One way for pilots to train for the physical demands of flying at high speeds is
ID: 1837286 • Letter: O
Question
One way for pilots to train for the physical demands of flying at high speeds is with a device called the "human centrifuge." It involves having the pilots travel in circles at high speeds so that they can experience forces greater than their own weight. The diameter of the NASA device is 17.2 m. 1) Suppose a pilot starts at rest and accelerates at a constant rate so that he undergoes 30.0 rev in 2.00 min.
1. What is his angular acceleration (in rad/s2)? (Express your answer to three significant figures.)
2. What is his angular velocity (in rad/s) at the end of that time? (Express your answer to three significant figures.)
3. After the 2-min period, the centrifuge moves at a constant speed. The gg-force experienced is the centripetal force keeping the pilot moving along a circular path. How many gg's is the pilot experiencing? The acceleration can be expressed as ____*gg where gg is the acceleration due to gravity. (Express your answer to three significant figures.)
4. The pilot can tolerate 12 gg’s in the horizontal direction. How long would it take the centrifuge to reach that state if it starts at the angular speed found in the third part and accelerates at the rate found in the first part? (Express your answer to two significant figures.)
Explanation / Answer
1. angular displacement = initial angular speed *t + alpha*t^2 / 2
(30 x 2 x pi rad ) = (0 * t) + ( alpha * (2 x 60)^2 /2 )
188.5 = 7200 alpha
alpha = 0.0262 rad/s^2
2. wf = wi + alpha*t
w = 0 + (0.0262 * 2 * 60) =3.14 rad/s
3. a_c = w^2 r = (3.14^2) ( 17.2 / 2) = 84.8 m/s^2
in gg
a_C = (84.8 / 9.81) gg = 8.64 gg
Ans 8.64
4. at 12gg :
12 x 9.81 = w^2 (17.2 /2 )
w = 3.7 rad/s
applying wf = wi + alpha*t
3.7 = 3.14 + (0.0262t)
t = 21.37 sec
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