**Problem Statement:**A bar produces a lateral strain of magnitude \(60 \times 10^{-5} \, \text{m/m}\) when subjected to a tensile stress of magnitude \(300 \, \text{MPa}\) along the axial direction. What is the elastic modulus of the material if the Poisson’s ratio is 0.3?**Explanation:**In this problem, we are given the following:1. Lateral Strain, \(\epsilon_l = 60 \times 10^{-5} \, \text{m/m}\).2. Tensile Stress, \(\sigma = 300 \, \text{MPa}\).3. Poisson’s Ratio, \(\nu = 0.3\).We need to determine the elastic modulus, \(E\), of the material.**Key Concepts:**1. **Lateral Strain** - The deformation per unit length in the perpendicular direction to the applied stress.2. **Tensile Stress** - The force applied per unit area in the axial direction.3. **Poisson's Ratio** - A constant that describes the ratio of lateral strain to axial strain in a material.4. **Elastic Modulus (Young’s Modulus, \(E\))** - A measure of the stiffness of a material, defined as the ratio of tensile stress to axial strain.**Solution:**The relationship between lateral strain (\(\epsilon_l \)), axial strain (\(\epsilon_a \)), and Poisson’s ratio (\(\nu\)) is given by:\[ \epsilon_l = -\nu \epsilon_a \]Rearranging for axial strain:\[ \epsilon_a = -\frac{\epsilon_l}{\nu} \]Substitute the known values:\[ \epsilon_a = -\frac{60 \times 10^{-5} \, \text{m/m}}{0.3} = -200 \times 10^{-5} \, \text{m/m} \]Now using Hooke's Law:\[ \sigma = E \epsilon_a \]\[ 300 \, \text{MPa} = E \times -200 \times 10^{-5} \, \text{m/m} \]Solving for \(E\):\[ E = \frac{300 \, \text{MPa}}{-200 \times 10^{-5}} \]\[ E

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A bar produces a lateral strain of magnitude 60x105 m/m when subjected to a tensile stress of magnitude 300 MPa along the axial direction. What is the elastic modulus of the material if the Poisson's ratio is 0.3?

A bar produces a lateral strain of magnitude 60x105 m/m when subjected to a tensile stress of magnitude 300 MPa along the axial direction. What is the elastic modulus of the material if the Poisson's ratio is 0.3?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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