# Analyzing pulleys via Newton's Laws of Motion

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 $$m1$$

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

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:

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

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 $$T' > 2T$$.