A uniform rope of length L and mass M rests on a table.

(a) If you lift one end of the rope upward with a constant speed, v, show that the rope's center of mass moves upward with constant acceleration.

(b) Next, suppose you hold the rope suspended in air, with its lower end just touching the table. If you now lower the rope with a constant speed, v, onto the table, is the acceleration of the rope's center of mass upward or downward? Explain your answer.

(c) Find the magnitude and direction of the acceleration of the rope's center of mass for the case described in part (b). Compare with part (a).