In a large centrifuge used for training pilots and astronauts, a small chamber i

Question

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 3.0 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 3.0 rad/s, the trainee experiences a total acceleration equal to 4.6 times the acceleration due to gravity. How long is the arm of the centrifuge?

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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