Question

The National Aeronautics and Space Administration (NASA) studies the physiological effects of large accelerations on astronauts. Some of these studies use a machine known as a centrifuge. This machine consists of a long arm, to one end of which is attached a chamber in which the astronaut sits. The other end of the arm is connected to an axis about which the arm and chamber can be rotated. The astronaut moves on a circular path, much like a model airplane flying in a circle on a guideline. The chamber is located 20.0 m from the center of the circle. At what speed must the chamber move so that an astronaut is subjected to 5.64 times the acceleration due to gravity

Answer 1

w = 1,662 rad / s, v = 33.25 m / s

Step-by-step explanation:

This this exercise indicates that the acceleration felt by the astronauts is

a = 5.64 g

in a circular motion the centripetal acceleration is

a_c = v²/ r

angular and linear variables are related

v = w r

we substitute

a_c = w² r

we finally have

5.64 g = w² r

w² = 5.64 g / r

let's calculate

w =
`\sqrt{ (5.64 \ 9.8)/(20.0) }`

w = 1,662 rad / s

linear velocity is

v = w r

v = 1,662 20

v = 33.25 m / s