Question

Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 40.0 s to speed up from rest to its top speed of 1 rotation every 1.20 s. The astronaut is strapped into a seat 4.00 m from the axis.

What is the astronaut's tangential acceleration during the first 40.0 s?

How many g's of acceleration does the astronaut experience when the device is rotating at top speed? Each 9.80 m/s^2 of acceleration is 1 g.

Answer 1

Step-by-step explanation:

Given that,

Initial speed, u = 0

No of rotation is 1 in every 1.2 s

The astronaut is strapped into a seat 4.00 m from the axis, r = 4 m

(a) Let
`\alpha` is the angular acceleration during the first 40 s. It is given by :

`\alpha =(\omega)/(t)`

`\omega=(2\pi r)/(t)`

`\omega=(2\pi )/(1.1)`

`\omega=5.71\ rad/s`

`\alpha =(5.71)/(40)`

`\alpha =0.142\ rad/s^2`

Tangential acceleration is given by :

`a=r* \alpha`

`a=4* 0.142`

`a=0.568\ m/s^2`

(b) Let a is the centripetal acceleration. It is given by :

`a=\omega^2r`

`a=5.71^2* 4`

`a=130.41\ m/s^2`

Since,
`g=9.8\ m/s^2`

`a=13.3\ g`

Hence, this is the required solution.