Elastic Collisions
Explore the fundamental principles of momentum and energy conservation through interactive collision simulations.
Ball 1 (Blue)
Momentum: 50.0 kg·m/s
Kinetic Energy: 1250.0 J
Ball 2 (Red)
Momentum: 30.0 kg·m/s
Kinetic Energy: 450.0 J
Environment
Elastic Collision Theory
Conservation of Momentum
In any collision, total momentum is conserved:
m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f
Conservation of Kinetic Energy
In elastic collisions, kinetic energy is also conserved:
½m₁v₁ᵢ² + ½m₂v₂ᵢ² = ½m₁v₁f² + ½m₂v₂f²
Final Velocities (1D)
For one-dimensional elastic collisions:
v₁f = ((m₁ - m₂)v₁ᵢ + 2m₂v₂ᵢ) / (m₁ + m₂)
v₂f = ((m₂ - m₁)v₂ᵢ + 2m₁v₁ᵢ) / (m₁ + m₂)
Key Observations
- When equal masses collide head-on, they exchange velocities
- A light ball bounces back when hitting a heavy stationary ball
- A heavy ball continues forward when hitting a light stationary ball
- Total momentum and kinetic energy remain constant throughout
Learning Objectives
- ✓Understand conservation of momentum in isolated systems
- ✓Observe conservation of kinetic energy in elastic collisions
- ✓Analyze how mass ratios affect collision outcomes
- ✓Apply collision formulas to predict final velocities
- ✓Explore special cases: equal masses, stationary targets
💡 Experimentation Tips
- •Equal Masses: Set both masses to the same value and observe velocity exchange
- •Heavy vs Light: Try m₁ = 5kg, m₂ = 0.5kg to see dramatic effects
- •Head-on Collision: Set opposite velocities for classic collision scenario
- •Add Gravity: Enable gravity to see parabolic trajectories after collision
- •Watch Conservation: Monitor total momentum and KE - they should stay constant!
🌍 Real-World Applications
Billiards & Pool
Ball collisions approximate elastic collisions, allowing players to predict ball trajectories.
Particle Physics
Collision experiments in particle accelerators use these principles to study subatomic particles.
Molecular Dynamics
Gas molecules collide elastically, helping explain temperature and pressure in thermodynamics.
Vehicle Safety
Understanding collision physics helps design safer cars and predict crash outcomes.