Elastic Potential Energy Calculator
Calculate elastic potential energy stored in springs and elastic materials
Calculate Elastic Potential Energy
Proportionality constant describing spring stiffness
Distance stretched or compressed from equilibrium position
Calculation Results
Primary formula: U = ½kx² = ½ × 80 × 0.15² = 0.9 J
Hooke's Law: F = kx = 80 × 0.15 = 12 N
Alternative formula: U = ½Fx = ½ × 12 × 0.15 = 0.9 J
Example Calculation
Spring Compression Example
Given: Spring constant k = 80 N/m, Compression x = 0.15 m
Formula: U = ½kx²
Calculation: U = ½ × 80 × (0.15)² = ½ × 80 × 0.0225 = 0.9 J
Result: The spring stores 0.9 J of elastic potential energy
Alternative Method Using Force
Force: F = kx = 80 × 0.15 = 12 N
Energy: U = ½Fx = ½ × 12 × 0.15 = 0.9 J
Verification: Both methods give the same result
Applications
Mechanical Systems
Springs in vehicles, machines, and devices
Energy Storage
Rubber bands, bow strings, elastic materials
Engineering Design
Shock absorbers, suspension systems
Safety Systems
Crumple zones, elastic barriers
Important Notes
Elastic Limit: Springs have maximum deformation before permanent damage
Always Positive: Elastic potential energy is always positive regardless of compression or extension
Energy Conservation: Energy stored equals work done to deform the spring
Displacement: Measured from equilibrium position, not absolute position
Hooke's Law: Applies only within elastic limit of material
Understanding Elastic Potential Energy
What is Elastic Potential Energy?
Elastic potential energy is the energy stored in elastic materials when they are stretched, compressed, or deformed. This energy is "potential" because it has the capacity to do work when the material returns to its original shape.
Why is it Always Positive?
Whether you compress or stretch a spring, you're doing positive work against the restoring force. This work is stored as energy, making elastic potential energy always positive regardless of the direction of deformation.
Real-World Examples
- •Bow and arrow: Energy stored in bent bow propels arrow
- •Trampolines: Stretched fabric stores energy for bounce
- •Car suspension: Springs absorb road impact energy
Mathematical Formulas
Primary Formula (Hooke's Law)
U = ½kx²
- U = Elastic potential energy (Joules)
- k = Spring constant (N/m)
- x = Displacement from equilibrium (m)
Alternative Formula (Using Force)
U = ½Fx
Where F = kx (Hooke's Law)
Energy per Unit Volume
u = ½ × stress × strain
For materials under stress
Step-by-Step Calculation Guide
Method 1: Using Spring Constant
- 1. Identify the spring constant (k) in N/m
- 2. Measure displacement from equilibrium (x) in meters
- 3. Square the displacement: x²
- 4. Multiply by spring constant: k × x²
- 5. Divide by 2: U = ½kx²
Method 2: Using Applied Force
- 1. Measure the applied force (F) in Newtons
- 2. Measure displacement (x) in meters
- 3. Multiply force by displacement: F × x
- 4. Divide by 2: U = ½Fx
- 5. This equals ½kx² since F = kx
Energy Relationships
| Scenario | Energy Transformation | Example |
|---|---|---|
| Compression | Work → Elastic PE | Compressing a spring |
| Release | Elastic PE → Kinetic Energy | Spring returning to position |
| Oscillation | PE ↔ KE | Mass on a spring system |