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At its Ames Research Center, NASA uses its large 20-G centrifuge to test the effects of...

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 the astronaut is strapped in at the other end. Suppose that he is aligned along the arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this machine is typically 12.5 g.

a) How fast must the astronaut's head be moving to experience this maximum accleration?

b) What is the difference between the accleration of his head and feet if the astronaut is 2.00m tall?

c) How fast is rpm (rev/min) is the arm turning to produce the maximum sustained acceleration?

Please show all work, and what formulas are being used. Thank you!

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Answer #1

The maximum acceleration sustained is a= 12.5g -12.5(9.81 m/s2 122.62 m/s2 The centrifugal acceleration is earr ange the above equation for speed v of the astronauts head v= ar (122.62 m/s*)(8.84 m) -32.92 m/s The distance between the axis of rotation to the feet of the astronaut is -8.84 m -2 m -6.84 m The angular speed is, v_32.92 m/S 3.72 rads r 8.84 m The acceleration of the astronauts feet is, a(6.84 m) (3.72 rad s) 94.6 m/s The difference between the acceleration of his head and feet is, = 122.62 m/s2-94.6 m/s = 27.8 m/s The speed of the arm turning to produce the maximum acceleration is 3.72 rad/s 60 3.72- rev/min 35.54 rev/min

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