2. (30pts) Consider the following system. Motion occurs under the influence of gravity. k' 1277 7\\ J 77/ The uniform bar is of mass m and length [. Initially it is vertical and static. A variable force F is applied pgje_&'j_[, the contact point of the bar with the ground. Point P remains in contact with the ground as it slides with a coefficient of friction u. An arbitrary configuration is shown in the figure above where P is at a distance x from a fixed-point O and the bar is making an angle 8 with the vertical. (The moment of inertia of a uniform bar about its center is %mi*} a) (6pts) Sketch a free-body-diagram of the bar showing all applied forces clearly. b) (10pts) Derive the equations of motion of the bar using the Newtonian approach, i.e. derive the 2 translational equations of motion and one rotational equation of motion. c) (4pts) Suppose the force F is applied such that the bar has a constant angular velocity, i.e. 0 = w,. Derive an expression of such a force F in termsof m, [, g, u, 6, and w,,. d) (3pts) Derive a condition that ensures that P remains in contact with the ground as the bar falls with constant angular velocity wg. e) (4pts) What initial acceleration is produced as the bar falls with the constant angular velocity wg? f) (3pts) Determine the impulse F required to produce the constant angular velocity w, at the initial time