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If proportional limit is not exceeded, energy per unit volume in stretched wire is
- a)1/2 x stress x strain
- b)stress x strain
- c)stress x strain 2
- d)1/2 stress x strain 2
Correct answer is 'A'. Can you explain this answer?
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Verified Answer
If proportional limit is not exceeded, energy per unit volume in stret...
strain energy=1/2×stress × strain Work done by a force on a wire
W =2LAy(ΔL)2/2L
=1/2(yALΔ/L)ΔL
=1/2(yΔL/L)(ΔL/L)(AL)
=1/2(Stress)(Strain)(Volume)
(Work)/(volume)=1/2(stress)(strain)
W =2LAy(ΔL)2/2L
=1/2(yALΔ/L)ΔL
=1/2(yΔL/L)(ΔL/L)(AL)
=1/2(Stress)(Strain)(Volume)
(Work)/(volume)=1/2(stress)(strain)
Most Upvoted Answer
If proportional limit is not exceeded, energy per unit volume in stret...
Total energy is givn by 1/2 x stress x strain x Volume.. Hence total energy per unit volume i.e energy density is givn by 1/2 x stress x strain..
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If proportional limit is not exceeded, energy per unit volume in stret...
Energy per Unit Volume in Stretched Wire
Proportional Limit:
- Proportional limit is the maximum stress a material can withstand without undergoing permanent deformation.
- If the proportional limit is not exceeded, the material will return to its original shape when the stress is removed.
- Beyond the proportional limit, the material undergoes plastic deformation and will not return to its original shape.
Energy per Unit Volume:
- Energy per unit volume is the amount of energy required to stretch a material per unit volume.
- It is a measure of how much work is done in deforming the material.
Formula:
- If the proportional limit is not exceeded, the energy per unit volume in a stretched wire can be calculated using the formula: 1/2 x stress x strain.
- Stress is the force applied per unit area of the material.
- Strain is the change in length of the material per unit length.
Explanation:
- The formula 1/2 x stress x strain is derived from the work-energy principle.
- When a material is stretched, work is done on it, and this work is stored as potential energy in the material.
- The potential energy stored per unit volume is proportional to the stress and strain in the material.
- The factor of 1/2 in the formula accounts for the fact that the energy stored in a material is proportional to the square of the strain.
- Therefore, the energy per unit volume in a stretched wire is given by 1/2 x stress x strain if the proportional limit is not exceeded.
Conclusion:
- The formula 1/2 x stress x strain is used to calculate the energy per unit volume in a stretched wire if the proportional limit is not exceeded.
- This formula is derived from the work-energy principle and takes into account the potential energy stored in the material during the deformation process.
Proportional Limit:
- Proportional limit is the maximum stress a material can withstand without undergoing permanent deformation.
- If the proportional limit is not exceeded, the material will return to its original shape when the stress is removed.
- Beyond the proportional limit, the material undergoes plastic deformation and will not return to its original shape.
Energy per Unit Volume:
- Energy per unit volume is the amount of energy required to stretch a material per unit volume.
- It is a measure of how much work is done in deforming the material.
Formula:
- If the proportional limit is not exceeded, the energy per unit volume in a stretched wire can be calculated using the formula: 1/2 x stress x strain.
- Stress is the force applied per unit area of the material.
- Strain is the change in length of the material per unit length.
Explanation:
- The formula 1/2 x stress x strain is derived from the work-energy principle.
- When a material is stretched, work is done on it, and this work is stored as potential energy in the material.
- The potential energy stored per unit volume is proportional to the stress and strain in the material.
- The factor of 1/2 in the formula accounts for the fact that the energy stored in a material is proportional to the square of the strain.
- Therefore, the energy per unit volume in a stretched wire is given by 1/2 x stress x strain if the proportional limit is not exceeded.
Conclusion:
- The formula 1/2 x stress x strain is used to calculate the energy per unit volume in a stretched wire if the proportional limit is not exceeded.
- This formula is derived from the work-energy principle and takes into account the potential energy stored in the material during the deformation process.
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