Question

4. An astronaut rotates at the end of a test machine whose arms has a length of 10.0m, as shown in the diagram. The acceleration he experiences must not exceed 51 (take g = 10ms-2). Determine the maxi- mum number of revolutions per minute of the arm yecl 2.24S

Answer 1

As Astronaut on test machine is rotating in circular path, he must be experiencing centripetal acceleration,

Given as, a = v^2 / r ------(1)

   In question it is given radius,r = 10.0 m and acceleration not to exceed 5*g = 5*10 = 50 m/s^2

From equation 1 we have,

50 = v^2 / 10.0

or,v = (500)^0.5

Therefore, v = 22.3607 m/s

Now angular velocity ,w = v/r = 22.3607 / 10 = 2.24 rad/s.

Also w = (2 *pi * N )/60

or, 2.24 * 60 = 2*pi*N

therefore, N = 21.39 = 22 rpm(approx). [Answer]