A steel pipe of 72-mm diameter is to be used to transmit a torque of 2500 N. m. without exceeding an allowable shearing stress of 55 MPa. A series of 72-mm-outer-diameter pipes is available for use. Knowing that the wall thickness of the available pipes varies from 4 mm to 10 mm in 2-mm increments, choose the lightest pipe that can be used.

Wo small variable-thrust jets are actuated to keep the spacecraft angular velocity about the z-axis constant at ? 0 = 1.16 rad/s as the two telescoping booms are extended from r1 = 1.18 m to r2 = 4.69 m at a constant rate over a period of 124 seconds. the small 19-kg experiment modules at the ends of the booms may be treated as particles, and the mass of the rigid booms is negligible. determine the necessary thrust t for each jet as a function of time where t = 0 is the time when the telescoping action is begun. after you have the general expression for t, answer the questions. show work.