The pilot of an airplane executes a constant-speed loop-the-loop maneuver. His p
ID: 1413453 • Letter: T
Question
The pilot of an airplane executes a constant-speed loop-the-loop maneuver. His path is a vertical circle. The speed of the airplane is 285 mi/h, and the radius of the circle is 1450 ft.
(a) What is the pilot's apparent weight at the lowest point if his true weight is 160 lb? ______ lb
(b) What is his apparent weight at the highest point?__________ lb
(c) What If? Describe how the pilot could experience weightlessness if both the radius and the speed can be varied. (Note: His apparent weight is equal to the magnitude of the force exerted by the seat on his body.)
Explanation / Answer
Given,
v = 285 mi/hr = 418 ft/s ; R = 1450 ft ;
a) w = 160 lb => mg = 160 lb => m = 160/g = w/g
The pilots apparent weight at the bottom will be the sum of his actual weight and centripital force. So,
W = w + Fc = w + mv2/R = w + w/g (v2/R)
W = 160 + 160/32.2 ft/s^2 x 418 x 418 / 1450 = 758.75 lb
Hence, apparent weight = W = 758.75 lb
b)at the top, the apparent weight of the pilot will be, his weight minus centripital force on him. So,
W' = w - Fc = w - w/g (v2/R)
W' = 160 - 160/32.2 x 418 x 418 / 1450 = -438.75 lb
Hence, at the top, W' = -438.75 lb
c)The weigtlessness would be felt when,
Fc = w
w/g (v2/R) = w (w gets cancelled both the sides)
solving for R and v we get:
R = v2/g and v = sqrt (g R)
when, v = 418 ft/s R = 5426.21 ft and when, R = 1450 ft ; v = 216.07 ft/s
The radius and velocity required to attain weightlessness is independent of mass or weight of the pilot.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.