Elasticity limit of copper Problem

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SUMMARY

The elastic limit of copper is established at 1.50E8 N/m², which is critical for determining the minimum diameter of a copper wire under a load of 10.5 kg. The calculation reveals that the diameter must be at least 0.934 mm to avoid exceeding this elastic limit. The discussion clarifies the distinction between yield stress (σ_y) and modulus of elasticity (E), emphasizing that yield stress indicates the maximum stress before permanent deformation occurs, while modulus of elasticity describes the material's response to stress within the elastic range. Understanding these concepts is essential for solving related physics problems effectively.

PREREQUISITES
  • Understanding of Hooke's Law and its applications
  • Familiarity with stress and strain concepts in materials science
  • Basic knowledge of force calculations (F = ma)
  • Ability to manipulate algebraic equations for area and diameter calculations
NEXT STEPS
  • Study the relationship between yield stress and modulus of elasticity in materials
  • Learn about the stress-strain curve and its significance in material science
  • Explore practical applications of Hooke's Law in engineering design
  • Investigate the effects of different materials on elastic limits and their engineering implications
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Students in physics and engineering disciplines, materials scientists, and professionals involved in mechanical design and structural analysis will benefit from this discussion.

loudgrrl4_ever
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Okay, here is the problem:
If the elastic limit of copper is 1.50E8 N/m2, determine the minimum diameter a copper wire can have under a load of 10.5 kg if its elastic limit is not to be exceeded.
Obviously I am looking for d in this problem. I am given the downward force (102.9 N = ma); A = (pi * d2)/4.
I am having trouble identifying the correct symbol for the elastic limit. My professor has a habit of hading out worksheets full of formulas with no explanation on them. For some reason I know that when given modulus, it will be called modulus, so this is the TSmax? I'm quite confused.
Trying it with 1.50E8 = stress, I get stress = F/A; A = F/stress; (pi/4)d*d = F/stress; d = (sqrt)[(4*102.9)/(pi * 1.5E8)]; d=.000934m; d=0.93400mm
If I knew the unit strain, or the length and change in length this problem would be much easier. I haven't done any with so little information before.
I haven't tried that answer yet (I just checked and I answered 0.093400 earlier when I thought I used this) but I would just like to know that I have done it correctly. My textbook spends all of a page and a half talking about this section, and it makes little sense to me unless the problems are simple.
Any help you can give towards understanding this section of Physics would be very helpful and appreciated (especially links/explanations).
Thanks :)
 
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loudgrrl4_ever said:
Trying it with 1.50E8 = stress, I get stress = F/A; A = F/stress; (pi/4)d*d = F/stress; d = (sqrt)[(4*102.9)/(pi * 1.5E8)]; d=.000934m; d=0.93400mm
The elastic limit is the maximum stress (just check the units) that can be applied while staying within the parameters of Hooke's law. So your thinking here is just fine. (I did not check your arithmetic.)

If I knew the unit strain, or the length and change in length this problem would be much easier.
All that is irrelevant.
I haven't done any with so little information before.
This problem is probably easier than you are used to. :wink:
 
Following up on this, do not confuse the elastic stress limit of a material, often called yield stress, and quite often denoted as \sigma_y, which has units of force/length^2, with the modulus of elasticity of a material, often called E, which also has units of force/length^2. Both are properties of the material that are independent of each other. The yield stress denotes the stress level above which point the material will no longer obey Hookes law. The modulus of elasticity is the slope of the stress - strain curve within the elastic range, and is a measure of how much the material will strain (e) or elongate/compress under a given stress, per \sigma = eE. As Doc Al noted, you have the correct equation for determining the required diameter; the strain in the material is irrelevant in this problem.
 

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