Astronauts are trained to withstand g forces by utilizing human centrifuges in w

Question

Astronauts are trained to withstand g forces by utilizing human centrifuges in which the astronaunt is rotated about an axis to expose them to accelerations greater than that due to gravity. The maximum g-force that can be withstood for more than a few seconds (while retaining consciousness) is 9 g's (1g=9.80 m/s^2). If the axis of the centrifuge has a length (from the center of rotation) of 10.0 m, what is the speed of the centrifuge when the astronaut experiences 9.00 g's?

Is the astronaut conscious a little while later when the period of rotation of the centriuge has changed to 2.50 s?

Explanation / Answer

a = v^2/r

a = 9g = 9*9.8

r = radius = 10 m

9*9.8 = v^2/10

v = 29.7 m/s

++++++++

if time period T = 2.5 s

speed = v1 = 2*pi*r/T = (2*pi*10)/2.5 = 25.13 m/s

acceleration = a1 = v1^2/r = 25.13^2/10 = 63.15 m/s^2 = 63.15/9.8 g = 6.44 g

speed v1 < v

the astronaut is conscious

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