At its Ames Research Center, NASA uses its large “20-G” centrifug...

Question

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?

Accepted Answer

Welcome back everybody. We are going to be running some experiments with Earth's gravity and centripetal acceleration. And we have a volunteer who is tied down and safely strapped to the end of this arm and we are going to centrifuge them in this direction. Now we are told that fight plus the arm which accounts for the radius of this rotation is 7.5 m long. And we are trying to Achieve a centripetal acceleration of 9GS. And we are asked to find what the frequency needed in revolutions per minute to achieve this acceleration. Well, our acceleration we know is equal to four pi squared times the radius all over our period squared, rearranging some terms here we get that our period is equal to the square root of four pi squared times the radius all over our desired acceleration of nine Gs. But we're not looking for the period. We're looking for the frequency and in fact there is a relationship between the two. We know that the period is just the reciprocal of frequency. This means that our frequency plugging it into here is the square root of nine times our acceleration due to gravity. 9.8. All over four pi squared times r radius of 7. Plugging this into our calculator. We get that our frequency is one revolution every 0.546 seconds. However, we want this in revolutions per minute. So we are actually going to take our frequency and multiply it by 60 seconds per one minute. These terms cancel out giving us a final answer of a needed frequency of 32. rpm, which corresponds to our final answer choice of D. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one.

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