Question

91. Humans can endure accelerations over 45 times as great as g. One of the main ways of testing human endurance of these accelerations was the "human centrifuge" the first of which was built by the U.S. Navy in 1950 and operated by them from 1950 through 1996. This device consisted of a large metal sphere in which the subject sat. This sphere connected to the end of a 15.2 m metal arm, which rotated rapidly to create accelerations as great as 40g. Calculate the maximum rotational speed of the centrifuge. (3.4)

Answer 1

91.

We know that centripetal force is given by:

Fc = m*ac

Fc = m*V^2/R

V = linear speed = w*R

w = rotational speed = ?

R = radius of centrifuge = 15.2 m

So

ac = centripetal acceleration = V^2/R = (w*R)^2/R

ac = w^2*R

w = sqrt (ac/R)

Now given that

ac = 40*g & R = 15.2 m

g = 9.8 m/sec^2

So

w = sqrt (40*9.8/15.2)

w = 5.08 rad/sec

w = (5.08 rad/sec)*(1 rev/2*pi rad)*(60 sec/1 min)

w = 48.5 rev/min = 48.5 rpm

Please Upvote.