Hooke's Law Calculator
Spring force & energy calculator
Calculation Mode
Spring Parameters
Spring Visualization
Spring Properties
Force vs Displacement
Energy vs Displacement
Real-World Hooke's Law Examples
Click on an example to use its values in the calculator
| Scenario | Spring Constant | Displacement | Force | Energy |
|---|
Car Suspension Spring Analysis
Force and energy for a typical car suspension spring (k = 25,000 N/m) at various compressions
| Compression | Displacement | Spring Force | Potential Energy | Equivalent Weight |
|---|
Interesting Facts
Robert Hooke
Hooke's Law was discovered by Robert Hooke in 1660, published in 1678 as "Ut tensio, sic vis" (As the extension, so the force)
Car Suspension
Typical car suspension springs have k = 20,000-40,000 N/m, compressing 5-15 cm under vehicle weight
Bungee Jumping
Bungee cords have k = 50-200 N/m, stretching 20-50 m to safely stop a jumper
Pendulum Clocks
Pendulum period T = 2π√(L/g) is independent of mass, making clocks accurate
Understanding Hooke's Law
What is Hooke's Law?
Hooke's Law states that the force needed to extend or compress a spring is directly proportional to the distance of extension or compression. It's a fundamental principle in physics and engineering.
- Formula: F = -kx (the negative sign indicates restoring force)
- Linear relationship: Force is proportional to displacement
- Elastic limit: Law only applies within elastic limit
- Named after: Robert Hooke (1635-1703), English physicist
Key Formulas
The fundamental equations of spring mechanics:
- Hooke's Law: F = -kx
- Spring Constant: k = F/x
- Displacement: x = F/k
- Elastic Potential Energy: PE = ½kx²
- Work Done: W = ½kx²
- Oscillation Period: T = 2π√(m/k)
- Frequency: f = 1/T = (1/2π)√(k/m)
- Angular Frequency: ω = √(k/m) = 2πf
Spring Constant (k)
The spring constant measures stiffness:
- High k: Stiff spring (hard to compress/stretch)
- Low k: Soft spring (easy to compress/stretch)
- Units: N/m (Newtons per meter)
- Example: Car suspension ~25,000 N/m, pen spring ~10 N/m
Elastic Potential Energy
Energy stored in a compressed or stretched spring:
- Formula: PE = ½kx²
- Proportional to x²: Doubling displacement quadruples energy
- Conservation: PE converts to kinetic energy in oscillation
- Maximum PE: At maximum displacement (amplitude)
Simple Harmonic Motion
When a mass is attached to a spring, it oscillates:
- Period: T = 2π√(m/k) (independent of amplitude)
- Frequency: f = 1/T
- Maximum velocity: v_max = ωA = A√(k/m)
- Maximum acceleration: a_max = ω²A = A(k/m)
- Energy conservation: PE + KE = constant
Real-World Applications
- Vehicle Suspension: Car, truck, motorcycle springs
- Mechanical Watches: Mainspring stores energy
- Bungee Jumping: Elastic cord deceleration
- Trampolines: Elastic surface for jumping
- Shock Absorbers: Vehicle and building damping
- Scales: Spring-based weight measurement
Limitations
Hooke's Law has important limitations:
- Elastic limit: Only valid within elastic limit
- Plastic deformation: Beyond limit, permanent deformation
- Non-linear springs: Some springs don't follow linear relationship
- Temperature effects: Spring constant changes with temperature
Key Takeaways
F = -kx
Spring force is proportional to displacement, directed opposite to displacement
PE = ½kx²
Elastic potential energy is proportional to the square of displacement
T = 2π√(m/k)
Oscillation period depends only on mass and spring constant
Elastic Limit
Hooke's Law only applies within the elastic limit of the material
Understanding Hooke's Law
Hooke's Law is a fundamental principle in physics that describes the relationship between the force applied to a spring and its resulting displacement. From car suspensions to mechanical watches, Hooke's Law governs the behavior of elastic materials in countless applications. Understanding these principles is essential for physics, engineering, and many practical applications.
Hooke's Law Formulas
Key formulas for spring mechanics:
- Hooke's Law: F = -kx (Force = -spring constant × displacement)
- Spring Constant: k = F/x
- Elastic Potential Energy: PE = ½kx²
- Oscillation Period: T = 2π√(m/k)
- Frequency: f = 1/T = (1/2π)√(k/m)
Key Relationships
Important relationships in spring mechanics:
- Force ∝ x: Force is directly proportional to displacement
- PE ∝ x²: Energy is proportional to the square of displacement
- T ∝ √m: Period is proportional to the square root of mass
- T ∝ 1/√k: Period is inversely proportional to the square root of spring constant
Real-World Examples
Hooke's Law in everyday life:
- Car suspension: Springs absorb road shocks (k ≈ 25,000 N/m)
- Bungee jumping: Elastic cord decelerates jumper (k ≈ 50-200 N/m)
- Trampolines: Elastic surface stores and releases energy
- Mechanical watches: Mainspring stores energy for timekeeping
- Spring scales: Measure weight by spring extension
Using This Calculator
Follow these steps:
- Step 1: Select calculation mode (Force, Spring Constant, Displacement, or Energy)
- Step 2: Enter the known values with appropriate units
- Step 3: Optionally enter mass for oscillation calculations
- Step 4: Click "Calculate" to see all spring properties
- Step 5: View spring visualization with compression/extension
- Step 6: See force vs displacement and energy vs displacement charts
- Step 7: Check the Examples tab for real-world cases
- Step 8: Read the Guide tab to learn spring physics theory
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