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

In summary, 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, the force that can be used to calculate Young's Modulus is 1.5f.
  • #1
gianeshwar
226
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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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  • #2
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?
 
  • #3
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.
 
  • #5
Then how can I calculate Young's modulus only under these given conditions.
 
  • #6
There is no physical condition with stable object by non zero external force. If I understand your problem.
 
  • #7
I need to find tensile stress on rod as I want to find elongation for calculating young's modulus
 
  • #8
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.
 
  • #9
According to my understanding so far rod is moving here with accleration (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
 
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  • #12
https://mmi130.whatsapp.net/d/l-CffzhTrS1R5PpPeDk30FVjLnU/Ard1QFFL7XB255nzwRl_0yw8Xxy2I-ChbVHnl1qLgWAY.jpg
 
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  • #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!
 

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

1. What is Young's modulus?

Young's modulus is a measure of the stiffness of a material. It is the ratio of stress to strain in a material under tensile or compressive forces. In simpler terms, it measures how much a material will deform when a force is applied to it.

2. How is Young's modulus calculated?

Young's modulus is calculated by dividing the stress (force per unit area) by the strain (change in length relative to the original length). It is typically measured in units of pascals (Pa) or newtons per square meter (N/m^2).

3. What factors affect Young's modulus?

The factors that affect Young's modulus include the type of material, its structure and composition, and the temperature at which it is tested. Generally, materials with stronger intermolecular forces and a more rigid structure will have a higher Young's modulus.

4. Why is Young's modulus important?

Young's modulus is an important property because it allows us to compare the stiffness of different materials. It is also a crucial factor in designing and selecting materials for various applications, such as building structures, bridges, and mechanical components.

5. How does Young's modulus relate to a material's elasticity?

Young's modulus and a material's elasticity are closely related. A material with a higher Young's modulus will have a higher elasticity, meaning it will be less likely to deform under stress. On the other hand, a material with a lower Young's modulus will have a lower elasticity and will be more prone to deformation.

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