A jet pilot takes his aircraft in a vertical loop, as seen in figure below. If t

Question

A jet pilot takes his aircraft in a vertical loop, as seen in figure below. If the jet is moving at a speed of 1450 km/hr 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 5.55 g

(a) Determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 5.55 g.

(b) Calculate also the 81.8 kg pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle (assume the same speed).

(c) Calculate also the 81.8 kg pilot's effective weight (the force with which the seat pushes up on him) at the top of the circle.

Explanation / Answer

speed

v = 1450 km/h = 1450 *5/18 = 402.8 m/s

mass m=81.8 kg

a) given a = 5.55*g =5.55*9.8
centripetal acceleration

a = v^2/r

5.55*9.8 = v^2/r

r = 402.8^2/(5.55*9.8) = 2982.7 m

b) effective weight, W = m*g + m*5.55*g = 5250.742 N(upward)


c) effective weight, W = m*g - m*v^2/r = 81.8*9.8 - (81.8*402.8^2)/2982.7 = 801.64 -4449.61 = 3647.98 N

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