Can anyone solve this shape of a string puzzle?

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Discussion Overview

The discussion revolves around a physics puzzle involving an infinite massless and elastic string subjected to a constant upward force at one end. Participants explore the resulting wave profile or shape of the string over time, considering various dynamics and assumptions about the string's properties.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant poses a question about the wave profile of a string when a constant force is applied at one end, asking whether the resulting shape is a curve or a combination of slope and horizontal sections.
  • Another participant inquires about the acceleration of the end of the string where the upward force is applied, noting that the string is massless.
  • A third participant references established literature on the dynamics of elastic strings, suggesting that the problem is standard in advanced mechanics and that lifting the end will generate waves unless done adiabatically.
  • A later reply corrects the initial assumption, stating that the string has mass uniformly distributed along its length, which alters the dynamics of the problem.
  • Another participant humorously notes that if the string were massless, it would have to move at the speed of light, implying that mass is a critical factor in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are competing views on the properties of the string (massless vs. having mass) and the implications for the wave profile and dynamics involved.

Contextual Notes

The discussion includes assumptions about the string's properties, such as whether it is massless or has mass, which significantly affects the analysis. There is also mention of the conditions under which the force is applied, such as whether the lifting is adiabatic.

Twukwuw
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Can anyone solve this... "shape of a string" puzzle?

Let's say there is an infinite massless and elastic string, which laid horizontally and one of the ends is extended to infinite distance.
The string is "pulled" thoroughly and somehow, so that there is a tension T along it.
There is a CONSTANT force F acting upwards on the other end(at the POINT) :eek: , which will then "drag" the nearer part of the string upwards.
My question is simple,
What will be the wave profile(or the shape of the wave) after a duration t?

Is it a curve...or is it a combination of 1 section of slope string and 1 section of horizontal string? The horizontal section of the string "haven't experience the force yet."

Assume there is no other force other than F. The force F ONLY acts at the "end-POINT" of the string.

Welcome anyone who like to accept challenge.
Thanks.

Twukwuw. :biggrin:
 
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What will be the acceleration of the end where upward force is applied? (The string is massless)
 
The dynamics of an elastic string, finite or infinte, are discussed in many textbooks -- classical mechanics(Goldstein, Synge&Griff), quantum field theory(Zee, Gross), E&M(Jackson, Panofsky and Phillips), mathematical physics (Courant&hHilbert). As the end is lifted, it will generate waves in the string -- unless the lifting is adiabatic. Your problem is relatively standard -- a good problem for an advanced mechanics final exam.

Regards,
Reilly Atkinson
 
correction

:-p :-p
 
sorry, correction here:
the string has mass,
its mass is uniformly distributed along the line.
thanks~!
 
good, if it didnt had a mass it would have to move at the speed of light
 

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