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Chapter 4: Problem 35

An astronaut is rotated in a centrifuge of radius \(5.2 \mathrm{~m} .(a)\) What is the speed if the acceleration is \(6.8 g ?(b)\) How many revolutions per minute are required to produce this acceleration?

Short Answer

Expert verified
The speed of rotation is approximately 24.69 m/s, and the centrifuge needs to make approximately 45.19 revolutions per minute to produce an acceleration of 6.8g.

Step by step solution

01

Calculate Speed

We will use the formula for Centripetal Acceleration, which is \(a_c = \frac{v^2}{r}\), where \(a_c\) is the Centripetal Acceleration, \(v\) is the speed, and \(r\) is the radius. We are given \(a_c = 6.8g\) (also needs to be converted to m/s^2), and the radius is \(r = 5.2\) m. We can solve for \(v\) using this formula.
02

Calculate revolutions per minute

To find the number of revolutions per minute, we first need to find the time it takes for one revolution. This time is called the period, \(T\), and is equal to \(T = \frac{2πr}{v}\). Once we know the period, we can calculate the number of revolutions per minute as \(Revolutions = \frac{60}{T}\).

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