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 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. How fast must the astronaut's head be moving to experience the maximum acceleration?

Answer 1

v=32.9m/s

Step-by-step explanation:

The acceleration needed to mantain a circular motion of radius r and speed v is given by the equation
`a=v^2/r`

This is the centripetal acceleration. The person will feel what is called a centrifugal acceleration, of the same value, because he is not in an inertial frame (thus subject to fictitious forces, product of inertia).

We want to know the speed of his head when it is subject to 12.5 times the value of the acceleration of gravity while moving on a 8.84m radius circle, so we must do:

`v=√(ar) = √(12.5gr)=√((12.5)(9.8m/s)(8.84m))=32.9m/s`