = the magnitude of the normal force N
bottom: N = m•g – m•a = m• (g - 5.5•g) = - 4.5•m•g
W = - N = 4.5•m•g =4.5•68•9.8 =2998.8 N.
top: N = - m•g – m•a = -m• (g+a) = -m• (g+5.5•g) ,
W = - N = 6.5•m•g =6.5•68•9.8 =4331.6 N.