If The Stress On A Wire Is 10 7 Nm − 2 10^7 \, \text{Nm}^{-2} 1 0 7 Nm − 2 And The Wire Is Stretched From Its Original Length Of 10.00 Cm To 10.05 Cm, What Is The Young's Modulus Of The Wire?A. 5.0 × 10 4 Nm − 2 5.0 \times 10^4 \, \text{Nm}^{-2} 5.0 × 1 0 4 Nm − 2 B. $5.0 \times 10^5 ,
Introduction
Young's Modulus, also known as the modulus of elasticity, is a fundamental concept in physics that describes the relationship between stress and strain in a material. It is a measure of a material's ability to withstand deformation under stress. In this article, we will explore the concept of Young's Modulus and how it can be used to determine the properties of a wire under stress.
What is Young's Modulus?
Young's Modulus is defined as the ratio of stress to strain within the proportional limit of a material. Mathematically, it can be expressed as:
Y = \frac{\text{Stress}}{\text{Strain}}
where Y is the Young's Modulus, stress is the force applied per unit area, and strain is the resulting deformation per unit length.
Calculating Young's Modulus
To calculate the Young's Modulus of a wire, we need to know the stress and strain values. The stress value can be calculated using the formula:
Stress = \frac{F}{A}
where F is the force applied and A is the cross-sectional area of the wire.
The strain value can be calculated using the formula:
Strain = \frac{\Delta L}{L}
where \Delta L is the change in length and L is the original length of the wire.
Given Values
In this problem, we are given the following values:
- Stress =
- Original length (L) = 10.00 cm
- Final length (L + \Delta L) = 10.05 cm
We need to calculate the Young's Modulus of the wire using these values.
Calculating Strain
First, we need to calculate the strain value using the given values.
Strain = \frac{\Delta L}{L} = \frac{10.05 - 10.00}{10.00} = 0.005
Calculating Young's Modulus
Now that we have the stress and strain values, we can calculate the Young's Modulus using the formula:
Y = \frac{\text{Stress}}{\text{Strain}} = \frac{10^7}{0.005} = 2 \times 10^{10} , \text{Nm}^{-2}
Conclusion
In this article, we have explored the concept of Young's Modulus and how it can be used to determine the properties of a wire under stress. We have calculated the Young's Modulus of a wire using the given values and have found that it is equal to . This value indicates that the wire has a high degree of elasticity and can withstand significant stress without deforming.
Answer
The correct answer is:
Introduction
Young's Modulus is a fundamental concept in physics that describes the relationship between stress and strain in a material. In our previous article, we explored the concept of Young's Modulus and how it can be used to determine the properties of a wire under stress. In this article, we will answer some frequently asked questions about Young's Modulus.
Q: What is the difference between Young's Modulus and modulus of rigidity?
A: Young's Modulus and modulus of rigidity are both measures of a material's ability to withstand deformation under stress. However, they measure different types of deformation. Young's Modulus measures the deformation of a material under tensile or compressive stress, while the modulus of rigidity measures the deformation of a material under shear stress.
Q: What is the unit of Young's Modulus?
A: The unit of Young's Modulus is typically measured in pascals (Pa) or newtons per square meter (N/m^2).
Q: How is Young's Modulus related to the strength of a material?
A: Young's Modulus is related to the strength of a material in that it measures the material's ability to withstand deformation under stress. A material with a high Young's Modulus is more resistant to deformation and can withstand higher stresses before failing.
Q: Can Young's Modulus be used to predict the behavior of a material under different types of stress?
A: Yes, Young's Modulus can be used to predict the behavior of a material under different types of stress. By knowing the Young's Modulus of a material, engineers can predict how it will behave under different types of stress, such as tensile, compressive, or shear stress.
Q: How is Young's Modulus affected by temperature?
A: Young's Modulus can be affected by temperature. As the temperature of a material increases, its Young's Modulus typically decreases. This is because the molecules of the material are moving more rapidly and are more easily deformed.
Q: Can Young's Modulus be used to predict the failure of a material?
A: Yes, Young's Modulus can be used to predict the failure of a material. By knowing the Young's Modulus of a material, engineers can predict when it will fail under different types of stress. This is because the material's ability to withstand deformation under stress is directly related to its Young's Modulus.
Q: What are some common applications of Young's Modulus?
A: Young's Modulus has many common applications in engineering and materials science. Some examples include:
- Designing bridges and buildings to withstand wind and seismic loads
- Developing new materials with improved strength and durability
- Predicting the behavior of materials under different types of stress
- Optimizing the design of mechanical systems, such as gears and bearings
Conclusion
In this article, we have answered some frequently asked questions about Young's Modulus. We have discussed the difference between Young's Modulus and modulus of rigidity, the unit of Young's Modulus, and how it is related to the strength of a material. We have also discussed how Young's Modulus can be used to predict the behavior of a material under different types of stress and how it can be affected by temperature. Finally, we have discussed some common applications of Young's Modulus in engineering and materials science.
Additional Resources
For more information on Young's Modulus, we recommend the following resources:
- "Young's Modulus" by Wikipedia
- "Young's Modulus" by HyperPhysics
- "Young's Modulus" by Engineering Toolbox
We hope this article has been helpful in answering your questions about Young's Modulus. If you have any further questions, please don't hesitate to contact us.