The pilot of an airplane executes a constant-speed loop-the-loop maneuver in a v

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 2.00 102 m/s, and the radius of the circle is 3.23 103 m. (a) What is the pilot's apparent weight at the lowest point of the circle if his true weight is 655.1 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? This answer has not been graded yet. (d) What speed would have resulted in the pilot experiencing weightlessness at the top of the loop? m/s

Explanation / Answer

(a)at bottom , a=V^2/r

a=(2*10^2)^2/3.23*10^3=12.38

then apparent weight will be - Wa= M(g+a)= 1483.33 N

(b) apparent weight at top will be

Wt=M(g-a)=-172.47N

(c) if a=g then Wt= o , so pilot feel weightless at top of circle.

(d) a=g, V^2/r=g

V^2=g*r=(9.8)*(3.23*10^3)

V=177.92 m/s or 1.78*10^2 m/s

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