A jet pilot takes his aircraft in a vertical loop (Fig. 5-43). (a) If the jet is

Question

A jet pilot takes his aircraft in a vertical loop (Fig. 5-43).

(a) If the jet is moving at a speed of 1100 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 6.0 g's.
m
(b) Calculate also the 74 kg pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle.
N
(c) Calculate the pilot's effective weight at the top of the circle. (Assume the same speed.)
N

Explanation / Answer

Here,

a) let the radius of cirle is r

speed, v = 1100 km/hr

v = 306 m/s

acceleration = v^2/R

6 * 9.8 = 306^2/R

R= 1592 m

the minimum radius is 1592 m

b)

at the bottom

effective weight = m * g + m * v^2/r

effective weight = m * g + 6 mg

effective weight = 7 * 74 * 9.8

effective weight = 5076 N

c)

at the top of circle

effective weight = -m * g + m * v^2/r

effective weight = -m * g + 6 mg

effective weight = 5 * 74 * 9.8

effective weight = 3626 N

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