If A Wire $30 \, \text{cm}$ Long Is Extended To $1030.5 \, \text{cm}$ By A Force Of $300 \, \text{N}$, Find The Strain Energy Of The Wire.

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Introduction

Strain energy is the energy stored in a material when it is subjected to stress, such as when a wire is stretched or compressed. In this article, we will explore the concept of strain energy and how to calculate it using the given information about a wire that is extended by a force of $300 \, \text{N}$.

What is Strain Energy?

Strain energy is a measure of the energy stored in a material when it is subjected to stress. It is a fundamental concept in physics and engineering, and is used to describe the energy stored in a material when it is deformed or stretched. Strain energy is typically measured in units of joules (J) or newton-meters (N·m).

Calculating Strain Energy

To calculate the strain energy of a wire, we need to know the force applied to the wire, the distance over which the force is applied, and the cross-sectional area of the wire. The formula for calculating strain energy is:

$$U = \frac{1}{2} F \Delta x$$

where $U$ is the strain energy, $F$ is the force applied to the wire, and $\Delta x$ is the distance over which the force is applied.

Given Information

We are given that a wire $30 \, \text{cm}$ long is extended to $1030.5 \, \text{cm}$ by a force of $300 \, \text{N}$. We can use this information to calculate the strain energy of the wire.

Calculating the Distance Over Which the Force is Applied

To calculate the strain energy, we need to know the distance over which the force is applied. We can calculate this distance by subtracting the initial length of the wire from the final length of the wire:

$$\Delta x = 1030.5 \, \text{cm} - 30 \, \text{cm} = 1000.5 \, \text{cm}$$

Converting the Distance to Meters

We need to convert the distance from centimeters to meters in order to use it in the formula for calculating strain energy. There are $100 \, \text{cm}$ in $1 \, \text{m}$, so we can convert the distance as follows:

$$\Delta x = 1000.5 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 10.005 \, \text{m}$$

Calculating the Strain Energy

Now that we have the distance over which the force is applied, we can calculate the strain energy using the formula:

$$U = \frac{1}{2} F \Delta x$$

Substituting the values we have, we get:

$$U = \frac{1}{2} \times 300 \, \text{N} \times 10.005 \, \text{m} = 1500.75 \, \text{J}$$

Conclusion

In this article, we have explored the concept of strain energy and how to calculate it using the given information about a wire that is extended by a force of $300 \, \text{N}$. We have calculated the strain energy of the wire using the formula $U = \frac{1}{2} F \Delta x$, and have found that the strain energy is $1500.75 \, \text{J}$.

References

• [1] Physics for Scientists and Engineers, 3rd edition, by Paul A. Tipler and Gene Mosca.
• [2] Mechanics of Materials, 7th edition, by Russell C. Hibbeler.

Further Reading

• Strain Energy, Wikipedia.
• Mechanics of Materials, Wikipedia.

Glossary

• Strain Energy: The energy stored in a material when it is subjected to stress.
• Force: A push or pull that causes an object to change its motion or shape.
• Distance: A measure of the length between two points.
• Joule: A unit of energy, equal to $1 \, \text{N} \cdot \text{m}$.

FAQs

• Q: What is strain energy? A: Strain energy is the energy stored in a material when it is subjected to stress.
• Q: How do I calculate the strain energy of a wire? A: To calculate the strain energy of a wire, you need to know the force applied to the wire, the distance over which the force is applied, and the cross-sectional area of the wire. You can use the formula $U = \frac{1}{2} F \Delta x$ to calculate the strain energy.
• Q: What is the unit of strain energy? A: The unit of strain energy is joules (J) or newton-meters (N·m).
  

Q: What is strain energy?

A: Strain energy is the energy stored in a material when it is subjected to stress, such as when a wire is stretched or compressed. It is a measure of the energy stored in a material due to its deformation.

Q: How do I calculate the strain energy of a wire?

A: To calculate the strain energy of a wire, you need to know the force applied to the wire, the distance over which the force is applied, and the cross-sectional area of the wire. You can use the formula $U = \frac{1}{2} F \Delta x$ to calculate the strain energy.

Q: What is the unit of strain energy?

A: The unit of strain energy is joules (J) or newton-meters (N·m).

Q: What is the difference between strain energy and potential energy?

A: Strain energy is the energy stored in a material due to its deformation, while potential energy is the energy stored in an object due to its position or configuration.

Q: Can strain energy be negative?

A: No, strain energy cannot be negative. It is always a positive quantity, representing the energy stored in a material due to its deformation.

Q: How does strain energy relate to the stiffness of a material?

A: Strain energy is directly proportional to the stiffness of a material. The stiffer a material is, the more strain energy it will store when deformed.

Q: Can strain energy be used to predict the failure of a material?

A: Yes, strain energy can be used to predict the failure of a material. When the strain energy stored in a material exceeds a certain threshold, it can lead to material failure.

Q: How does strain energy relate to the stress-strain curve of a material?

A: Strain energy is related to the stress-strain curve of a material. The area under the stress-strain curve represents the strain energy stored in the material.

Q: Can strain energy be used to design structures?

A: Yes, strain energy can be used to design structures. By analyzing the strain energy stored in a structure, engineers can determine its stability and potential for failure.

Q: How does strain energy relate to the concept of fatigue?

A: Strain energy is related to the concept of fatigue. Repeated loading and unloading of a material can lead to the accumulation of strain energy, which can cause material failure.

Q: Can strain energy be used to predict the behavior of materials under dynamic loading?

A: Yes, strain energy can be used to predict the behavior of materials under dynamic loading. By analyzing the strain energy stored in a material, engineers can determine its response to dynamic loading.

Q: How does strain energy relate to the concept of vibration?

A: Strain energy is related to the concept of vibration. The vibration of a structure can lead to the accumulation of strain energy, which can cause material failure.

Q: Can strain energy be used to design vibration-damping systems?

A: Yes, strain energy can be used to design vibration-damping systems. By analyzing the strain energy stored in a system, engineers can design systems that can effectively dampen vibrations.

Q: How does strain energy relate to the concept of thermal expansion?

A: Strain energy is related to the concept of thermal expansion. The thermal expansion of a material can lead to the accumulation of strain energy, which can cause material failure.

Q: Can strain energy be used to predict the behavior of materials under thermal loading?

A: Yes, strain energy can be used to predict the behavior of materials under thermal loading. By analyzing the strain energy stored in a material, engineers can determine its response to thermal loading.

Q: How does strain energy relate to the concept of creep?

A: Strain energy is related to the concept of creep. The creep of a material can lead to the accumulation of strain energy, which can cause material failure.

Q: Can strain energy be used to predict the behavior of materials under creep loading?

A: Yes, strain energy can be used to predict the behavior of materials under creep loading. By analyzing the strain energy stored in a material, engineers can determine its response to creep loading.

Q: How does strain energy relate to the concept of fracture mechanics?

A: Strain energy is related to the concept of fracture mechanics. The fracture of a material can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to design fracture-resistant materials?

A: Yes, strain energy can be used to design fracture-resistant materials. By analyzing the strain energy stored in a material, engineers can design materials that are resistant to fracture.

Q: How does strain energy relate to the concept of material failure?

A: Strain energy is related to the concept of material failure. The failure of a material can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to predict the behavior of materials under impact loading?

A: Yes, strain energy can be used to predict the behavior of materials under impact loading. By analyzing the strain energy stored in a material, engineers can determine its response to impact loading.

Q: How does strain energy relate to the concept of material damage?

A: Strain energy is related to the concept of material damage. The damage of a material can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to design damage-resistant materials?

A: Yes, strain energy can be used to design damage-resistant materials. By analyzing the strain energy stored in a material, engineers can design materials that are resistant to damage.

Q: How does strain energy relate to the concept of material degradation?

A: Strain energy is related to the concept of material degradation. The degradation of a material can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to predict the behavior of materials under cyclic loading?

A: Yes, strain energy can be used to predict the behavior of materials under cyclic loading. By analyzing the strain energy stored in a material, engineers can determine its response to cyclic loading.

Q: How does strain energy relate to the concept of material fatigue?

A: Strain energy is related to the concept of material fatigue. The fatigue of a material can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to design fatigue-resistant materials?

A: Yes, strain energy can be used to design fatigue-resistant materials. By analyzing the strain energy stored in a material, engineers can design materials that are resistant to fatigue.

Q: How does strain energy relate to the concept of material failure under dynamic loading?

A: Strain energy is related to the concept of material failure under dynamic loading. The failure of a material under dynamic loading can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to predict the behavior of materials under dynamic loading?

A: Yes, strain energy can be used to predict the behavior of materials under dynamic loading. By analyzing the strain energy stored in a material, engineers can determine its response to dynamic loading.

Q: How does strain energy relate to the concept of material failure under thermal loading?

A: Strain energy is related to the concept of material failure under thermal loading. The failure of a material under thermal loading can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to predict the behavior of materials under thermal loading?

A: Yes, strain energy can be used to predict the behavior of materials under thermal loading. By analyzing the strain energy stored in a material, engineers can determine its response to thermal loading.

Q: How does strain energy relate to the concept of material failure under creep loading?

A: Strain energy is related to the concept of material failure under creep loading. The failure of a material under creep loading can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to predict the behavior of materials under creep loading?

A: Yes, strain energy can be used to predict the behavior of materials under creep loading. By analyzing the strain energy stored in a material, engineers can determine its response to creep loading.

Q: How does strain energy relate to the concept of material failure under impact loading?

A: Strain energy is related to the concept of material failure under impact loading. The failure of a material under impact loading can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to predict the behavior of materials under impact loading?

A: Yes, strain energy can be used to predict the behavior of materials under impact loading. By analyzing the strain energy stored in a material, engineers can determine its response to impact loading.

Q: How does strain energy relate to the concept of material failure under cyclic loading?

A: Strain energy is related to the concept of material failure under cyclic loading. The failure of a material under cyclic loading can be predicted by analyzing the strain energy stored in the material.

Q: Can strain energy be used to predict the behavior of materials under cyclic loading?

A: Yes, strain energy can be used to predict the behavior of materials under cyclic loading. By analyzing the strain energy stored in a material, engineers can determine its response to cyclic loading.

Q: How does strain energy relate to the concept of material failure under dynamic loading?

A: Strain energy is related to the concept of material failure under dynamic loading. The failure