Potential Energy of a Spring
Understanding the elastic potential energy stored in a stretched or compressed spring and its mathematical expression.
What is Potential Energy of a Spring?
Energy stored by deformation, U = (1/2)k x2, measured from the natural length and positive for both extension and compression
Key formula / rule: Hooke's law
Key points
- Use Hooke's law and U = (1/2)k x2 in spring-block energy problems
Common exam trap
Writing the stored energy as k x2 or F x
Definitions
- Name
Elastic potential energy
- Definition
Energy stored by deformation, U = (1/2)k x2, measured from the natural length and positive for both extension and compression
- Name
Spring constant
- Definition
Stiffness k in N/m from Hooke's law F = -k x, the minus sign showing a restoring force
- Name
Exam insight
- Definition
Maximum compression occurs when the block's kinetic energy is fully stored: (1/2)mv2 = (1/2)k x2
- Name
Worked example
- Definition
k = 200 N/m compressed 0.1 m stores 1 J, launching a 0.5 kg block at about 2 m/s
Learning objectives
Use Hooke's law and U = (1/2)k x2 in spring-block energy problems
Formulae
- Name
Hooke's law
- Expression
F = -k x
- Name
Spring energy
- Expression
U = (1/2) k x2
Common mistakes
Writing the stored energy as k x2 or F x
Measuring x from a point other than the natural length
Keywords
spring
hooke's law
spring constant
elastic potential energy
compression
conservative force
energy