According to my book, "tension is the reaction of a rope when it is stressed". Then it also said when the string is massless, tension is same everywhere. However in a,let, pulley-rope system,when there is friction between the pulley & the rope, the tensions are not same. Why the tension is not same in this case? Does tension arise due to Newton's third law? When a block is attached to the rope ,the rope gets streched and can I say tension then arises due to Newton's third law or only to undo the deformation? If Newton's 3rd law is cause, then how can there be different tensions in a same rope? Plz explain.
[Physics] How does friction and mass of the string influence the tension force
forcesfree-body-diagramnewtonian-mechanicsstring
Related Solutions
It is always best to draw a diagram to convince yourself of things in a case like this.
This is intended to represent a steady state situation: nobody is moving / winning. As you can see, there are two horizontal forces on A: the floor (pushing with 100N) and the rope (pulling with 100N). There will be two vertical forces (gravity pulling down on center of mass, and ground pulling up) to balance the torques - I did not show them because they are not relevant to the answer.
Now I drew a dotted line between A and B. Consider this a curtain. A cannot see whether the rope is attached to B (an opponent) or a wall. A can measure the tension in the rope by looking (for instance) at the speed at which a wave travels along the rope - or by including a spring gage.
Now ask yourself this question: if A feels a tension of 100N in the rope (this is the definition of the force on A), and can confirm (by looking at the gage) that the tension is 100 N, but he cannot see whether the rope is attached to a ring or to an opponent, then how can the tension be 200N? If I pull on a gage with a force of 100N, it will read 100N - it cannot read anything else (in a static situation, and where the gage is massless, ... )
I think I understand the source of your confusion based on the earlier q/a that you referenced - so let me draw another diagram:
In this diagram, I have move the point of attachment of the rope with which A pulls B away from B's hands, to his waist. Similarly, the rope with which B pulls on A is moved to A's waist.
What happens? Now there are two distinct points where A experiences a force of 100 N: one, his hands (where he is pulling on the rope attached to B's waits); and another where the rope that B is pulling on is tied around his waist.
The results is that there are two ropes with a tension of 100N each, that together result in a force of 200N on A (two ropes) offset by a force of 200N from the floor, etc.
This is NOT the same thing as the first diagram, where the point on which B's rope is attached is the hands of A - there is only a single line connecting A and B with a tension of 100 N in that case.
As was pointed out in comments, you can put a spring gauge in series with your rope to measure the tension in it; and now the difference between "a single person pulling on a rope attached to a ring at the wall (taken to be the dotted line) and two people pulling across a curtain (so they cannot see what they are doing) is that in one case, a single spring (with spring constant $k$) expands by a length $l$, while in the second case you find a spring that's twice as long, with constant $k/2$), expanding by $2l$.
These are all different ways to look at the same thing.
Your question has nothing to do with Newton's third law.
You are having trouble identifying forces. That's not unusual. It takes some time and practice. A good book would help. Evidently your book is not very good at all, because the sentence you quote is practically unintelligible. Please don't waste your energy trying to make sense of it.
Wikipedia has fairly good statements of Newton's laws, although I think the statement of the second law, while correct, could be even better.
First you have to define your system. You have implicitly chosen your system to be the rope. Then you have to find the forces on the system. In Newtonian mechanics, a force is either a non-contact force (gravity, electrostatic, magnetic) or a contact force (everything else: normal forces, tension, the push of your finger, friction...).
In your question, we are implicitly neglecting all of the non-contact forces. That makes things a little easier. We are looking for contact forces. These only occur when the system is in contact with something it its environment. Here, they occur where the forces are applied to the rope, say, by your hand pulling on it. So there are two forces on the rope, one on each end.
A force that is a "pull" is usually called a tension force. So you have two tension forces, and they happen to be applied in opposite directions. Now, the rope is at rest, is it not? It's acceleration is zero. Newton's second law tells us that the net force, the algebraic sum of the two forces, is zero. Thus, the forces must be of equal magnitude and opposite direction. This has nothing to do with Newton's third law, although it shares some of the words used in the statement of Newton's third law.
Note that if the rope were accelerating, then the two tension forces would be in opposite directions, but unequal magnitude.
So here's what we have: two forces on the rope. Each one is applying a tension force on the rope. Those two forces are equal in magnitude, and opposite in sense (direction).
The only introductory book that I've seen that spells all of this out clearly is out of print.
Best Answer
Say you have a weight tied to each side a a rope which is strung over a pulley with friction. Here's a really easy way to see why the tensions on each side of the rope can't be equal.
Imagine a really stiff pulley - in other words, ${\bf F}_\text{friction}$ is high. If that's the case, it'll be possible to balance unequal loads on this pulley system - i.e. a heavy weight on the right side and a lighter weight on th left - without the system moving. If the weights don't move, then we can say that the forces acting on each weight add up to zero:
For the heavy weight, there's the weight downward, ${\bf w}_\text{heavy}$ and there's the tension of the right side of the rope upward, ${\bf T}_\text{right}$. The tension pulls up and the weight down, and the system doesn't move, so
$$ {\bf T}_\text{right} - {\bf w}_\text{heavy} = 0 $$
or
$$ {\bf T}_\text{right} = {\bf w}_\text{heavy} $$
Similarly for the left (light) side,
$$ {\bf T}_\text{left} - {\bf w}_\text{light} = 0 \quad \Rightarrow \quad{\bf T}_\text{left} = {\bf w}_\text{light} $$
As you can see, the tension on the right, ${\bf T}_\text{right}$ is equal in magnitude to the heavy weight, while the tension on the left, ${\bf T}_\text{left}$ is equal to that of the lighter weight. The friction is introducing an extra force which changes the tensions on each side.
As far as your question about rope stretching goes, if you anchor a rope on one side and pull, the rope will pull back, creating a tension. This is indeed because of stretching in the rope. This is not really what Newton's 3rd law is referring to. Newton's third law, in this case, tells us that the force that we feel from the rope, tension, is exactly the force the rope feels from us pulling. The two are equal and opposite. You can change the tension by changing the stiffness of the rope, but whatever the tension, Newton's 3rd law will still be true - the rope will feel us pulling it as much as we feel it pulling us.