Extreme accelerations. To simulate the extreme accelerations during launch, astr

Question

Extreme accelerations. To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of

Part A

If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of 4 g?

Express your answer with the appropriate units.

Part B

If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of 8 g?

Express your answer with the appropriate units.

Explanation / Answer

a_centripetal = w^2*r
The period, T = 2*pi/w

A) 4*g = w^2*r
w = sqrt(4*g/r) = sqrt(4*9.81/(13.5/2))=2.411 rad/s

T = 2*pi/w =2*3.14/2.411 = 2.6046 s Ans.

B) 8*g = w^2*r
w = sqrt(8g/r) = sqrt(8*9.81/6.75)= 3.409 rad/s

T = 2*pi/w = 2*3.14/3.409 = 1.8426 s Ans.

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