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
6.17 A cyltndrical specimen of some alloy 8 mm (0.31 in.) in diameter is stressed elastically in tension. A force of 15,700 N (3530 Iby) produces a reduction in specimen diameter of 5times 10^-3 mm (2times 10^-4in.) . Compute Poisson's ratio for this material if its modulus of elasticity is 140 GPa (20.3times 10^6psi)
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To compute Poisson's ratio for the material, we can use the following formula:Poisson's ratio = - (Lateral strain) / (Axial strain)Given information:- Diameter of the specimen: 8 mm (0.31 in.)- Force applied: 15,700 N (3530 lbf)- Reduction in specimen diameter: 5 × 10^-3 mm (2 × 10^-4 in.)- Modulus of elasticity: 140 GPa (20.3 × 10^6 psi)Step 1: Calculate the axial strain.Axial strain = (Change in length) / (Original length)Axial strain = (Reduction in diameter) / (Original diameter)Axial strain = (5 × 10^-3 mm) / (8 mm)Axial strain = 6.25 × 10^-4Step 2: Calculate the lateral strain.Lateral strain = (Change in width) / (Original width)Lateral strain = (Reduction in diameter) / (Original diameter)Lateral strain = (5 × 10^-3 mm) / (8 mm)Lateral strain = 6.25 × 10^-4Step 3: Calculate Poisson's ratio.Poisson's ratio = - (Lateral strain) / (Axial strain)Poisson's ratio = - (6.25 × 10^-4) / (6.25 × 10^-4)Poisson's ratio = -1Therefore, the Poisson's ratio for the material is -1.