How Fast Must an Astronaut Spin for 2.89g Acceleration?

[africanmasks]

Homework Statement

As their booster rockets separate, Space Shuttle astronauts typically feel accelerations up to 3g, where g = 9.80 m/s2. In their training, astronauts ride in a device where they experience such an acceleration as a centripetal acceleration. Specifically, the astronaut is fastened securely at the end of a mechanical arm that then turns at constant speed in a horizontal circle. Determine the rotation rate, in revolutions per second, required to give an astronaut a centripetal acceleration of 2.89g while in circular motion with radius 9.46 m.

Homework Equations

radial(centripetal) acceleration= v^(2) / r

v= 2(pi)(r) / T

The Attempt at a Solution

radial acc.= (9.8)(2.89)= 28.322 m/s^(s)

28.322 m/s^(2) = v^(2) / 9.46m

v= 16.368

T= 2(pi)(9.46m) / (16.368) = 3.631

Is that right?

 

[rock.freak667]

The Attempt at a Solution

radial acc.= (9.8)(2.89)= 28.322 m/s^(s)

28.322 m/s^(2) = v^(2) / 9.46m

v= 16.368

T= 2(pi)(9.46m) / (16.368) = 3.631

Is that right?

you want to find the angular velocity ω. So use v=rω and find ω.

Alternatively you could have used another expression for centripetal acceleration

a=ω²r

 

[tomcue]

I can confirm that your solution is correct. The rotation rate required to give an astronaut a centripetal acceleration of 2.89g while in circular motion with radius 9.46 m is 3.631 revolutions per second. Your use of the equations for centripetal acceleration and velocity were correct, and you arrived at the correct answer. Great job!