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Chapter 5: Problem 2

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 greatest force is exerted on the pilot at the top of the loop where gravity and the centripetal force are both acting in the same direction, adding together. The least force is exerted at the bottom of the loop where gravity and the centripetal force work against each other, reducing the net force exerted on the pilot.

Step by step solution

01

Analyze the situation

In this problem, we have two forces at play, gravity and the force from circular motion. At the top of the loop, these forces add up, and at the bottom of the loop, they partially cancel out. The pilot feels the 鈥榝orce鈥� which includes the force of the seat pushing on the pilot (which provides the centripetal force necessary for circular motion) plus the weight of the pilot. This is the net force which is responsible for the circular motion.
02

Calculate force at the top of the loop

At the top of the loop, gravity and the centripetal force work in the same direction, causing a greater force to be exerted on the pilot. The net force acting on the pilot is the sum of the gravitational force and the centripetal force. This force is exerted upwards, towards the centre of the loop.
03

Calculate force at the bottom of the loop

At the bottom of the circle, gravity and the centripetal force work in opposite directions. The net force acting on the pilot is the difference between the centripetal force and the gravitational force. This force is also directed upwards, towards the centre of the loop.

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