Massless string pulled by a force

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    Force Massless String
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Discussion Overview

The discussion revolves around the concept of tension in a massless string when subjected to a pulling force from one or both ends. Participants explore the implications of tension, the conditions under which it arises, and the effects of mass on the behavior of the string.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants question whether a massless string can have tension when pulled from one end and seek to derive the conditions for tension to exist.
  • Others assert that tension arises when a force is applied, suggesting that the force on one end must be transmitted through the string.
  • There is a discussion about the definition of tension, with some arguing it is the force exerted by one part of the string on another.
  • Participants explore the implications of Newton's second law, suggesting that if tension did not exist, the string would accelerate.
  • Some participants propose that tension must be constant throughout the string if it is not accelerating.
  • There is debate over whether a massless string can exist under unbalanced forces, with some arguing that such a scenario leads to infinite acceleration.
  • Others contend that if the string has mass, the tension will vary along its length depending on its density.

Areas of Agreement / Disagreement

Participants express differing views on whether tension can exist in a massless string pulled from one end, with some asserting it cannot while others maintain that tension arises from the forces applied. The discussion remains unresolved regarding the implications of mass and acceleration on tension.

Contextual Notes

Participants acknowledge that the assumptions about the string being massless and the nature of the forces applied are critical to the discussion. There is an ongoing exploration of how these assumptions affect the existence and behavior of tension in the string.

andyrk
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If we take one end of a mass-less string and pull it with force F, would the string have any tension in it? Would it have any tension when we pull it with force F from both the ends?
 
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Yes.
 
Why? And what would it be? Can we derive it?
 
If I take a small element dx of the string, and if T1 acts on one side and T2 acts on the other, net force is ##T_1-T_2=ma=0##. So T1=T2.
This means that net force on every element of string is zero right?
 
AdityaDev said:
If I take a small element dx of the string, and if T1 acts on one side and T2 acts on the other, net force is ##T_1-T_2=ma=0##. So T1=T2.
This means that net force on every element of string is zero.
Yes, but what I am asking is that why would Tension arise in the first place?
 
Why would it not? What is your understanding of tension?
 
Orodruin: 5053035 said:
Why would it not? What is your understanding of tension?
From the equation of in post 4, the force on every segment of the thread is zero. Then why does it need tension?
 
Orodruin said:
Why would it not? What is your understanding of tension?
That tension arises only when something is pulling at some particle. So the point which is being pulled with F has some pulling force on it. But what is pulling on the particles behind that first point at which force is being applied?
AdityaDev said:
From the equation of in post 4, the force on every segment of the thread is zero. Then why does it need tension?
The fact that you are using T1 and T2 on dx element itself means that tension is present.
 
AdityaDev said:
From the equation of in post 4, the force on every segment of the thread is zero. Then why does it need tension?

The net force is zero, yes. This is not the definition of tension. The definition of tension is the force which one part of the string exerts on the other part of the string. What you have shown in #4 is that the tension is constant.
 
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  • #10
andyrk said:
That tension arises only when something is pulling at some particle.

This is wrong. Tension (at point x) is the force that acts from one part of the string on the other part (for a given cut at the point x of the string).
 
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  • #11
Orodruin said:
This is wrong. Tension (at point x) is the force that acts from one part of the string on the other part (for a given cut at the point x of the string).
So how would you explain that different parts of the string impart forces on other parts so that tension exists throughout the string?
 
  • #12
It has to, otherwise the string would be accelerating as per Newton's 2nd law as shown in post #4 by Aditya. If you let one of the ends of the element you consider be an actual end of the string (where you are pulling with force F), the force on the other side of the element must also be F (but in the opposite direction). Thus, the tension in the string must be F.
 
  • #13
@Orodruin , so tension is not the net force on each part of the string but the force that is exerted by a nearby segment of the same string on it.
also, when the string has some mass and when equal forces are applied on both ends, since acceleration of body is zero, again the tension in each segment of the string has to be F right?
 
  • #14
AdityaDev said:
also, when the string has some mass and when equal forces are applied on both ends, since acceleration of body is zero, again the tension in each segment of the string has to be F right?

Assuming that acceleration is zero, yes.
 
  • #15
Orodruin said:
It has to, otherwise the string would be accelerating as per Newton's 2nd law as shown in post #4 by Aditya. If you let one of the ends of the element you consider be an actual end of the string (where you are pulling with force F), the force on the other side of the element must also be F (but in the opposite direction). Thus, the tension in the string must be F.
So how would you explain that this same tension exists at all points of the string besides the first? We know that F exists on the very first element. But what about the rest?
 
  • #16
andyrk said:
So how would you explain that this same tension exists at all points of the string besides the first? What force pulls on the other elements of the string?

One part of the string pulls on the other part of string and vice versa. If it did not, the different parts of the string would accelerate, as post #4 clearly shows. This is the very definition of what tension is.
 
  • #17
Orodruin said:
One part of the string pulls on the other part of string and vice versa. If it did not, the different parts of the string would accelerate, as post #4 clearly shows. This is the very definition of what tension is.
How do you know that one part pulls the other part with the same force as the first part was pulled by? Why can't they be different?
 
  • #18
andyrk said:
How do you know that one part pulls the other part with the same force as the first part was pulled by? They can be different too right?
Third law.
when one part pulls the nearby part, then that nearby part will pull the first part with the same force.
 
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  • #19
AdityaDev said:
Third law.
when one part pulls the nearby part, then that nearby part will pull the first part with the same force.
There are 2 parts. One is right at the end of the string, which is being pulled by force F. The second part which is adjacent to this part but not in direct contact with the point at which the force is being applied. So how does this second part get pulley by force F?
 
  • #20
andyrk said:
So how does this second part get pulley by force F?
By the internal forces of the string, how else?
 
  • #21
See this attachment. I accept the forces at x = 0. But why do the same forces exist at x = dx? You said tension is the force with which one part of the string pulls the other part. So, why does the other part pull (x= 0 to dx) pull at x = dx with F and not something else?
 

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  • #22
Because otherwise the string would accelerate (in fact, if the string is massless, it would have infinite acceleration).
 
  • #23
And why should the string not accelerate? The string is being pulled from only one direction. So it should accelerate.
 
  • #24
andyrk said:
The string is being pulled from only one direction. So it should accelerate.

You are referring to the case when you only pull one end? You simply cannot do that without giving the string infinite acceleration (if it is massless). I hope you realize that what breaks down in this case is your assumption that the string is massless. If the string has even the tiniest mass, the acceleration will not be infinite and the tension will change along the string depending on the string's density.
 
  • #25
Orodruin said:
You are referring to the case when you only pull one end? You simply cannot do that without giving the string infinite acceleration (if it is massless). I hope you realize that what breaks down in this case is your assumption that the string is massless. If the string has even the tiniest mass, the acceleration will not be infinite and the tension will change along the string depending on the string's density.
Right, but what I was asking was would tension exist in such a case or not? (String is massless and being pulled from only one direction)
 
  • #26
andyrk said:
Right, but what I was asking was would tension exist in such a case or not? (String is massless and being pulled from only one direction)

I just told you this situation cannot exist. If you are pulling one end of the string only and there is no other masses involved, you cannot approximate the string as massless. The tension in the (non-massless, i.e., massive) string will depend on how its mass is distributed.
 
  • #27
Oh..you mean if there exists an unbalanced force...then their has to be some mass...mass-less case can't exist side by side with unbalanced force?
 
  • #28
Not unless you like infinite accelerations. Generally, it just means you neglected a mass that you probably should not have neglected and the acceleration is large, but not infinite.
 
  • #29
Orodruin said:
Not unless you like infinite accelerations. Generally, it just means you neglected a mass that you probably should not have neglected and the acceleration is large, but not infinite.
And if I say that I am fine with infinite acceleration, then what would the tension be?
 
  • #30
You should not be fine with infinite acceleration apart from for an infinitely short moment as an approximation, which does not allow you to apply force considerations. It is unphysical, you cannot make a massless string.
 

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