Hooke's Law Calculator
Calculate spring force and elastic potential energy using Hooke's Law
Hooke's Law states that the force needed to extend or compress a spring by some distance is proportional to that distance. The law is expressed as:
Where:
- F = Force (in Newtons, N)
- k = Spring constant (in Newtons per meter, N/m)
- x = Displacement from equilibrium (in meters, m)
- The negative sign indicates that the force acts in the opposite direction to the displacement
When a spring is stretched or compressed, it stores elastic potential energy. This energy is calculated using the formula:
Where:
- PE = Potential Energy (in Joules, J)
- k = Spring constant (in N/m)
- x = Displacement from equilibrium (in m)
The elastic potential energy is always positive, regardless of whether the spring is stretched or compressed.
Hooke's Law has numerous practical applications:
- Engineering: Design of spring-based devices and mechanical systems
- Automotive: Suspension systems and shock absorbers
- Manufacturing: Quality control of elastic materials
- Sports Equipment: Design of trampolines and exercise equipment
- Musical Instruments: String instruments and their tuning
What is the elastic limit?
The elastic limit is the maximum stress that a material can withstand while still returning to its original shape when the stress is removed. Beyond this limit, Hooke's Law no longer applies and permanent deformation occurs.
Why is the spring constant important?
The spring constant (k) characterizes the stiffness of a spring. A higher spring constant means the spring is stiffer and requires more force to stretch or compress it by a given distance.
Does Hooke's Law apply to all materials?
Hooke's Law applies only within the elastic region of a material's behavior. Most materials follow Hooke's Law for small deformations, but deviate from it under larger stresses or strains.