A material has a shear modulus of 5.0 × 10⁹ N/m². A shear stress of 1.7 x 107 N/m² is applied to a piece of the material. What is the resulting shear strain?
A material has a shear modulus of 5.0 × 10⁹ N/m². A shear stress of 1.7 x 107 N/m² is applied to a piece of the material. What is the resulting shear strain?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
![**Example Shear Modulus Problem for Educational Context**
A material has a shear modulus of \( 5.0 \times 10^9 \, \text{N/m}^2 \). A shear stress of \( 1.7 \times 10^7 \, \text{N/m}^2 \) is applied to a piece of the material. What is the resulting shear strain?
In this example, the problem involves the following concepts:
- **Shear Modulus (\(G\))**: A property that describes a material's ability to resist shear deformation. It is usually denoted in Newtons per square meter (N/m²).
- **Shear Stress (\( \tau \))**: This is the force per unit area causing the deformation, also measured in Newtons per square meter (N/m²).
- **Shear Strain (\( \gamma \))**: The dimensionless measure of deformation representing the angle of deformation.
To find the resulting shear strain, use the relationship:
\[ \gamma = \frac{\tau}{G} \]
Given:
\[ G = 5.0 \times 10^9 \, \text{N/m}^2 \]
\[ \tau = 1.7 \times 10^7 \, \text{N/m}^2 \]
Solution:
\[ \gamma = \frac{1.7 \times 10^7 \, \text{N/m}^2}{5.0 \times 10^9 \, \text{N/m}^2} \]
\[ \gamma = 3.4 \times 10^{-3} \]
Thus, the shear strain \( \gamma \) is \( 3.4 \times 10^{-3} \).
This means the material experiences a shear strain of 0.0034 when subjected to the given shear stress.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70495d9e-d834-4a3c-919e-f23d4c42494e%2F79c9ff56-6f16-427a-94be-b41bea826167%2F3635ch_processed.png&w=3840&q=75)
Transcribed Image Text:**Example Shear Modulus Problem for Educational Context**
A material has a shear modulus of \( 5.0 \times 10^9 \, \text{N/m}^2 \). A shear stress of \( 1.7 \times 10^7 \, \text{N/m}^2 \) is applied to a piece of the material. What is the resulting shear strain?
In this example, the problem involves the following concepts:
- **Shear Modulus (\(G\))**: A property that describes a material's ability to resist shear deformation. It is usually denoted in Newtons per square meter (N/m²).
- **Shear Stress (\( \tau \))**: This is the force per unit area causing the deformation, also measured in Newtons per square meter (N/m²).
- **Shear Strain (\( \gamma \))**: The dimensionless measure of deformation representing the angle of deformation.
To find the resulting shear strain, use the relationship:
\[ \gamma = \frac{\tau}{G} \]
Given:
\[ G = 5.0 \times 10^9 \, \text{N/m}^2 \]
\[ \tau = 1.7 \times 10^7 \, \text{N/m}^2 \]
Solution:
\[ \gamma = \frac{1.7 \times 10^7 \, \text{N/m}^2}{5.0 \times 10^9 \, \text{N/m}^2} \]
\[ \gamma = 3.4 \times 10^{-3} \]
Thus, the shear strain \( \gamma \) is \( 3.4 \times 10^{-3} \).
This means the material experiences a shear strain of 0.0034 when subjected to the given shear stress.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON