Question

Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 40.0 ss to speed up from rest to its top speed of 1 rotation every 1.30 ss . The astronaut is strapped into a seat 5.90 mm 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

speed = 0.9 mm/s

Step-by-step explanation:

time, t = 40 s

initial angular speed, wo = 0 rad/s

final frequency, f = 1/1.03 rps = 0.97 rps

final angular speed, w = 2 x 3.14 x 0.97 = 6.1 rad/s

time, t = 40 s

distance, r = 5.9 mm

The angular acceleration is given y the first equation of motion.

`w =wo + \alpha t\\6.1 = 0 +\alpha * 40\\\alpha = 0.1525 rad/s^(2)`

The linear velocity is

`v =5.9* 10^(-3)* 0.1525 = 9* 10^(-4) m/s`

speed, v = 0.9 mm/s