Calculate initial diameter from longitudinal strain and final diameter

AI Thread Summary
To calculate the initial diameter of a wire with a longitudinal strain of 30% and a final diameter of 0.1 cm, the assumption of no volume change simplifies the problem. The lateral strain, derived from Poisson's ratio of 0.5, results in a 15% reduction in diameter. The correct approach involves using the geometry of the wire, specifically the relationship between initial and final dimensions. By applying the formula for volume conservation, the initial diameter can be accurately determined as 0.114 cm. This highlights the importance of understanding geometric relationships in strain calculations.
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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 excercise
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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