Tension in a chopped up string

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    String Tension
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Discussion Overview

The discussion revolves around the concept of tension in a string, particularly when the string is divided into segments. Participants explore how tension behaves in both massless and massive strings, and how different mass densities affect tension distribution.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why the tension in each segment of a chopped string remains T, suggesting it should be T/3 based on an analogy with blocks connected by strings.
  • Another participant explains that if the string is treated as massless, the tension remains constant throughout, as any segment must have a net force of zero.
  • A participant raises a scenario involving a string with different mass densities, questioning why tension remains the same across different sections when tension is applied to one end.
  • Another reply suggests that if one end of the string is fixed, the acceleration is zero, leading to uniform tension throughout the string.
  • A later reply acknowledges the role of acceleration in determining tension, indicating a shift in understanding.

Areas of Agreement / Disagreement

Participants express differing views on how tension behaves in strings of varying mass and density, with no consensus reached on the implications of mass and acceleration on tension distribution.

Contextual Notes

Assumptions about the mass of the string and the conditions of acceleration are not fully resolved, leading to varying interpretations of tension behavior.

Who May Find This Useful

This discussion may be useful for those interested in mechanics, particularly in understanding the principles of tension in strings and the effects of mass and acceleration on tension distribution.

quietrain
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if a string of length L has tension T,

when we chop it up into 3 equal pieces (of length L/3) , then tension experience by each string individually is still T...

why? shouldn't it be T/3?

issn't this analogous to a string pulling 3 blocks (each connected by a horizontal string and has mass m) horizontally together ? which means T = 3ma

so for the same acceleration, the first block has tension T, 2nd block has tension 2/3T and the third block has tension 1/3 T .

so what gives ?

thanks for the help!
 
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If you treat the string as massless (the usual assumption), then any segment of the string must have a net force of zero. Thus T1 = T2 (since T1-T2 = ma = 0), and the tension is the same throughout. But if the string has mass, then the tension will vary along the length according to T1-T2 = ma.

If you are pulling a massive string with nothing attached to its far end, then you are right. The tension will varying from a max of T at the end you pull to zero at the far end. But usually strings are treated as massless and they usually have things (other masses) tied to their ends.
 
ok, if the string L has 3 sections with different mass densities, why when we apply a tension to one end and fix the other, all 3 sections have the same tension?

shouldn't it be that the tension vary in accordance with the mass?
 
quietrain said:
ok, if the string L has 3 sections with different mass densities, why when we apply a tension to one end and fix the other, all 3 sections have the same tension?
What's the acceleration of the string? If one end is fixed, I suspect the acceleration is zero, thus the tension will be the same throughout. (Since T1-T2 = ma = 0.)
 
oh i see... so if the acceleration is the factor that we consider... thanks
 

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