Physics Olympiad - 2 Blocks Connected by a Rope Through a Horizontal Pulley Problem

In the system below there is friction between mass m1 and mass m2. There is also friction between mass m2 and the floor. The coefficient of friction (static is considered the same as kinetic) of both surfaces is the same, namely μ. The pulley is massless and the rope cannot stretch.
a) Draw a diagram of the forces on object 1 and object 2?
b) Write the equation of motion of object 1 and object 2?
c) How much external force F is needed so that the system can move at a constant speed?

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