   Chapter 7, Problem 66AP

Chapter
Section
Textbook Problem

The pilot of an airplane executes a constant-speed loop-the-loop maneuver in a vertical circle as in Figure 7.13b. The speed of the airplane is 2.00 × 102 m/s, and the radius of the circle is 3.20 × 103 m. (a) What is the pilot's apparent weight at the lowest point of the circle if his true weight is 712 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 scat 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?

(a)

To determine
The pilot’s apparent weight at the lowest point of the circle.

Explanation

Given info: The speed of the airplane (v) is 2.00×102m/s . Radius of the circle (r) is 3.20×103m . True weight of the pilot (W) is 712 N.

Explanation:

The apparent weight of the pilot is equal to the normal force.

From the diagram, the normal force at the lowest point of the circle is,

N=W+mv2r

Mass of the pilot is,

m=Wg

• g is the acceleration due to gravity.

From the above equations,

N=W(1+v2gr)

Substitute 712 N for W, 3.20×103m for r, 9

(b)

To determine
The pilot’s apparent weight at the highest point of the circle.

(c)

To determine
How the pilot experiences weightlessness.

(d)

To determine
The speed of the pilot when he experiences weightlessness.

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