Circular Motion Question-Not Given Weight/Mass?

Question

A device for training astronauts is designed to rotate the trainee in a horizontal circle of radius 11.5 m. If the force felt by the trainee is 7.18 times her own weight, how fast is she rotating in m/s?

Now express your answer in revolutions per second.

How would you solve this when not given her weight or mass?

Answer 1

The answer hippoterr... gave you was OK till the last step. It's always is wise to check the units and see if they make sense. His result is in sec/rev.

2 x Pi x11.5 / 30 = 2.4 He left out the units in the math part, but if you include them you see that the result is in sec/rev.

Unit conversion can be confusing. A better way - you know you want it to be something per sec so start with:

30 meter/sec. Then to convert to rev/sec multiply by 1, in a special form.

In the form 1 rev/(2 x Pi x11.5 meters). This = 1, right? The top and bottom are equivalent. So back to

30 meter/sec * 1 rev/(2 x Pi x11.5 meters) = .415 rev/sec

You understand why weight/mass wasn't needed? It's the acceleration that results from the rotation, and a = F/m.

Answer 2

1

Answer 3

Centripetal acceleration a = v x v / r

a must be 7.81 times that of earth to give a weight as stated

so:

9.81 x 7.81 = v x v / 11.5

V = Sq Rt (9.81 x 7.81 x 11.5) = 30 m/s

In revs per sec:

2 x Pi x11.5 / 30 = 2.4 revs per sec