Potential Energy of a Spring
Determining the elastic potential energy stored in a spring when it is compressed or stretched from its equilibrium position.
What is Potential Energy of a Spring?
A measure of the stiffness of an elastic object, such as a spring. It is the ratio of the force applied to the resulting displacement.
Key formula / rule: Potential Energy of a Spring
Key points
- Understand the concept of elastic potential energy.
- Derive the formula for the potential energy of a spring.
- Calculate the potential energy stored in a spring for a given displacement.
- Relate spring constant to potential energy.
Common exam trap
Confusing displacement 'x' with the total length of the spring.
Definitions
- Term
Spring Constant (k)
- Meaning
A measure of the stiffness of an elastic object, such as a spring. It is the ratio of the force applied to the resulting displacement.
- Term
Elastic Potential Energy
- Meaning
The potential energy stored in an elastic object (like a spring) as a result of stretching or compressing it.
- Term
Equilibrium Position
- Meaning
The position of a spring when it is neither stretched nor compressed; its natural length.
Learning objectives
Understand the concept of elastic potential energy.
Derive the formula for the potential energy of a spring.
Calculate the potential energy stored in a spring for a given displacement.
Relate spring constant to potential energy.
Formulae
- Name
Potential Energy of a Spring
- Note
Where U is potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
- Expression
U = ½kx²
- Name
Hooke's Law (Force)
- Note
Where F is the restoring force exerted by the spring, k is the spring constant, and x is the displacement from equilibrium.
- Expression
F = -kx
Prerequisites
Hooke's Law
Work and Energy concepts
Basic Calculus (Integration)
Common mistakes
Confusing displacement 'x' with the total length of the spring.
Forgetting to square the displacement in the potential energy formula.
Incorrectly applying Hooke's Law for non-ideal springs.
Using the wrong sign for force or displacement in calculations.
Keywords
Potential Energy
Spring
Elastic
Hooke's Law
Spring Constant
Displacement
Work
Energy
Practice preview
If the displacement of a spring from its equilibrium position is doubled, how does the elastic potential energy stored in it change?…
easy
A spring stores 8 J of elastic potential energy when it is stretched by 0.2 m. What is the spring constant of the spring?…
medium
A spring with a spring constant of 200 N/m is stretched by 0.1 m from its equilibrium position. Calculate the elastic potential energy stored in the spring.…
easy