# Dealing with pulleys and strings with mass [closed]

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$^2$.
Indeed, you're correct! The acceleration experienced by the system is determined by the total mass of the system and the applied force. Considering the masses involved (the man, the beam, and the rope), the total mass of the system is $$4 + 2 + 6 = 12 \,\text{kg}$$. With an applied force resulting in an acceleration of $$5 \,\text{m}/\text{s}^2$$, we can conclude that there must be a net force of $$10 \,\text{N}$$ acting on the rope. Consequently, the tension on the right side of the rope must be $$10 \,\text{N}$$ greater than the tension on the left side. In essence, the tension varies linearly along the rope, considering it as a series of masses connected by massless strings of negligible length. This clarifies how the tension is distributed throughout the rope in maintaining equilibrium.