The pilot of an airplane executes a constant-speed loop-the-loop maneuver in a v
ID: 1471502 • Letter: T
Question
The pilot of an airplane executes a constant-speed loop-the-loop maneuver in a vertical circle as in the figure below. The speed of the airplane is 2.50 102 m/s, and the radius of the circle is 3.35 103 m.
(a) What is the pilot's apparent weight at the lowest point of the circle if his true weight is 740 N?
N
(b) What is his apparent weight at the highest point of the circle?
N
(c) 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. Under what conditions does this occur?
Explanation / Answer
true weight of the piolet is
mg= 740 N
m = 740 N/ g = 740 N/ 9.8 = 75.51 kg
(a)
the apparent weight of the piolet at the lowest point of the circle is
n = mv^2/ R + mg
= 75.51 ( 250 m/s)^2/3.35 * 10 ^3 m + 740 N
= 2148.77 N
(b)
n = mv^2/ R - mg
= 75.51 ( 250 m/s)^2/3.35 * 10 ^3 m - 740 N
= 668.77N
(c)
the piolet will experiece weightlesness at the top of the circular path if the air plane exerts no force on him . the normal force on the piolet is zero . this can be done by making the centripetal force equal to weight of the piolet.
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