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Chapter 9: Problem 71

A \(80.0-\mathrm{kg}\) pilot in an aircraft moving at a constant speed of \(500 . \mathrm{m} / \mathrm{s}\) pulls out of a vertical dive along an arc of a circle of radius \(4000 . \mathrm{m}\).

Short Answer

Expert verified
Question: Calculate the centripetal force acting on a pilot with a mass of 80 kg when his aircraft is moving at a speed of 500 m/s and following a circular path with a radius of 4000 m as he pulls out of a dive. Answer: The centripetal force acting on the pilot when pulling out of the dive is 5000 N.

Step by step solution

01

Identify the given values

We are given the following information from the exercise: 1. Mass of the pilot (m) = 80 kg 2. Speed of the aircraft (v) = 500 m/s 3. Radius of the circular path (r) = 4000 m
02

Apply the centripetal force formula

We need to apply the formula for centripetal force, which is \(Fc = m*(v^2/r)\), in order to calculate the centripetal force acting on the pilot during the circular motion. We have all the required values, so we can plug them into the formula: \(Fc = 80 * (500^2/4000)\)
03

Calculate the centripetal force

Now we perform the calculations to find the centripetal force: \(Fc = 80 * (250000/4000)\) \(Fc = 80 * 62.5\) \(Fc = 5000 \mathrm{N}\) The centripetal force acting on the pilot when pulling out of the dive is 5000 N.

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