The figure below shows forces acting at various points on a metal cylinder. The angles a = 50, B = 29, y = 15. The length l = 3.8 m. Find the net torque (in N m) on the cylinder about the following axes. 30 N 25 N Ty 10 N (a) an axis through O perpendicular to the page magnitude direction out of the page N-m (b) an axis through C perpendicular to the page magnitude direction out of the page N.m You have a summer internship at NASA and are working on plans for a new space station to be launched into orbit around the Earth. The design of the space station is shown. It is to be constructed in the shape of a hollow ring of mass 41,000 kg. The structures other than the ring shown in the figure have negligible mass compared to the ring. Members of the crew will walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 140 m. The thickness of the ring is very small compared to the radius, so we can model the ring as a hoop. At rest when constructed, the ring is to be set rotating about its axis so that the people standing inside on this deck experience an effective free-fall acceleration equal to g. The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. Your supervisor asks you to determine the following: (a) the time interval during which the rockets must be fired if each exerts a thrust of 120 N and (b) the period of rotation of the space station after it has reached its target rotation. (a) Determine the time interval (in hr) during which the rockets must be fired if each exerts a thrust of 120 N. hr (b) Determine the period of rotation of the space station (in s) after it has reached its target rotation. S