BIO Hypergravity.? 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 12.5 g. (a) How fast must the astronaut’s head be moving to experience this maximum acceleration? (b) What is the ?difference? between the acceleration of his head and feet if the astronaut is 2.00 m tall? (c) How fast in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration?
Solution 30E Step 1: Given Radius of the arm ( r ) = 8.84 m Maximum sustained acceleration a = 1m.5g = 122.5 m/s 2 Problem (a) Step 1: Speed of the man’s head to experience maximum sustained acceleration a = v2 or r v = ar * v = 122.5 8.84 * v = 32.9 m/s Problem (b) To find the difference between the acceleration of head and foot Step 1: Angular velocity = r = 8.84 = 3.72 rad/s