Question

An astronaut is rotated in a horizontal centrifuge at a radius of 5.0 m. (a) What is the astronaut’s speed if the centripetal acceleration has a magnitude of 7.0g? (b) How many revolutions per minute are required to produce this acceleration? (c) What is the period of the motion?

Answer 1

Step-by-step explanation:

Given that,

Radius of circular path, r = 5 m

Centripetal acceleration,
`a=7g\ m/s^2`

(a) Let v is the astronaut’s speed. The formula for the centripetal acceleration is given by :

`a=(v^2)/(r)`

`v=√(ar)`

`v=√(7* 9.8* 5)`

v = 18.5 m/s

(b) Let T denotes the time period. It is given by :

`T=(2\pi r)/(v)`

`T=(2\pi * 5)/(18.5)`

T = 1.69 s

Let N is the number of revolutions. So,

`N=(60)/(1.69)=35.5\ rev/min`

So, the number of revolutions per minute is 35.5

(c) T = 1.69 seconds

Hence, this is the required solution.