In the question above, what I don't understand is how to calculate the tension in the second case (case in which the pulley is there). I realized after reading some questions, that the arrangement in question is an Atwood machine. While I can do this question by using the formulae, I do not understand how to obtain the formulae.
Wikipedia states that (http://en.wikipedia.org/wiki/Atwood_machine#Equation_for_constant_acceleration) when T is the tension and m1 and m2 are the masses in the Atwood machine, such that m1 > m2, i.e." Forces affecting m1 = m1g - T = m1a and forces affecting m2 = T - m2g = m2a
I do not understand how we got this, and this is probably because I don't understand how the tension divides in such a case. Please help me by explaining what pulls what which leads to which equation and how these equations (from Wikipedia) are true.
EDIT: To me, I imagine this question as if the tension is exerted by the midpoint of the string of the pulley and the tension exerted for each side = Mg N. which makes the total 2Mg N tension, leading to 2l elongation. But pulleys are supposed to make life easier, and my calculation does not show anything like that. Please clarify.
EDIT 2: OK, I try to comprehend what Wikipedia says. So the first question: How can the tension be UPWARDS at BOTH sides of the pulley? By the definition of tension, it seems fine, but how does this work in the real world at the midpoint of the pulley string? The tensions are coming in opposite directions, so if they are equal, tension at midpoint = 0?