Calculate variation in volume using given Poisson's ratio

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SUMMARY

The discussion focuses on calculating the percentage variation in volume of a cylinder when elongated by 2% of its original length, given a Poisson's ratio of 0.3. The formula for volume, V = πr²l, is utilized, but confusion arises regarding the correct application of Poisson's ratio. A participant suggests that the definition of Poisson's ratio should be inverted and negated, indicating a misunderstanding in the initial setup. The conversation emphasizes the importance of correctly applying material properties in volume calculations.

PREREQUISITES
  • Understanding of Poisson's ratio and its implications in material science.
  • Familiarity with calculus, specifically differentiation techniques.
  • Knowledge of geometric formulas, particularly for the volume of cylinders.
  • Basic principles of elasticity and deformation in materials.
NEXT STEPS
  • Review the definition and application of Poisson's ratio in material mechanics.
  • Study the differentiation of volume formulas in calculus.
  • Explore the relationship between elongation and volume change in cylindrical objects.
  • Learn about the implications of material properties on structural integrity and performance.
USEFUL FOR

Students in engineering or physics, material scientists, and anyone involved in structural analysis or mechanics who needs to understand the effects of deformation on volume.

abhishek4
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Homework Statement

: A cylinder is elongated by 2% of its original length. If Poisson's ratio of its material is 0.3. Calculate the percentage variation in volume.[/B]

Homework Equations


V = πr^2l
η= 0.3= Δl/l/Δr/r[/B]

The Attempt at a Solution


I tried using calculus to differentiate V to find change in volume and then divided it by the given volume but could not find and answer as r^2 was left.
 
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I think you have the definition of Poisson's ratio wrong. It should be the other way up and negated: ##-\frac{\Delta r/r}{\Delta l/l}##.
Please post your working.
 

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