Elastic Potential Energy in a Stretched Wire
The energy stored per unit volume in a deformed elastic material due to the work done in deforming it.
What is Elastic Potential Energy in a Stretched Wire?
The potential energy stored in an elastic object as a result of stretching or compressing it.
Key formula / rule: Work Done (Average Force)
Key points
- Define elastic potential energy.
- Derive the formula for elastic potential energy stored in a stretched wire.
- Calculate the elastic potential energy for given parameters.
- Relate elastic potential energy to work done and material properties.
Common exam trap
Using the final force instead of the average force to calculate work done.
Definitions
- Term
Elastic Potential Energy
- Meaning
The potential energy stored in an elastic object as a result of stretching or compressing it.
- Term
Work Done
- Meaning
The energy transferred to or from an object by the application of force along a displacement.
- Term
Energy Density
- Meaning
The amount of potential energy stored per unit volume of a material.
Learning objectives
Define elastic potential energy.
Derive the formula for elastic potential energy stored in a stretched wire.
Calculate the elastic potential energy for given parameters.
Relate elastic potential energy to work done and material properties.
Formulae
- Name
Work Done (Average Force)
- Note
Where Fapplied is the force causing extension and x is the extension.
- Expression
W = (1/2) * Fapplied * x
- Name
Elastic Potential Energy (in terms of Force and Extension)
- Note
This is the energy stored in the wire, equal to the work done.
- Expression
U = (1/2) * F * x
- Name
Elastic Potential Energy (in terms of Young's Modulus)
- Note
Where Y is Young's Modulus, A is cross-sectional area, x is extension, and L is original length.
- Expression
U = (1/2) * Y * A * (x2 / L)
- Name
Elastic Potential Energy (in terms of Stress and Strain)
- Note
Volume = A * L. This represents energy per unit volume multiplied by volume.
- Expression
U = (1/2) * Stress * Strain * Volume
- Name
Energy Density (Energy per unit volume)
- Note
This is the elastic potential energy stored per unit volume of the material.
- Expression
u = (1/2) * Stress * Strain
Prerequisites
Hooke's Law
Stress and Strain
Young's Modulus
Work and Energy
Common mistakes
Using the final force instead of the average force to calculate work done.
Confusing elastic potential energy with kinetic energy.
Forgetting to consider the volume of the wire when calculating energy density.
Assuming the force is constant during stretching.
Keywords
Elastic Potential Energy
Stretched Wire
Work Done
Young's Modulus
Stress
Strain
Energy Density
Hooke's Law
Practice preview
What is the unit of elastic potential energy stored in a stretched wire?…
easy
If the force applied to a wire is doubled, while keeping other factors constant, how does the elastic potential energy stored in the wire change?…
medium
If a wire of length L and cross-sectional area A is stretched by a force F, and its extension is x, what is the work done in stretching the wire, assuming the force is applied gradually?…
medium