Question

In a large centrifuge used for training pilots and astronauts, a small chamber is fixed at the end of a rigid arm that rotates in a horizontal circle. A trainee riding in the chamber of a centrifuge rotating with a constant angular speed of 2.6 rad/s experiences a centripetal acceleration of 3.3 times the acceleration due to gravity. In a second training exercise, the centrifuge speeds up from rest with a constant angular acceleration. When the centrifuge reaches an angular speed of 2.6 rad/s, the trainee experiences a total acceleration equal to 4.8 times the acceleration due to gravity.
(a) How long is the arm of the centrifuge?
(b) What is the angular acceleration in the second training exercise?

Answer 1

Answer:

4.7889 m

7.14037 rad/s²

Explanation:

r = Radius

$\omega$ = Angular velocity = 2.6 rad/s

Centripetal acceleration = 3.3g = $3.3\times 9.81=32.373\ m/s^2$

$\alpha=r\omega^2=3.3g\\\Rightarrow r=\frac{3.3\times 9.81}{2.6^2}\\\Rightarrow r=4.7889\ m$

Length is the arm of the centrifuge is 4.7889 m

Acceleration felt by the trainee = 4.8g = $4.8\times 9.81=47.088\ m/s^2$

Angular acceleration

$\alpha r=\sqrt{47.088^2-32.373^2}\\\Rightarrow \alpha=\frac{34.19456}{4.7889}\\\Rightarrow \alpha=7.14037\ rad/s^2$

Angular acceleration acceleration of the second exercise is 7.14037 rad/s²