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If we consider a simple case like the following we can write the acceleration of the block as $(m2-m1)g/(m1+m2)$ considering that $m2$ is heavier than $m1$

enter image description here

It is possible if the pulley is frictionless and massless and the string too is fricionles and massless and also inextensible

But what if

  1. the string is not massless

  2. not frictionless

  3. string is not frictionless

  4. string is frictioless but the pulley has mass

etc Etc...... please help me applying my concepts.

edit: another doubt too arised Is it true that wherever the rope touchs an object it applies a force same as its tension? If yes then how is the following valid:

enter image description here

If no then how is $N = 2T$?

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All of the points you raise can be important when considering pulley systems in real life, but they are often ignored in basic dynamics problems in order to simplify the analysis of the system. For example:

  1. If the string has mass then the mass on each side of the pulley will depend on the length of string on that side of the pulley, so it is no longer constant. Also the tension in the string will vary along its length.
  2. If there is friction between the string and the pulley then the tension on the two sides of the pulley will be different. Also, the moment of inertia of the pulley must be considered if the system is starting from rest.
  3. If there is friction in the bearing of the pulley then the couple exerted by the string on the pulley must be sufficient to overcome this friction before the pulley can start to turn.

Once you are confident solving basic problems that involve ideal massless and frictionless pulleys and ideal massless and inextensible strings, then you can start to add in some of these "real life" factors.

In your second diagram, I assume $N$ is the weight of the pulley. The relation $T'=2T$ only holds if the pulley has a negligible mass i.e. if $N=0$. If the pulley has mass, then $N>0$ and $T' > 2T$.

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  • $\begingroup$ If the string has mass then the mass on each side of the pulley will depend on the length of string on that side of the pulley, so it is no longer constant. Also the tension in the string will vary along its length. If there is friction between the string and the pulley then the tension on the two sides of the pulley will be different. Also, the moment of inertia of the pulley must be considered ....... please can you give some examples. $\endgroup$ Mar 20 at 15:36
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    $\begingroup$ @chittaranjanrout There is an analysis of a real life pulley system with inertia and friction at en.wikipedia.org/wiki/…. $\endgroup$
    – gandalf61
    Mar 20 at 15:53

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