Question

After a space station is constructed, it is spun up from rest, using rockets attached tangentially to the outside hull, in order to simulate earth gravity for the occupants inside, shown in the figure. We can model the station as a hoop that rotates around its axis, and ignore the rest of the structure for the moment of inertia.

The mass of the station is m = 50,000 kg, the outer radius is r = 100 m.

a) The two rockets attached to the outside of the station are each capable of exerting a force of 125 N. If they are both used, what is the angular acceleration of the station? Answer in ?rad/s² (1 ?rad = 10^-6 rad).

b) If the station starts at rest, how long does it take, in seconds, until it has the angular velocity needed such that the centripetal acceleration is a_c = 9.8 m/s², to simulate earth gravity?

c) How much work did the two rockets do together on the station, in Joules, to make it spin at this rate?

Answer 1

@ ! - . 18 (6 9를 joo 100 Torque - Fotfr Ix=afr x= aff af 2x 125 Mrz roooo x100 +6 x=50 Motoradi = 50 Mosad/s² a c=ow? 9.8 m/s 9.8 29= / que -0.313 from Wp = Clotar ta 0.313-0 50x106 t= 6260.99 sec work done ws change in rotational Kinetic Energy Iw=Ž I w? = 1/2 x 50000 (1008 x 9.8 w= 24.50106 J We-Wi x 100 6