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Chapter 5: Problem 3

A jet plane flies at constant speed in a vertical circular loop. At what point in the loop does the seat exert the greatest force on the pilot? The least force?

Short Answer

Expert verified
The seat exerts the greatest force on the pilot at the top of the loop and the least force at the bottom of the loop.

Step by step solution

01

Understanding the forces

Identify the two forces acting on the pilot: The gravitational force, which always acts downward towards the center of the Earth, and the centripetal force, which always acts towards the center of the circle along which the jet is moving. At the top of the circle, both the gravitational force and the centripetal force act downward. At the bottom of the circle, while the gravitational force still acts downward, the centripetal force acts upward.
02

Analyzing force at the top of the loop

At the top of the loop, both the gravitational force and the centripetal force are acting in the same direction (downwards). This results in the total force being the sum of the gravitational force and the centripetal force, which would act on the pilot, pushing him into the seat. This is when the seat would exert the greatest force on the pilot.
03

Analyzing force at the bottom of the loop

At the bottom of the loop, the gravitational force acts downward, but the centripetal force acts upward. Because these forces act in opposite directions, the total force is the difference between these two forces. Thus, the seat exerts less force on the pilot at the bottom of the loop compared to at the top as these forces partially cancel out each other.

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