An astronaut is rotated in a horizontal centrifuge at a radius of 5.0 m. a) What

Question

An astronaut is rotated in a horizontal centrifuge at a radius of 5.0 m. a) What is her speed if the centripetal acceleration has a magnitude of 7.0 g? b) How many revolutions per minute are required to produce this acceleration?
An astronaut is rotated in a horizontal centrifuge at a radius of 5.0 m. a) What is her speed if the centripetal acceleration has a magnitude of 7.0 g? b) How many revolutions per minute are required to produce this acceleration?
An astronaut is rotated in a horizontal centrifuge at a radius of 5.0 m. a) What is her speed if the centripetal acceleration has a magnitude of 7.0 g? b) How many revolutions per minute are required to produce this acceleration?

Explanation / Answer

a) radius, r = 5m

acceleration a =7g = 7 x 9.81 = v2/r where v is velocity and r is radius

v2 = 7 x 9.81 x 5 = 343.5

v = 18.533 m/s

hence the speed is 18.533 m/s

b. circumference of circle of rotation = 2*pi*r = 2*3.14*5 = 31.416m

in 1 rotation the distance covered is 31.416

so number of rotations = 18.533/31.416 = 0.59 revelutions per second

= 0.59 *60 rotations per minute

= 35.4 rotations per minute to produce the acceleration

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