An aluminum (E = 10 x 106 lb/in2, ν = 0.333) bar of length (L = 49 inch) has a circular cross-section of radius (r = 0.7 inch). The beam is fixed at one end. A torque (T = 1,666 lb-in) is applied to the free end. Calculate the twist of the bar free-end. (Units: degree)

Ablock having mass m slides down an inclined plane. the force of friction between the block and the inclined plane is f, the block's weight is m g, and the normal force is n. (a) draw a free – body force diagram showing the forces acting on the block. (b) write down all relevant newton’s equations for a given situation.