# Dealing with pulleys and strings with mass

So far, Ive been solving problems where the pulleys and strings were assumed to be massless. But how to write free body diagrams for a string/pulley with mass? This was the question I was trying to solve:

Two blocks of masses 6 kg and 4 kg connected by a rope of mass 2 kg are resting on a frictionless floor as shown in the following figure. If a constant force of 60 N is applied to 6 kg block, the acceleration of the system is: I can draw the fbd for the two blocks. For the string what is feel is since the tension at any point on the string is same net force in horizontal direction is 0. But the string must be moving with som acceleration. Please correct me if im going wrong anywhere.

EDIT 1: Ok i realised that i was doing a few silly mistakes and i rectified them. Is this correct? You are right - the string will be accelerating with the same acceleration as the rest of the system, so the total system has a mass of 4+2+6 = 12 kg, and the acceleration is 5 m/s$^2$.