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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

Sagot :

Answer:

w = 1,662 rad / s,    v = 33.25 m / s

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 = [tex]\sqrt{ \frac{5.64 \ 9.8}{20.0} }[/tex]

         w = 1,662 rad / s

linear velocity is

        v = w r

        v = 1,662 20

         v = 33.25 m / s

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