5. In this problem we are pressing or pulling on the top of a cylinder that...

  

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5. In this problem we are pressing or pulling on the top of a cylinder that initially has height ho and diameter do. Poisson's ratio was discussed in class (Jan 14 notes) but because strain is a differential quantity, the formulas given there were only valid for small values of strain. The exact formula is: (h/ho)=d/do a. Find a formula for the relative volume (meaning, final volume over initial volume) of the cylinder as a function of Poisson's ratio v, and the relative height change h/ho. b. For h/ho= 0.8 (squashing the cylinder to 80 percent of its original height), plot the relative volume change vs. Poisson's ratio, where v ranges from -1 to 0.5. c. What is happening at negative values of Poisson's ratio? What Poisson's ratio gives no volume change? 5. In this problem we are pressing or pulling on the top of a cylinder that initially has height ho and diameter do. Poisson's ratio was discussed in class (Jan 14 notes) but because strain is a differential quantity, the formulas given there were only valid for small values of strain. The exact formula is: (h/ho)=d/do a. Find a formula for the relative volume (meaning, final volume over initial volume) of the cylinder as a function of Poisson's ratio v, and the relative height change h/ho. b. For h/ho= 0.8 (squashing the cylinder to 80 percent of its original height), plot the relative volume change vs. Poisson's ratio, where v ranges from -1 to 0.5. c. What is happening at negative values of Poisson's ratio? What Poisson's ratio gives no volume change?

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1 The formula for the relative volume of the cylinder is hho6 d do The rela... View the full answer