Trouble with the concept of tension....

In summary: If there is an unbalanced force on the rope, then the tension will vary slightly along the length of the rope depending on its mass. If we assume the mass of the rope is small compared to the forces involved, then the tension is still approximately constant.
  • #1
Achintya
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Homework Statement
Two persons A & B are pulling the two ends of a rope (As people do in tug war).Person A pulls rope with a force=10N and the person B is pulling another end of the rope with a force =20N. According to Newton's 3rd, rope will also pull person A with force=10N and B with a force=20N. It means tension at one end of the rope is 10N and at the other end tension is 20N(Because of the definition of tension).Is it correct? If yes ,then pulling force on A by the rope will only depend on force exerted by A on rope and will not depend upon the force applied by B on the rope. In that case , if B is pulling the rope with a force=1000N and A is pulling the other end of rope with a force=10N, then the tension at that end(where A is applying force) will be only 10N.It means the force by which rope is pulling A will be only 10N. Is it possible?
Relevant Equations
Newton's laws and fundamental of mechanics
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  • #2
This is very confused. There can only be one tension along the rope between the two people. If there is an unbalanced force on the rope, then the rope will accelerate (in which case the tension will vary slightly along the length of the rope depending on its mass). If we assume the mass of the rope is small compared to the forces involved, then the tension is still approximately constant.

In a tug of war, the two people are also pushing on the ground.
 
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  • #3
PeroK said:
This is very confused. There can only be one tension along the rope between the two people. If there is an unbalanced force on the rope, then the rope will accelerate (in which case the tension will vary slightly along the length of the rope depending on its mass). If we assume the mass of the rope is small compared to the forces involved, then the tension is still approximately constant.

In a tug of war, the two people are also pushing on the ground.
even if the rope is light(but not completely massless), then what forces will A experience...will it be just the Newton's 3rd law reaction pair force of his own force or the force exerted by B from the other side...pleasez it will be really helpful if you could explain with help of an example and on the basis of Newtonic mechanics...
i would really appreciate the help!
 
  • #4
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  • #5
A will experience the reaction force + the force applied by B (in the direction opposite to which A pulls)
 
  • #6
Achintya said:
even if the rope is light(but not completely massless), then what forces will A experience...will it be just the Newton's 3rd law reaction pair force of his own force or the force exerted by B from the other side...pleasez it will be really helpful if you could explain with help of an example and on the basis of Newtonic mechanics...
i would really appreciate the help!
The simplest way to think about it is that there is a tension ##T## in the rope. And both people are pulling and being pulled with the same force ##T##. For an idealised, massless rope there can be no unbalanced force. The forces at either end must be the same.

The difference in a tug-of-war comes from the forces exerted on the ground.

Alternatively, analyse a tug-of-war in space.
 
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  • #7
Adesh said:
A will experience the reaction force + the force applied by B (in the direction opposite to which A pulls)
then what will be the tension in the rope? Because we know that for a massive rope the tension won't be constant throughout the string rather it would be a function of the distance x from the end of the rope...by Newton's 3rd law if A pulls on the rope with 30 N , the rope will also pull A with 30 N ...so the tension of the rope segment connected to A will be 30N , then what about the force that B is exerting on the rope ...will it be of no significance to A?
 
  • #8
If the rope has no mass then then tension in the rope will be the same everywhere (regardless of its state of acceleration). The force exerted by the rope at each end will be T in the obvious directions. If the rope has mass then the tension will depend upon the acceleration of the system of rope + people and will vary according to mass distribution in the rope (linear in a uniform rope) .
PLEASE ask one particular question at a time...not an incoherent jumble.
 
  • #9
Achintya said:
then what will be the tension in the rope? Because we know that for a massive rope the tension won't be constant throughout the string rather it would be a function of the distance x from the end of the rope...by Newton's 3rd law if A pulls on the rope with 30 N , the rope will also pull A with 30 N ...so the tension of the rope segment connected to A will be 30N , then what about the force that B is exerting on the rope ...will it be of no significance to A?

The two ends of the rope cannot be pulled with different forces without the rope itself accelerating. And, if the rope is light, the difference in forces (tension) at each end will be small.

In an ideal analysis, you have ##T## constant throughout the rope.

If you add the mass of the rope, then you have ##T + am## at one end and ##T## at the other. The difference in tension along the rope is only ##am##, where ##a## is the acceleration of the rope/system and ##m## is the mass of the rope. In the idealised scenario, you neglect the ##am## term, as it is small.

Your scenario of an approximately static, light rope pulled by ##30N## at one end and ##20N## at the other is physically impossible. That isn't a valid free-body diagram for a stationary rope.
 
  • #10
Achintya said:
then what will be the tension in the rope? Because we know that for a massive rope the tension won't be constant throughout the string rather it would be a function of the distance x from the end of the rope...by Newton's 3rd law if A pulls on the rope with 30 N , the rope will also pull A with 30 N ...so the tension of the rope segment connected to A will be 30N , then what about the force that B is exerting on the rope ...will it be of no significance to A?
If the forces on the rope don’t cancel each other then the rope will accelerate. Tension exists in the static situation .
 
  • #11
Adesh said:
If the forces on the rope don’t cancel each other then the rope will accelerate. Tension exists in the static situation .
Let us be precise. Tension will exist for any (non-slack) rope. It will be uniform for a massive rope only if not accelerated.
 
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  • #12
PeroK said:
The two ends of the rope cannot be pulled with different forces without the rope itself accelerating. And, if the rope is light, the difference in forces (tension) at each end will be small.

In an ideal analysis, you have ##T## constant throughout the rope.

If you add the mass of the rope, then you have ##T + am## at one end and ##T## at the other. The difference in tension along the rope is only ##am##, where ##a## is the acceleration of the rope/system and ##m## is the mass of the rope. In the idealised scenario, you neglect the ##am## term, as it is small.

Your scenario of an approximately static, light rope pulled by ##30N## at one end and ##20N## at the other is physically impossible. That isn't a valid free-body diagram for a stationary rope.
But i never said that the rope is stationary...it is obvious that if there are unbalanced forces on a system then the system would accelerate according to Newton's 2nd law
 
  • #13
Adesh said:
If the forces on the rope don’t cancel each other then the rope will accelerate. Tension exists in the static situation .
so you mean once the system accelerates there will be no tension in the rope?
 
  • #14
Achintya said:
so you mean once the system accelerates there will be no tension in the rope?
Take a rope which is not attached to any thing, if you pull it then it will certainly going to move and the stretch in the rope will be due to molecular attraction/repulsion.
 
  • #15
Achintya said:
But i never said that the rope is stationary...it is obvious that if there are unbalanced forces on a system then the system would accelerate according to Newton's 2nd law

Okay, but what about the case where two people are anchored to the ground and one pulls the rope with ##30N## and the other pulls the rope with ##20N##?

That's impossible.

It's also invalid for a massless rope, since any unbalanced force would lead to an infinite acceleration of the rope.

It's also invalid for a light rope (##1kg##, say), unless the rope and the whole system is accelerating at ##10m/s^2##.

Fundamentally, you cannot have different forces pulling two ends of a rope without the rope accelerating under those forces. If there are other objects in the system stopping it from accelerating, then those cannot be the forces on the rope.
 
  • #16
hutchphd said:
Let us be precise. Tension will exist for any (non-slack) rope. It will be uniform for a massive rope only if not accelerated.
yes i have understood the fact that if system is in static equilibrium(0 acceleration), then tension would be constant throughout the string whether it be massless or massive...but what happens when the system accelerates like in my original question(20N and 30N forces are acting at each end of the string, making the system accelerate)...i hope i am clear.
 
  • #17
Achintya said:
yes i have understood the fact that if system is in static equilibrium(0 acceleration), then tension would be constant throughout the string whether it be massless or massive...but what happens when the system accelerates like in my original question(20N and 30N forces are acting at each end of the string, making the system accelerate)...i hope i am clear.
That's physically impossible.
 
  • #18
Adesh said:
Take a rope which is not attached to any thing, if you pull it then it will certainly going to move and the stretch in the rope will be due to molecular attraction/repulsion.
yes i could feel this
 
  • #19
PeroK said:
That's physically impossible.
it would be really helpful if you can explain me why is it physically impossible.
 
  • #20
Achintya said:
it would be really helpful if you can explain me why is it physically impossible.
Newton's second law: ##F = ma##.

The net force on the rope (tension at one end minus tension at the other) must equal the mass of the rope times its acceleration. In this case:

##F = T_2 - T_1 = ma \approx 0##
 
  • #21
Achintya said:
yes i could feel this
Consider this scenario:

We got a sponge, I push it from east and you push it from west with same force. Would the sponge going to be squeezed?
 
  • #22
Are the people in your original question rigidly attached to the earth? Are they holding the ends of a fixed length string? So they must also be accelerating. Please succinctly rephrase your question because it is inconsistent as stated.
 
  • #23
Adesh said:
Consider this scenario:

We got a sponge, I push it from east and you push it from west with same force. Would the sponge going to be squeezed?
I fail to see the relevance of this.
 
  • #24
PeroK said:
I fail to see the relevance of this.
I’m trying to explain to him with that sponge example because deformation in sponge is very intuitive. If we have unequal forces on sponge it will move with some net deformation in it.
 
  • #25
unless your rope stretches I don't see the relevance. Stick to original
 
  • #26
hutchphd said:
unless your rope stretches I don't see the relevance. Stick to original
Tension will be caused only when there is a stretch, in my opinion.
 
  • #27
Your opinion is incorrect. Tension implies nothing about stretch inherently. An "ideal" rope is absolutely inexstensible but still has tension. Not a contradiction. In practice all things stretch a little (although Carbon Fiber is remarkably resistant) but the approximation is fine. Rigid bodies aren't absolutely rigid either!
So restate your original question in a concise and precise way please, and it will be addressed..
 
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  • #28
hutchphd said:
Your opinion is incorrect. Tension implies nothing about stretch inherently.
It seems that you’re using this definition of tension :
The tension force is the force that is transmitted through a cable, rope, wire or string when it is pulled tight by forces acting from opposite ends. It is directed along the length of the cable and pulls equally on the objects on the opposite ends of the wire..

What I meant by the tension was the restoring force that the rubber band exerts when we pull (keeping one it’s ends fixed).
 
  • #29
The two are not mutually exclusive. You may use what you like but the rest of the world uses the more generic one you quote. If you wish to describe an elastic rope then you need to indicate that and characterize it as to details. Otherwise everyone will be confused as you have witnessed. Hopefully lesson learned!
 
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  • #30
hutchphd said:
The two are not mutually exclusive. You may use what you like but the rest of the world uses the more generic one you quote. If you wish to describe an elastic rope then you need to indicate that and characterize it as to details. Otherwise everyone will be confused as you have witnessed. Hopefully lesson learned!
Yes! I should use those things the way everyone uses it (if I’m posting it in public).
 
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  • #31
PeroK said:
Newton's second law: ##F = ma##.

The net force on the rope (tension at one end minus tension at the other) must equal the mass of the rope times its acceleration. In this case:

##F = T_2 - T_1 = ma \approx 0##
here you are considering massless string but i am asking you about massive string(m not equals 0)
 
  • #32
hutchphd said:
Are the people in your original question rigidly attached to the earth? Are they holding the ends of a fixed length string? So they must also be accelerating. Please succinctly rephrase your question because it is inconsistent as stated.
no they are not rigidly attached to the earth...they are simply standing on the Earth's surface and are free to accelerate.. yes they are holding the ends of the fixed length massive string and are applying forces of different magnitudes(20N and 30N in my case)...which would make the system accelerate with a net force of 10N...so i want to know the tension produced in the string in this case...it would be better if you could explain me what is exactly happening to the string at the molecular level with the help of Newton's laws
 
  • #33
Achintya said:
here you are considering massless string but i am asking you about massive string(m not equals 0)
Okay. Let's assume the rope has a mass of ##1kg## and is accelerating at ##1m/s##. Then:

##T_2 - T_1 = 1N \ne 10N##

You cannot have ##T_2 = 30N## and ##T_1 = 20N## unless the rope is accelerating at ##10m/s^2##. Assuming the mass of th e rope is ##1kg##.

If you focus on the rope, the forces on the rope (and only the forces on the rope) determine its acceleration. If you have a large unbalanced force on the rope it must be accelerating rapidly.

If the rope is attached to things that stop it accelerating, then that influences the tension. The tension at either end must balance if the rope is not accelerating.
 
  • #34
PeroK said:
Okay. Let's assume the rope has a mass of ##1kg## and is accelerating at ##1m/s##. Then:

##T_2 - T_1 = 1N \ne 10N##

You cannot have ##T_2 = 30N## and ##T_1 = 20N## unless the rope is accelerating at ##10m/s^2##. Assuming the mass of th e rope is ##1kg##.

If you focus on the rope, the forces on the rope (and only the forces on the rope) determine its acceleration. If you have a large unbalanced force on the rope it must be accelerating rapidly.

If the rope is attached to things that stop it accelerating, then that influences the tension. The tension at either end must balance if the rope is not accelerating.
but the net force on the rope is 10N..so why did you take it 1N.
 
  • #35
Achintya said:
but the net force on the rope is 10N..so why did you take it 1N.

It can't be. It's physically impossible, Which part of ##F = ma## don't you understand? The tension in the rope and its acceleration are governed by Newton's laws. You can have a difference of ##10N## but if you do a ##1kg## rope must accelerate at ##10m/s##. You can't have arbitrary tension at either end. Newton's laws forbid it.

If you tie a rope to a wall and pull, then whatever force you apply is equalled by the wall. You can't have an unbalanced force in that case, If you ask: how come the wall pulls back with the same force?, then you have Isaac Newton to thank for the answer: ##F = ma##. There is no acceleration, hence the force (and tension) at the wall equals the force you apply at the other end.

If you ask how does nature achieve this? Then, the answer is because she's clever!
 
<h2>What is tension?</h2><p>Tension is a force that is applied to an object in a way that causes it to stretch or elongate. It is a type of mechanical stress that can be found in various materials, such as ropes, cables, and springs.</p><h2>What are the different types of tension?</h2><p>There are three main types of tension: static, dynamic, and surface. Static tension is a constant force applied to an object, while dynamic tension is a force that changes over time. Surface tension is a force that is found on the surface of liquids, caused by the cohesive forces between molecules.</p><h2>What factors affect tension?</h2><p>The amount of tension in a material is affected by various factors, such as the material's elasticity, length, and cross-sectional area. Additionally, the force applied and the direction of the force can also impact tension.</p><h2>What are some real-world examples of tension?</h2><p>Tension can be found in many everyday objects and situations. Some common examples include a stretched rubber band, a guitar string, a suspension bridge, and even muscles in the human body.</p><h2>How is tension measured?</h2><p>Tension is typically measured in units of force, such as newtons or pounds. It can also be measured indirectly by measuring the amount of deformation or elongation in the material under tension. In some cases, specialized equipment such as tension gauges may be used to measure tension more accurately.</p>

What is tension?

Tension is a force that is applied to an object in a way that causes it to stretch or elongate. It is a type of mechanical stress that can be found in various materials, such as ropes, cables, and springs.

What are the different types of tension?

There are three main types of tension: static, dynamic, and surface. Static tension is a constant force applied to an object, while dynamic tension is a force that changes over time. Surface tension is a force that is found on the surface of liquids, caused by the cohesive forces between molecules.

What factors affect tension?

The amount of tension in a material is affected by various factors, such as the material's elasticity, length, and cross-sectional area. Additionally, the force applied and the direction of the force can also impact tension.

What are some real-world examples of tension?

Tension can be found in many everyday objects and situations. Some common examples include a stretched rubber band, a guitar string, a suspension bridge, and even muscles in the human body.

How is tension measured?

Tension is typically measured in units of force, such as newtons or pounds. It can also be measured indirectly by measuring the amount of deformation or elongation in the material under tension. In some cases, specialized equipment such as tension gauges may be used to measure tension more accurately.

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