Find the Young's Modulus of a Wire

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SUMMARY

The Young's Modulus of a wire made from a specific material was calculated based on a load of 500 N, a diameter of 1 mm, and a length of 2.5 m, which resulted in a stretch of 8 mm. The calculated Young's Modulus was determined to be 1.98 x 1011 Pa. However, the model answer provided was 2.5 x 1010 Pa, indicating a discrepancy in the strain calculation. The correct stress was calculated as 6.366 x 108 Pa, and the strain was derived from the change in length over the original length.

PREREQUISITES
  • Understanding of Young's Modulus and its formula (E = stress/strain)
  • Knowledge of stress calculation (stress = Force/Area)
  • Familiarity with strain calculation (strain = change in length/original length)
  • Basic geometry for calculating the area of a circle (A = πr2)
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  • Review the derivation of Young's Modulus in material science
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  • Explore the effects of material properties on Young's Modulus
  • Investigate common errors in experimental measurements of Young's Modulus
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Students in physics or engineering, material scientists, and professionals involved in mechanical testing and material properties analysis will benefit from this discussion.

Reema
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A wire made of a particular material is loaded with a lod of 500 N. The diameter of the wire is 1mm. The length of the wire is 2.5 m, and it stretched 8mm when under load. What is the young modulus of this material?


My work

E= stress\strain

stress= F\A
r= d/2 ==> 1x10^-3 \ 2 = 0.0005
= 500\3.14 x (0.0005)^2 = 6.36x10^8

strain change in (L) / L
= 8x10^-3 \2.5
=3.2x10^-3

E= 6.36x10^8 \ 3.2x10^-3 = 1.98x10^11



BUT, the model answer is 2.5x 10^10 pa
 
Last edited:
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Stress = P/A
= (500)/(3.14159*0.0005^2) = 6.366*10^8
Strain = (deltaL)/L
= 8/1 = 8
E = 8.295*10^7Pa
Are you sure you're giving the correct lengths? Where are you getting 2.5 from?
 
sorry, the length of the wire is 2.5 m
 

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