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)

To compute Poisson's ratio for the material, we can use the following formula:<br /><br />Poisson's ratio = - (Lateral strain) / (Axial strain)<br /><br />Given information:<br />- Diameter of the specimen: 8 mm (0.31 in.)<br />- Force applied: 15,700 N (3530 lbf)<br />- Reduction in specimen diameter: 5 × 10^-3 mm (2 × 10^-4 in.)<br />- Modulus of elasticity: 140 GPa (20.3 × 10^6 psi)<br /><br />Step 1: Calculate the axial strain.<br />Axial strain = (Change in length) / (Original length)<br />Axial strain = (Reduction in diameter) / (Original diameter)<br />Axial strain = (5 × 10^-3 mm) / (8 mm)<br />Axial strain = 6.25 × 10^-4<br /><br />Step 2: Calculate the lateral strain.<br />Lateral strain = (Change in width) / (Original width)<br />Lateral strain = (Reduction in diameter) / (Original diameter)<br />Lateral strain = (5 × 10^-3 mm) / (8 mm)<br />Lateral strain = 6.25 × 10^-4<br /><br />Step 3: Calculate Poisson's ratio.<br />Poisson's ratio = - (Lateral strain) / (Axial strain)<br />Poisson's ratio = - (6.25 × 10^-4) / (6.25 × 10^-4)<br />Poisson's ratio = -1<br /><br />Therefore, the Poisson's ratio for the material is -1.