Question

Astronauts are put into a centrifuge in order to test their reactions to accelerations much greater than gravity. A particular test involves an acceleration of 3 g’s (so three times gravity) at a speed of 17 m/s.

A) What is the radius of the centrifuge?
B) How much time does it take the astronaut to complete one revolution?

Answer 1

The radius of the centrifuge is approximately 9.88 meters, and it takes approximately 3.68 seconds for the astronaut to complete one revolution.

Step-by-step explanation:

To find the radius of the centrifuge, we can use the formula for centripetal acceleration: a = v^2 / r. In this case, the centripetal acceleration is 3 times the acceleration due to gravity, so we have 3g = v^2 / r. We also know that the speed is 17 m/s, so we can substitute this value into the equation to get: 3g = (17 m/s)^2 / r. Solving for r, we find that the radius of the centrifuge is approximately 9.88 meters.

To calculate the time it takes for the astronaut to complete one revolution, we can use the formula for period: T = 2πr / v. Plugging in the values we know, we get: T = 2π(9.88 m) / (17 m/s). Simplifying the equation gives us a period of approximately 3.68 seconds.