Question

A future use of space stations may be to provide hospitals for severely burned persons. It is very painful for a badly burned person on Earth to lie in bed. In a space station, the effect of gravity can be reduced or even eliminated. How long should each rotation take for a doughnut-shaped hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal gravity of Earth? A) 91 min B) 8.7 min C) 4.6 min D) 1.5 min E) 0.011 min

Answer 1

1.5min

Step-by-step explanation:

To solve the problem it is necessary to take into account the concepts related to Period and Centripetal Acceleration.

By definition centripetal acceleration is given by

`a_c = (V^2)/(r)`

Where,

V = Tangencial velocity

r = radius

With our values we know that

`a_c = (V^2)/(r)`

`(V^2)/(r) = (1)/(10)g`

Therefore solving to find V, we have:

`V = \sqrt{(1)/(10)g*r}`

`V = \sqrt{(9.81*200)/(10)}`

`V = 14m/s`

For definition we know that the Time to complete are revolution is given by

`t = (Perimeter)/(Speed)`

`t = (2\pi R)/(V)`

`t = (2\pi * 200)/(14)`

`t = 1.5min`