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.

  • #31
andyrk said:
And if I say that I am fine with infinite acceleration, then what would the tension be?
This just results in a math fail. It's like asking if God can create a rock so big he can't lift it. It doesn't have an answer. Indeed, even stating that you apply a force to this string is impossible. So you're going to have to decide what you want to get out of this problem.
 
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  • #32
In reality the string will have a small mass density ρ . Assuming that is moving with a finite acceleration a (because for example it is attached to other main bodies that do so) a length dx of the string will have a net force F=(ρdx)a=T(x+dx)-T(x)=dT as it follows from Newton's 2nd law. If the acceleration a is not too big such that the product ρa is small we can approximately say that the net force is zero from which it follows that dT=0 that is the tension along the string remain constant.

Finally i want to say something general that i find quite important when studying physics. It is quite often when studying physics that we do silent simplifying assumptions that simplify the calculations a lot and brighten only the key points of a phenomenon.If we don't make those assumption the study can become quite complex sometimes, so complex that we can't make any usefull conclusions.
 
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