A Piece Of Rubber 10 Cm Long Stretches 6 Mm When A Load Of 100 N Is Hung From It. What Is The Strain?A. ${ 60\$} B. ${ 6\$} C. ${ 6 \times 10^{-2}\$} D. ${ 6 \times 10^{-3}\$}

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Understanding Strain: A Fundamental Concept in Physics

In the world of physics, strain is a crucial concept that helps us understand how materials respond to external forces. It's a measure of the deformation of a material when a force is applied to it. In this article, we'll delve into the concept of strain, its formula, and how to calculate it using a simple example.

What is Strain?

Strain is a dimensionless quantity that represents the ratio of the change in length of a material to its original length. It's a measure of how much a material stretches or compresses when a force is applied to it. Strain is usually denoted by the symbol ε (epsilon) and is expressed as a decimal value.

Formula for Strain

The formula for strain is:

ε = ΔL / L

where ε is the strain, ΔL is the change in length, and L is the original length.

Example Problem

Let's consider the example given in the problem statement: a piece of rubber 10 cm long stretches 6 mm when a load of 100 N is hung from it. We need to calculate the strain in this case.

Step 1: Convert the change in length to the same unit as the original length

First, we need to convert the change in length (6 mm) to the same unit as the original length (10 cm). We can do this by converting 6 mm to centimeters:

6 mm = 0.6 cm

Step 2: Calculate the strain

Now that we have the change in length in the same unit as the original length, we can calculate the strain using the formula:

ε = ΔL / L = 0.6 cm / 10 cm = 0.06

Step 3: Express the strain in scientific notation

We can express the strain in scientific notation as:

ε = 6 × 10^(-2)

Conclusion

In conclusion, the strain in the given example is 6 × 10^(-2). This means that the rubber stretches by 6% of its original length when a load of 100 N is hung from it.

Comparison with Answer Options

Now that we have calculated the strain, let's compare it with the answer options:

A. 60 B. 6 C. 6 × 10^(-2) D. 6 × 10^(-3)

Our calculated value of 6 × 10^(-2) matches with option C.

Importance of Strain in Real-World Applications

Strain is an important concept in various real-world applications, such as:

  • Engineering: Strain is used to design and analyze structures, such as bridges, buildings, and machines.
  • Materials Science: Strain is used to study the properties of materials, such as their strength, stiffness, and ductility.
  • Biomechanics: Strain is used to study the movement and deformation of living tissues, such as bones, muscles, and tendons.

Conclusion

In conclusion, strain is a fundamental concept in physics that helps us understand how materials respond to external forces. By calculating the strain in a given example, we can gain insights into the properties of materials and their behavior under different loads.
Frequently Asked Questions (FAQs) on Strain

Q: What is the difference between strain and stress?

A: Strain and stress are two related but distinct concepts in physics. Stress is the force applied to a material per unit area, while strain is the resulting deformation of the material. In other words, stress causes strain.

Q: How is strain measured?

A: Strain is typically measured using instruments such as strain gauges, extensometers, or laser interferometers. These instruments measure the change in length or deformation of a material under a given load.

Q: What are the units of strain?

A: Strain is a dimensionless quantity, which means it has no units. However, it can be expressed in terms of a percentage or a decimal value.

Q: What is the relationship between strain and Young's modulus?

A: Young's modulus is a measure of a material's stiffness, and it is related to strain by the following equation:

Y = E / ε

where Y is Young's modulus, E is the stress, and ε is the strain.

Q: Can strain be negative?

A: Yes, strain can be negative. This occurs when a material is compressed or shrinks under a given load.

Q: What is the difference between elastic and plastic strain?

A: Elastic strain is a reversible deformation that occurs when a material is loaded within its elastic limit. Plastic strain, on the other hand, is an irreversible deformation that occurs when a material is loaded beyond its elastic limit.

Q: How does strain affect the properties of a material?

A: Strain can affect the properties of a material in several ways, including:

  • Strength: Strain can reduce the strength of a material by causing it to deform or break.
  • Stiffness: Strain can reduce the stiffness of a material by causing it to become more flexible.
  • Ductility: Strain can increase the ductility of a material by allowing it to deform without breaking.

Q: Can strain be used to predict the behavior of a material under different loads?

A: Yes, strain can be used to predict the behavior of a material under different loads. By analyzing the strain response of a material to various loads, engineers can design and optimize structures and systems to withstand different types of loading.

Q: What are some common applications of strain in engineering?

A: Strain is used in a wide range of engineering applications, including:

  • Structural analysis: Strain is used to analyze the behavior of structures under various loads, such as wind, earthquakes, and traffic.
  • Materials selection: Strain is used to select materials for specific applications based on their properties and behavior.
  • Design optimization: Strain is used to optimize the design of structures and systems to minimize weight, maximize strength, and improve performance.

Conclusion

In conclusion, strain is a fundamental concept in physics that plays a critical role in understanding the behavior of materials under different loads. By analyzing the strain response of a material, engineers can design and optimize structures and systems to withstand various types of loading.