Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The

Question

Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 30.0 s to speed up from rest to its top speed of 1 rotation every 1.40 s. The astronaut is strapped into a seat 5.60 m from the axis.

a) What is the astronaut's tangential acceleration during the first 30.0 s ?

b) How many g's of acceleration does the astronaut experience when the device is rotating at top speed? Each 9.80 m/s2 of acceleration is 1 g.

Thanks!

a) What is the astronaut's tangential acceleration during the first 30.0 s ?

b) How many g's of acceleration does the astronaut experience when the device is rotating at top speed? Each 9.80 m/s2 of acceleration is 1 g.

Thanks!

Explanation / Answer

Angular velocity at the end of 30 second is:- omega = [2pi / 1.4] = 4.49 radian /s

Linear velocity at the end of 30 second is r*omega = 5.6 x 4.49 = 25.144 m/s
So,
a:- Tangential acceleration = change in velocity / time = 25.144 / 30 = 0.838 m/s^2.

b:- The centripetal acceleration is r ^2 = r * = 25.144* 4.49 = 112.896 m/s^2
So, in terms of g, it is:-
centripetal acceleration = 112.896/ 9.8 = 11.52g force.

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