A jet pilot takes his aircraft in a vertical loop As shown i

A jet pilot takes his aircraft in a vertical loop. As shown in the figure

(A)If the jet is moving at a speed of 1150 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 6.5 g\'s.

(B)Calculate the 83 kg pilot\'s effective weight (the force with which the seat pushes up on him) at the bottom of the circle.

(C)Calculate the 83 kg pilot\'s effective weight (the force with which the seat pushes up on him) at the top of the circle (assume the same speed).

Solution

a)

V=1150 Km/h =1150*1000/3600

V=319.44 m/s

Centripetal acceleration

a=V²/r

=>r=V²/a =319.44²/(6.5*9.8)

r=1602 m

b)

At the bottom of the loop ,Normal force is given by

N=mV²/r + mg =83[319.44²/1602 + 9.8]

N=6100.4 N

c)

At the top of the loop ,Normal force is given by

N=mV²/r - mg =83[319.44²/1602 - 9.8]

N=4473.4 N