(B) In designing rotating space stations to provide for artificial-gravity envir

Question

(B)In designing rotating space stations to provide for artificial-gravity environments, one of the constraints that must be considered is motion sickness. Studies have shown that the negative effects of motion sickness begin to appear when the rotational motion is faster than approximately 2.1 revolutions per minute. On the other hand, the magnitude of the centripetal acceleration at the astronauts' feet should equal the magnitude of the acceleration due to gravity on earth. Thus, to eliminate the difficulties with motion sickness, designers must choose the distance between the astronaut's feet and the axis about which the space station rotates to be greater than a certain minimum value. What is this minimum value?

A centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. Such a device is used in medical laboratories, for instance, to cause the more dense red blood cells to settle through the less dense blood serum and collect at the bottom of the container. Suppose the centripetal acceleration of the sample is 6.85 103 times as large as the acceleration due to gravity. How many revolutions per minute is the sample making, if it is located at a radius of 4.30 cm from the axis of rotation? In designing rotating space stations to provide for artificial-gravity environments, one of the constraints that must be considered is motion sickness. Studies have shown that the negative effects of motion sickness begin to appear when the rotational motion is faster than approximately 2.1 revolutions per minute. On the other hand, the magnitude of the centripetal acceleration at the astronauts' feet should equal the magnitude of the acceleration due to gravity on earth. Thus, to eliminate the difficulties with motion sickness, designers must choose the distance between the astronaut's feet and the axis about which the space station rotates to be greater than a certain minimum value. What is this minimum value?

Explanation / Answer

acceleration due to gravity = 9.8 m/s^2

centripetal acceleration = 6.85E3 * 9.8 m/s^2
centripetal acceleration also equals v^2 / r, where they give you r = .0430m

so v^2 / .0430 = 6.85E3 * 9.8
v = sqrt(.0430 * 6.85E3 * 9.8)

v=2886.59m/s

v is the object tangential speed.

v (m/s) * 1 rev / 2piR m * 60 sec/min = speed in rev/min.=2886.59*(1/2pi.0430)*60=641369.4m/s

a=v^2/r= (r x omega)^2 / r
solve for r
r=(omega)^2/a=(omega)^2/g

omega is the angular velocity of rotation. 2.1rev/min must be changed to revs per sec. That is 126 revs/sec. The angular velocity is 2pi times this.

So r= (2pi)^2/g= (6.28)^2/9.8= about 4 meters.

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