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I have heard many people tell me that the tensional force is bi-directional. Consider the following case where a (mass-less) rope is used to transmit tension.

The rope is being pulled (by hand) with a force of 5 newtons. Thus the mass (along with the rope) will have an acceleration of 5 ms^(-2). (Neglect friction)

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1) Considering a point P on the rope, have I represented the tensional force on the rope correctly?

2) By Newton's Third Law, if the rope is pulling on the block, the block must exert an equal and opposite force on the rope. So, shouldn't the body not have any motion? A similar question was asked here: With Newton's third law, why are things capable of moving?. According to the answer provided, it is the force of the muscles that is responsible for the resulting acceleration.

So then what force is transmitted across the rope? It has to be the force of the muscles and not any other force since the tension in the rope is 5 newtons. But if it is so, the force exerted by the block on the rope (reaction) should also be 5 newtons. This means that the object will have no motion! Am I misunderstanding something here?

Qmechanic
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Gokulakrishnan Shankar
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    The key point of the third law is that "action" and "reaction" are applied on different objects, so they do not cancel each other. – Gravitino Mar 24 '18 at 10:50
  • Here, the mass only feels a net force to the right. Imagine two different situation: if the rope is inelastic, substitute it by a rigid rod; if, on the contrary, it is elastic, change the rope by a long spring. Try to analyse these situations (as an exercise). – Gravitino Mar 24 '18 at 10:57
  • The force of the muscle is transmitted to the rope which results in the reaction force. So, the reaction force (which is also 5 newtons) is what keeps the rope taut but does not prevent the body from accelerating correct ? – Gokulakrishnan Shankar Mar 24 '18 at 11:42
  • But in https://physics.stackexchange.com/questions/45653/with-newtons-third-law-why-are-things-capable-of-moving, there is no reaction force for F (muscles). Why ? – Gokulakrishnan Shankar Mar 24 '18 at 11:47
  • First , at point P , the mass is being extended towards the right . In such cases, the string used is inextinsible . So the tension developed will resist the force applied to it ...that's why , while considering free body diagrams , the tension should be towards the left ... –  Mar 24 '18 at 11:56
  • Second , the ropes applied force be $action$ , while the blocks force be $reaction$ . For a body to be in equilibrium , two forces acting on it must be opposite to each other and they must act on the same body ... The action and reaction forces act on different bodies ... –  Mar 24 '18 at 11:58
  • When you applying Newton's second law to an object, you include only the forces that other bodies exert on your object, not the forces that your object exerts on other bodies. In the case of your mass, you include only the force that the rope exerts on the mass, not the force that the mass exerts on the rope. – Chet Miller Mar 24 '18 at 12:34
  • You can think of the block and the rope as a single rigid body with total mass 1 kg. – Alchimista Mar 24 '18 at 12:48
  • @GokulakrishnanShankar ... Right , couldn't write it properly ... The answer by Farcher explains it neatly ... You just have to draw the case of all the three things and point out forces working on them ... Hope , you understood the equilibrium condition too ... –  Mar 24 '18 at 14:31
  • @Ultra Instincts 'Inextensible' means unable to be stretched, correct? But for the rope to have tension it should be stretched both ways, is it not so? Then why is it that while considering free body diagrams , the tension should be towards the left ? – Gokulakrishnan Shankar Mar 24 '18 at 14:32

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There are three parts to the situation you are considering:
Yourself Rope
Block

You exert a force of 5 N on the rope to the right and by Newton’s third law the rope exerts a force of 5 newton on you to the left.

The rope exerts a force of 5 N on the block to the right and by Newton’s third law the block exerts a force of 5 N on the rope to the left.

The end result is that

  • the block has on it a net force of 5 N to the right and it will accelerate to the right.
  • there is a net force of 5 N to the left on you. If you were not anchored to the ground this force would cause you to accelerate to the left.
  • the rope has a net force of zero on it which is a consequence of the assumption that the rope is massless. You can think of the rope as transferring forces between you and the block and there is no reason why the rope cannot move.
Farcher
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  • Neatly written ... –  Mar 24 '18 at 14:34
  • @Farcher "the rope has a net force of zero on it which is a consequence of the assumption that the rope is massless." Even if the rope did have mass, wouldn't the 5 N force exerted by me on the rope and the 5 N force exerted by the block on the rope cancel out so that the net force on the rope is zero ? – Gokulakrishnan Shankar Mar 24 '18 at 15:34
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    @GokulakrishnanShankar If the rope had mass and the forces at each end of the rope were of equal magnitude and opposite in direction then the rope could not accelerate. If the rope had mass then to make the rope accelerate there must be a net force on the rope which might be provided by you pulling on the rope with a force of 5 N and the block pulling on the rope with a force of 3 N resulting in a net force of 2 N on the rope. In such a case the force on the block due to the rope would be 3 N. – Farcher Mar 24 '18 at 16:25
  • In other words, out of the 5 newtons of the force applied by me, 2 goes into pulling the rope and 3 into pulling the block, correct? Just one more question: these 3 newtons and 2 newtons are just random numbers, right? Are they just for me to understand ? – Gokulakrishnan Shankar Mar 24 '18 at 16:36
  • @GokulakrishnanShankar Correct, I plucked those numbers out of thin air. – Farcher Mar 24 '18 at 17:12