Change in length of wire after adding a load

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Homework Help Overview

The discussion revolves around the change in length of a wire subjected to a load, specifically addressing the interpretation of the original length of the wire and the implications of pre-existing weights. The subject area includes concepts from mechanics and material science, particularly focusing on strain and stress relationships.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the ambiguity of the problem statement regarding whether a previous weight was present on the wire. Questions arise about the significance of this weight on the calculations of strain and the appropriateness of using the original length of 1.8 m for calculations.

Discussion Status

The discussion is ongoing, with participants questioning the assumptions made about the initial conditions of the wire and the impact of small weights on the overall calculations. Some guidance has been provided regarding the application of Hooke's law and the concept of small strains, but no consensus has been reached on the implications of these factors.

Contextual Notes

There is a noted ambiguity in the problem statement regarding the presence of a previous weight on the wire, which may affect the interpretation of the original length and the calculations involved. Participants are also discussing the implications of small changes in length relative to the original length of the wire.

coconut62
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Homework Statement



Please refer to the image attached.

I don't understand why can they just take 1.8m as the original length, since there is already a load hanging there.

My calculations yield the value of strain to be e/L, but in the answer it is e/1.8.

Please explain this to me.

Homework Equations



E=stress/strain

The Attempt at a Solution



My working is together with the question.
 

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The problem statement is a little ambiguous. It isn't clear whether there was a previous weight hanging from the wire, or whether the 25 N force represents the weight. Either way, it doesn't really matter much. If there was already a small weight hanging on the wire, the change in the length of the wire would have been insignificant compared to the 1.8 m. So, even in the incremental problem, the length of the wire could still be taken as 1.8 m (with virtually no loss in accuracy of the answer).
 
Chestermiller said:
If there was already a small weight hanging on the wire, the change in the length of the wire would have been insignificant compared to the 1.8 m.

Why is this so? If there was initially no weight hanging, would the change in length be more significant?
 
coconut62 said:
Why is this so? If there was initially no weight hanging, would the change in length be more significant?

Consider this: If, with the small weight, the length of the wire had increased to 1.8001, would this really have materially changed the answer to your problem (for the incremental change in length). Try it out in your problem and see.

When we use Hooke's law, we assume that all strains are small and linearly superimposible, so that the changes in length are always small compared to the original length. If the change in length were larger, and comparable to the original length, we would have to use large strain theory.
 
What is "linearly superimposible" ?
 
coconut62 said:
What is "linearly superimposible" ?
It means that the strains from each of the two individual loads (in isolation) can be added together to get the strain from the combined load.
 
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