The pilot of an airplane executes a loop-the-loop maneuver in a vertical circle.

Question

The pilot of an airplane executes a loop-the-loop maneuver in a vertical circle. The speed of the airplane is 355 mi/h, at the top of the loop and 450 mi/h at the bottom, and the radius of the circle is 1 380 ft. Note: His apparent weight is equal to the magnitude of the force exerted by the seat on his body.
(a) What is the pilot's apparent weight at the lowest point if his true weight is 160 lb?

(b) What is the magnitude of his apparent weight at the highest point?

(c) Describe how the pilot could experience weightlessness if both the radius and the speed can be varied.

Explanation / Answer

at lowest point apparent weight = 72.57*9.8 N + 72.57*v^2/r = 711.186 + 72.57*201.17^2/420.62 = 711.186 + 6982.22 N = 7693.41 N at highest point apparent weight = 72.57*158.69^2/420.62 - 711.186 = 4344.77-711.186 N = 3633.58 N Weightlesness can be occured only at highest point when for certain values of R and V the force becomes equal to its weight so he feels weightless

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