Hooke's Law Calculator
Calculate spring force, displacement, or spring constant using Hooke's Law formula F = -kΔx
Calculate Using Hooke's Law
Calculate displacement from initial and final spring lengths
Stiffness of the spring (resistance to deformation)
Distance spring is stretched or compressed
Hooke's Law Results
Formula used: F = -kΔx (absolute value shown)
Note: The negative sign indicates the restoring force acts opposite to displacement
Elastic PE formula: PE = ½kx²
Example Calculation
Spring Force Problem
Given:
• Spring constant (k) = 80 N/m
• Displacement (Δx) = 0.15 m (stretched)
Find: Spring force (F)
Solution
Using Hooke's Law: F = kΔx
F = 80 N/m × 0.15 m
F = 12 N
Note: Actual force direction is opposite to displacement (restoring force)
Spring Stiffness Guide
Soft Springs
k < 100 N/m
Easy to stretch/compress
Medium Springs
100-1000 N/m
Moderate resistance
Stiff Springs
k > 1000 N/m
High resistance to deformation
Hooke's Law Tips
Force is proportional to displacement for elastic springs
Restoring force always acts opposite to displacement
Higher spring constant means stiffer spring
Hooke's Law applies only within elastic limit
Energy stored in spring = ½kx²
Understanding Hooke's Law
What is Hooke's Law?
Hooke's Law describes the relationship between the force applied to an elastic object (like a spring) and the resulting displacement. It states that the force is proportional to the displacement, provided the elastic limit is not exceeded.
Key Principles
- •Force is directly proportional to displacement
- •Restoring force opposes the applied force
- •Spring constant determines stiffness
- •Only valid within elastic limit
Formula Explanation
F = -kΔx
- F: Spring force (Newtons, N)
- k: Spring constant (N/m)
- Δx: Displacement from equilibrium (meters, m)
- Negative sign: Indicates restoring force direction
Remember: The larger the spring constant (k), the stiffer the spring and the more force required for the same displacement.
Elastic Potential Energy
When a spring is compressed or stretched, it stores elastic potential energy. This energy can be calculated using the formula PE = ½kx², where the energy is proportional to the square of the displacement.
Applications of Hooke's Law:
- • Automotive suspension systems
- • Mechanical scales and balances
- • Elastic materials and rubber bands
- • Shock absorbers and dampers
- • Watch springs and clockwork
- • Trampolines and bungee cords