(a) What is the pilot\'s apparent weight at the lowest point of the circle if hi

Question

(a) What is the pilot's apparent weight at the lowest point of the circle if his true weight is 658 N.

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

(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?

(d) What speed would have resulted in the pilot experiencing weightlessness at the top of the loop?

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 2.00 ? 102 m/s, and the radius of the circle is 3.14 times 103 m. What is the pilot's apparent weight at the lowest point of the circle if his true weight is 658 N. What is his apparent weight at the highest point of the circle? 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? What speed would have resulted in the pilot experiencing weightlessness at the top of the loop?

Explanation / Answer

Weight of pilot = mg = 658N

Mass of pilot, m = 658/9.8 = 67.14kg

a/ centripetal acceleration from the constant-speed looping

a = v2/r = 2002/3.14*103 = 12.74 m/s2

apparent weight of the pilot at the lowest point = mg+ma

= 67.14(9.8+12.74) = 1513.25 N

b/apparent weight at the highest point = mg-ma =

= 67.14(9.8-12.74) = -197.4N (meaning he is feeling being thrown upward)

c/ the pilot can experience weightlessness at the top of the loop if the centripetal force is equal to his weight. In part b, the centripetal part is larger than his weight so if the radius of the loop is a little bigger OR speed is a little lower than 200m/s the weightlessness could happen

d/ for weightlessness to happen at the top of the loop:

mg

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