A block, a string and Newton's third law 
So this is a general force diagram of the system shown. My question is, according to the third law, if the block is exerting a force of magnitude mg on the thread in the down direction, then the thread should exert an equal and opposite reaction on the block. So, it should exert a force of mg in the upward direction, and nothing should move, as the block experiences equal and opposite forces by the thread and the earth. But this doesn't happen always in real life. Can you please help?
 A: nice question (I'm just being formal). Things are not as simple in real life, bwoy...
The reason the teacher did mg-T is because that there is a limit to which the string can hold. In real life , you obviously would not see a heavy object attached by a thin rope. That is because that "almost massless" rope does not have the tensile strength to hold the heavy object (mg>>T), where T is the maximum tension the string can hold. You already must have seen questions like "if a string can hold max. 30N then how much mass it can handle", etc. . Also, real life strings are bundles of fibre, which when get non uniformly distributed weight tend to break.
Also, by this, you might ask why things move with the third Motion. I know you
know it, but just to clarify, because it acts on different bodies, and since here
 such a huge force acts on the string , it breaks. If the string can withstand the force, the system is stable. You are simply just questioning the tensile strength of the string.
I know you Raje,please don't pounce to attack me with your comments all of a sudden, just read and understand what I just said (wrote?) and then react. If you want me to explain this you can always contact me.
