a jet pilot takes his aircraft in a vertical loop.

Question

a) if the jet is moving at a speed of 2000 km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0g's
b) calculate also the 76kg pilot's effective weight ( the force with which the seat pushes up on him) at the bottom of the circle.
c) calculate the pilot's effective weight at the top the circle. (Assume the same speed.)

Answer 1

a)
v=2000 km/h = 2000/3.6 m/s = 555.6 m/s
centripetal acceleration, a
=v²/r
Therefore
6g=v²/r
r=v²/(6g)
=555.6²/(6*9.8)
= 5249 m

b)
76*(6g + g) = 76*7*9.8 = 5214 N

c)
76*(6g-g) = 76*5*9.8 = 3724 N

Answer 2

If the jet is moving at a speed of 1040 km / h at the lowest point of the loop , determine the minimu radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.6 g's . Express your answer to two significant figures and include the appropriate units .