Two blocks in figure are connected by a heavy uniform rope

Question

1. Two blocks in figure are connected by a heavy uniform rope with a mass of 4.00 kg. An upward force of 200 N is applied as shown.

(a) Draw three free-body diagrams: one for the 6.00-kg block, one for the 4.00-kg rope, and another one for the 5.00-kg block. For each force, indicate what body exerts that force.

(b) What is the acceleration of the system?

(c) What is the tension at the top of the heavy rope?

(d) What is the tension at the midpoint of the rope?

2. An object of mass m is at rest in equilibrium at the origin. AT t = 0 a new force F^→(t) is applied that has components F_x(t) = k₁ + k₂y , F_y(t) = k₃t ,  where k1, k2 and k3 are constant. Calculate the position r^→(t) and velocity v^→(t) vectors as function of time.