Compute the elastic modulus of hypothetical alloy

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Discussion Overview

The discussion revolves around the calculation of the elastic modulus of a hypothetical metal alloy based on provided dimensions and material properties. Participants analyze the calculations involved in determining the elastic modulus, including stress, strain, and the implications of unit conversions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a calculation for the elastic modulus based on a tensile force and a change in diameter, leading to a result of 100 GPa.
  • Another participant questions the unit conversions involved, specifically the meanings of 'giga' and 'mega' and the normalization factor used in the calculations.
  • A third participant reflects on their initial conversion to MPa and the implications of switching to GPa, seeking clarity on the magnitude of the final answer.
  • One participant agrees with the calculations but notes that the expected elastic modulus for metals typically exceeds 50 GPa, suggesting the provided answer may be incorrect.
  • A later reply suggests that a potential error in the calculations could stem from an incorrect factor applied to the diameter measurement when computing lateral strain.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correctness of the calculated elastic modulus, with some agreeing on the calculations but questioning the final answer's validity. Multiple competing views remain about the accuracy of the calculations and the expected properties of the hypothetical alloy.

Contextual Notes

Participants note potential issues with unit conversions and assumptions about the material properties of the hypothetical alloy, which may not align with typical values for known metals and alloys.

physicsnnewbie
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Homework Statement


Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 10mm. A tensile force of 1500 N produces an elastic reduction in diameter of 6.7e-4mm. Compute the elastic modulus of this alloy, given that poisson's ratio is 0.35.


Homework Equations


stress = eleastic modulus*strain
poisson's ratio = lateral strain/axial strain


The Attempt at a Solution


Calculate pressure in Pa:
1500/(5e-3^2*3.14159) = 1.90986e+7

Convert to GPa:
1.90986e+7/1e6 = 1.90986e+1

Calculate lateral strain:
6.7e-4/10 = 6.7e-5

Calculate axial strain:
6.7e-5/.35 = 1.91429e-4

Calculate Elastic Modulus:
1.90986e+1/1.91429e-4 = 9.97686e+4

=100GPa


The correct answer is 100MPa. I'm not sure where I've made the mistake though.
 
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physicsnnewbie said:

The Attempt at a Solution


Calculate pressure in Pa:
1500/(5e-3^2*3.14159) = 1.90986e+7

Convert to GPa:
1.90986e+7/1e6 = 1.90986e+1

What does the prefix 'giga' mean? And what does the prefix 'mega' mean? And what unit are you normalising by in this step? Add in the fact that you're a factor of 103 out and you know there is going to be an error in your consideration of units somewhere in your solution...
 
Well I originally converted it to MPa but decided to convert it to GPa instead (I'm not sure why). Anyway this shouldn't be the cause of the magnitude difference because it just means i will get the answer in GPa instead of MPa right?

So where have I gone wrong with the magnitudes?
 
Sorry, was on autopilot there and spotted a difference between what you said you were expressing it in terms of and what you actually have. I agree with your calculations and answer. I know it's not a reliable guideline in this case (especially as the original problem states 'hypothetical') but most metals and their alloys do exhibit moduli upwards of 50 GPa, so the given answer does seem erroneous.
 
Ok thanks.
 
It looks like you are right and whoever did the calculations for the answer improperly added a factor of 1e-3 to the diameter measurement when computing lateral strain. Since the deflection number was already stated in mm, you are correct in your approach.
 

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