What force should be used to calculate Young's Modulus?

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Discussion Overview

The discussion revolves around the calculation of Young's Modulus for a rod subjected to varying forces at each end. Participants explore the implications of these forces on tensile stress and elongation, considering the conditions of motion and stability of the rod.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether to use a force of 3f or 1.5f in calculating Young's Modulus, seeking clarification on the appropriate force to consider.
  • Another participant suggests that the rod will be accelerated, implying that it is not stationary, which raises questions about the forces acting on it.
  • Concerns are raised about the applicability of Newton's laws in the context of the problem, with references to the need for stable conditions.
  • Some participants note that tensile stress will vary along the length of the rod, indicating that calculus may be necessary for accurate calculations.
  • One participant mentions the need to analyze an infinitesimal section of the rod and set up an integral to find the stress distribution.
  • There is a discussion about the similarity of this problem to those involving rotating rods, with references to external resources for further understanding.
  • Participants express uncertainty about whether the original question has a straightforward answer or if it is incomplete or irrelevant.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the appropriate force to use for calculating Young's Modulus, with multiple competing views and uncertainties regarding the conditions of the rod and the implications of acceleration.

Contextual Notes

Limitations include the dependence on the assumptions about the rod's motion and the varying tensile stress throughout its length, which complicates the calculation of Young's Modulus.

gianeshwar
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If a rod with cross section area A and length L is lying on a smooth table with one end being pulled by f Newtons and other end by 2f Newtons.
What force I can use in calculating Young's Modulus and why?
my doubt is whether it will be 3N or 1.5N and why?
Stretched length is given.
 
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gianeshwar said:
If a rod with cross section area A and length L is lying on a smooth table with one end being pulled by f Newtons and other end by 2f Newtons.
What force I can use in calculating Young's Modulus and why?
my doubt is whether it will be 3N or 1.5N and why?
Stretched length is given.

It will be accelerated by a = F/m, not sitting still on the table, no?
 
berkeman said:
It will be accelerated by a = F/m, not sitting still on the table, no?
Thanks! I want to know value of force i.e., 1.5f or 3f.
 
Then how can I calculate Young's modulus only under these given conditions.
 
There is no physical condition with stable object by non zero external force. If I understand your problem.
 
I need to find tensile stress on rod as I want to find elongation for calculating young's modulus
 
gianeshwar said:
I need to find tensile stress on rod as I want to find elongation for calculating young's modulus

The tensile stress will vary throughout the length of the rod...density & some calculus is needed.
Have you done any elongation or stress of a rotating rod type questions? This are similar.
 
According to my understanding so far rod is moving here with acceleration (2f-f) /m and it is also stretched having tensile stress f/2.
 
  • #10
Thanks billy! I have not done many problems as you asked.
 
  • #11
Stating same problem in a different wayhttps://mmi240.whatsapp.net/d/yywezFW6TcxsIWacjmME81VjKfY/AunnYXfkq2P8Blmy__wJQyRLQ4aL4z8kQXlZUs2wGVPB.jpg
 
Last edited by a moderator:
  • #12
https://mmi130.whatsapp.net/d/l-CffzhTrS1R5PpPeDk30FVjLnU/Ard1QFFL7XB255nzwRl_0yw8Xxy2I-ChbVHnl1qLgWAY.jpg
 
Last edited by a moderator:
  • #13
No, as was stated earlier, you need to take into account that the tension varies throughout the rod.
 
  • #14
Then here in new case answer is F?
 
  • #15
gianeshwar said:
Then here in new case answer is F?

No.

billy_joule said:
The tensile stress will vary throughout the length of the rod...density & some calculus is needed.
Have you done any elongation or stress of a rotating rod type questions? This are similar.

Imagine accelerating a long chain by pulling one end. Where is the chain most likely to break?
The first link must support every other link. The last link supports only it's own self weight. Therefore, the stress & elongation in each link is not the same.
Your problem looks at a chain with an opposing force on the last link.
You need to analyse an infinitesimal section of your bar, set up an integral, find the integration constant from the boundary conditions, perform the integration over the length of the bar. (Or similar, It's been a while for me..)
Every decent mechanics of materials textbook (I found Hibbeler good) will likely have multiple examples of the very similar rotating bar situation.
 
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  • #16
Thanks!Why are you saying "very similar rotating bar". Specifically rotating.
Also I want to know whether my question has a simple answer or the question is not complete or the question is irrelevant...(restated question)
 
  • #17
gianeshwar said:
Thanks!Why are you saying "very similar rotating bar". Specifically rotating.

They are very similar because they are analysed in a similar way.

http://www.mathalino.com/reviewer/m...als/solution-to-problem-218-axial-deformation

and exe 1.296 here
http://exir.ru/solutions/Elastic_Deformations_of_Solid_Body.htm
Also I want to know whether my question has a simple answer or the question is not complete or the question is irrelevant...(restated question)

There is enough information given to reach a meaningful answer. Whether it's simple or not would depend on the student.
 
  • #18
Thank you billy!
 

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