At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. (c) How fast in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration?

Video transcript

Welcome back everybody. We are studying the effects of acceleration on humans. So we have a human which we will just represent with a particle here at the edge of a centrifugal arm. Now we are told A couple of different things about the system. We're told that the radius of rotation for this centrifuge is 7.5 m. And we are told that the radial acceleration we wish to achieve is 9GS. And we are tasked with finding what is the required frequency to achieve this. What we have a formula for this that relates all of these terms we have that the centripetal acceleration is equal to four pi squared times r radius times our desired frequency squared. So let me divide both sides here by four pi squared times the radius or pi squared times the radius. And you'll see that these terms cancel out. Now if I just take the square root of both sides, this power is going to go away and we get that our frequency is equal to the square root of our centripetal acceleration divided by four pi squared times R. So let's go ahead and plug in all of our values for this. So we have that. Our frequency is equal to nine Gs, which is nine times 9.8 divided by four pi squared times r radius of 7.5 squared. This gives us a frequency of 1/ 0.546 seconds. However, we need this in revolutions per minute. So let's multiply this by 60 seconds. Since we know there are 60 seconds per one minute. These units are going to cancel out, And we get that our frequency is equal to 32.7 rotations per minute, in order to achieve nine Gs corresponding to our final answer of D. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.