Energy Conservation
Discover how energy transforms between kinetic, potential, and spring forms while total energy remains constant.
Energy Conservation Principle
Law of Conservation of Energy
In a closed system with no external forces, total mechanical energy remains constant:
E_total = KE + PE + SE = constant
Kinetic Energy (KE)
Energy of motion, depends on mass and velocity:
KE = ½mv²
Potential Energy (PE)
Stored energy due to position in a gravitational field:
PE = mgh
Spring Potential Energy (SE)
Energy stored in a compressed or stretched spring:
SE = ½kx²
Energy Transformations
- Pendulum: PE ↔ KE (at highest point: max PE, at lowest: max KE)
- Free Fall: PE → KE (potential energy converts to kinetic as object falls)
- Ramp: PE → KE (gravitational PE converts to motion)
- Spring: PE ↔ KE ↔ SE (three-way energy exchange)
Learning Objectives
- ✓Understand the law of conservation of energy
- ✓Observe energy transformations between kinetic and potential forms
- ✓Calculate energy in different scenarios (pendulum, free fall, ramp, spring)
- ✓Recognize how damping affects total mechanical energy
- ✓Apply energy conservation to predict motion outcomes
📚 Scenario Guide
🎯 Pendulum
Watch energy oscillate between maximum potential (at peaks) and maximum kinetic (at bottom). Perfect demonstration of PE ↔ KE transformation.
⬇️ Free Fall
Observe gravitational PE converting entirely to KE as the object falls. After bouncing, energy gradually dissipates.
📐 Ramp
See how PE converts to KE as the ball rolls down the incline. The angle affects acceleration but not final energy.
🔄 Spring
Complex three-way energy exchange: gravitational PE, kinetic energy, and elastic spring energy all interact.
💡 Experimentation Tips
- •Watch the Energy Bars: The sum of all energy bars should stay constant (when damping = 100%)
- •Adjust Mass: Heavier objects have more total energy for the same height/speed
- •Change Gravity: Try different gravitational strengths (Moon: 1.6 m/s², Earth: 9.8 m/s², Jupiter: 24.8 m/s²)
- •Damping Effect: Set damping below 100% to see energy gradually lost to friction
- •Compare Scenarios: Notice how the same initial energy manifests differently in each scenario
🌍 Real-World Applications
Roller Coasters
Designed using energy conservation: PE at the top converts to KE at the bottom, creating thrilling speeds.
Hydroelectric Dams
Water's gravitational PE is converted to electrical energy through turbines.
Pendulum Clocks
Rely on consistent energy oscillation between PE and KE for accurate timekeeping.
Regenerative Braking
Electric vehicles convert kinetic energy back to stored electrical energy when braking.
Bungee Jumping
Gravitational PE converts to elastic PE in the cord, then back again.
Satellite Orbits
Satellites constantly exchange KE and PE as they orbit Earth.
📐 Energy Equations Reference
Total Mechanical Energy
E = KE + PE (+ SE for springs)
Kinetic Energy
KE = ½mv² where m = mass, v = velocity
Gravitational Potential Energy
PE = mgh where g = gravity, h = height
Spring Potential Energy
SE = ½kx² where k = spring constant, x = compression