Chapter 8, Problem 50 In a large centrifuge used for training pilots and astrona

Question

Chapter 8, Problem 50

In a large centrifuge used for training pilots and astronauts, a small chamber is fixed at the end of a rigid arm that rotates in a horizontal circle. A trainee riding in the chamber of a centrifuge rotating with a constant angular speed of 2.9 rad/s experiences a centripetal acceleration of 2.7 times the acceleration due to gravity. In a second training exercise, the centrifuge speeds up from rest with a constant angular acceleration. When the centrifuge reaches an angular speed of 2.9 rad/s, the trainee experiences a total acceleration equal to 5.0 times the acceleration due to gravity. (a) How long is the arm of the centrifuge? (b) What is the angular acceleration in the second training exercise?

Explanation / Answer

a) v2/r = 3*9.8

v = r*w

(rw)2/r = 29.4

r = 7.35 m

b)   

atotal = 4.4*9.8 = 43.12

V = r*w =7.35*2 = 14.7

centripetal acc. = v2/r = 14.72/7.35 = 29.4

angular acc = 43.122-29.42 =31.54 rad/sec2

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