   Chapter 7, Problem 20P

Chapter
Section
Textbook Problem

Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g (88.2 m/s2) without losing consciousness, (a) If a human centrifuge has a radius of 4.50 m, what angular speed results in a centripetal acceleration of 9g? (b) What linear speed would a person in the centrifuge have at this acceleration?

(a)

To determine
The angular speed of the human centrifuge with centripetal acceleration of 9g .

Explanation

Given Info: The centripetal acceleration of the human centrifuge is 9g and the radius of the centrifuge is 4.50m .

Explanation: The centripetal acceleration of the human centrifuge ac is v2/r and the linear speed of the centrifuge v is replaced with angular speed as rω . Now the centripetal acceleration ac becomes rω2 . The formula for the angular speed of the human centrifuge is,

w=acr

• ac  is centripetal acceleration of the human centrifuge.
• r is radius of the centrifuge.

Substitute 9g for ac , 9.8m/s2 for g , and 4

(b)

To determine
The linear speed of the person in the centrifuge.

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