A jet pilot takes his aircraft in a vertical loop, as shown in the figure(Figure

Question

A jet pilot takes his aircraft in a vertical loop, as shown in the figure(Figure 1) .

Part A

If the jet is moving at a speed of 940 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 6.4 g's.

Express your answer to two significant figures and include the appropriate units.

Part B

Calculate the 73-kg pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and at the top of the circle (assume the same speed).

Express your answers using two significant figures separated by a comma.

Explanation / Answer

Given,

a)v = 940 km/h = 940 X 1000/3600 = 261.11 m/s

centripiatal acceleration, = v2 /r

6.4 g = 261.112 /R

R = 1087.03 m

b) effective weight is what normal reaction he experience

at bottom ,

N = mg + mv2 /R = 73 x (g + 6.4 g)

N = 5293.96 N

c) when he at top,

N = mg - mv2 /R

N = mg - 6.4 mg

N = - 5.4 x 73 g = -3863.16 N

He experiences a force of 3863.16 N in the upward direction. So, the seat exerts a normal force of 3863.16 N

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