Calculate initial diameter from longitudinal strain and final diameter

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SUMMARY

The discussion focuses on calculating the initial diameter of a wire subjected to a longitudinal strain of 30%, resulting in a final diameter of 0.1 cm. The assumption of no volume change leads to the application of Poisson's ratio, set at 0.5, which indicates a lateral strain of 15%. However, the correct approach involves using the geometric relationship of the wire's dimensions, specifically the equation pi r1^2 L1 = pi r2^2 L2, where L2 equals 1.3 times L1. The accurate initial diameter is determined to be 0.114 cm.

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  • Understanding of longitudinal strain and its effects on material dimensions
  • Familiarity with Poisson's ratio and its application in strain calculations
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  • Ability to manipulate algebraic equations for solving geometric problems
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"Calculate the initial diameter of a wire that has been longitudinally strained by 30% and whose final diameter is 0.1cm. Assume no volume change."

Now I know that if there is no volume change, v=poisson's ratio= 0.5. Thus the lateral strain would equal 30%*0.5= 15%. But when I plug it into the strain equation and use a diameter of 0.1cm as the initial length, I get 0.1176. The answer is supposed to be 0.114cm.

Any thoughts?
 
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If there is no volume change you don't have to know about wires or poisson ratio.
It's just a simple geometry exercise
pi r1^2 L1 = pi r2^2 L2 and L2 = 1.3 L1 just rearrange in terms of r1
 
Wow I way over thought that one, thanks.
 

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