Conservation of Momentum Calculator
Calculate collision outcomes using the principle of conservation of momentum
The conservation of momentum is a fundamental principle of physics stating that the total momentum of an isolated system remains constant over time. In collisions:
Total Momentum Before = Total Momentum After
m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f
Where:
- m₁, m₂ are the masses of the objects
- v₁ᵢ, v₂ᵢ are initial velocities
- v₁f, v₂f are final velocities
There are three main types of collisions:
- Elastic Collision: Both momentum and kinetic energy are conserved. Common in atomic and subatomic collisions.
- Inelastic Collision: Only momentum is conserved, while some kinetic energy is converted to other forms (heat, sound, deformation).
- Perfectly Inelastic Collision: Objects stick together after collision, moving with the same final velocity. Maximum loss of kinetic energy.
Key equations for different collision types:
Elastic Collision:
v₁f = ((m₁-m₂)v₁ᵢ + 2m₂v₂ᵢ)/(m₁+m₂)
v₂f = (2m₁v₁ᵢ - (m₁-m₂)v₂ᵢ)/(m₁+m₂)
Perfectly Inelastic:
v₁f = v₂f = (m₁v₁ᵢ + m₂v₂ᵢ)/(m₁+m₂)
Important quantities to consider:
- Total momentum (always conserved)
- Kinetic energy (conserved only in elastic collisions)
- Relative velocity (changes based on collision type)
Conservation of momentum has numerous practical applications:
- Vehicle Collisions: Analyzing car crashes and designing safety features
- Sports Physics: Understanding billiards, bowling, and ball games
- Space Travel: Rocket propulsion and satellite maneuvers
- Particle Physics: Studying subatomic particle collisions
- Industrial Processes: Design of impact testing and material processing
Why is momentum always conserved in collisions?
Momentum conservation is a consequence of Newton's laws and the symmetry of space. In an isolated system, with no external forces, the total momentum must remain constant.
What happens to "lost" kinetic energy in inelastic collisions?
The kinetic energy that appears to be "lost" is actually converted to other forms of energy, such as heat, sound, or the energy of deformation in the colliding objects.
Are perfectly elastic collisions possible in real life?
True perfectly elastic collisions are rare in macroscopic systems. They occur mainly at the atomic and subatomic level. However, some collisions, like those between billiard balls, can be very close to elastic.