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

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 :

$a=\dfrac{v^2}{r}$

$v=\sqrt{ar}$

$v=\sqrt{7\times 9.8\times 5}$

v = 18.5 m/s

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

$T=\dfrac{2\pi r}{v}$

$T=\dfrac{2\pi \times 5}{18.5}$

T = 1.69 s

Let N is the number of revolutions. So,

$N=\dfrac{60}{1.69}=35.5\ rev/min$

So, the number of revolutions per minute is 35.5

(c) T = 1.69 seconds

Hence, this is the required solution.