Question

In: Physics

Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 30.0...

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 1.10 s . The astronaut is strapped into a seat 4.00 m from the axis.

Part A

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

Express your answer with the appropriate units.

Solutions

Expert Solution

Initial angular speed of the centrifuge = 1 = 0 rad/s (Starts from rest)

Top speed of the centrifuge is 1 rotation every 1.1 sec.

Final rotational speed of the centrifuge = N2 = 1/1.1 = 0.909 rev/s

Final angular speed of the centrifuge = 2

2 = 2N2

2 = 2(0.909)

2 = 5.711 rad/s

Angular acceleration of the centrifuge =

Time taken by the centrifuge to reach top speed = t = 30 sec

2 = 1 + t

5.711 = 0 + (30)

= 0.1903 rad/s2

Distance of the astronaut from the axis = R = 4 m

Tangential acceleration of the astronaut = a

a = R

a = (0.1903)(4)

a = 0.7612 m/s2

A) Astronaut's tangential acceleration during the first 30 sec = 0.7612 m/s2

genius_generous answered 2 hours ago
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