Conservation of Momentum Calculator
Calculate momentum before and after collisions for elastic, inelastic, and 2D collisions. Visualize physics principles with instant results.
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In an elastic collision, both momentum and kinetic energy are conserved. The objects bounce off each other with no loss of kinetic energy.
Understanding Conservation of Momentum
What is Conservation of Momentum?
The law of conservation of momentum states that in an isolated system (one with no external forces), the total momentum before a collision equals the total momentum after the collision. Momentum is the product of an object’s mass and velocity (p = mv).
Elastic vs. Inelastic Collisions
Elastic Collisions: Both momentum and kinetic energy are conserved. Objects bounce off each other without permanent deformation or heat generation. Examples include billiard balls colliding or atoms in ideal gases.
Inelastic Collisions: Only momentum is conserved; kinetic energy is not conserved. Some energy is transformed into other forms like heat, sound, or deformation. In perfectly inelastic collisions, objects stick together after impact.
Partially Elastic Collisions: These are intermediate cases where some kinetic energy is conserved. The coefficient of restitution (e) measures how “bouncy” the collision is, ranging from 0 (perfectly inelastic) to 1 (perfectly elastic).
Real-World Applications
Conservation of momentum principles are essential in:
- Vehicle crash analysis and safety design
- Rocket propulsion systems
- Sports physics (e.g., billiards, baseball)
- Particle physics experiments
- Astronomy and celestial mechanics
Example Calculation
Consider two cars: Car A (mass = 1500 kg) moving at 20 m/s collides with stationary Car B (mass = 1000 kg). If it’s a perfectly inelastic collision:
Total momentum before = (1500 kg × 20 m/s) + (1000 kg × 0 m/s) = 30,000 kg·m/s
After collision, both cars move together with velocity v: (1500 kg + 1000 kg) × v = 30,000 kg·m/s
v = 30,000 / 2500 = 12 m/s
Frequently Asked Questions
The general formula is: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, where m is mass, u is initial velocity, and v is final velocity.
Yes, momentum is always conserved in isolated systems regardless of the collision type. However, kinetic energy is only conserved in perfectly elastic collisions.
Heavier objects transfer more momentum in collisions. In elastic collisions between objects of equal mass, they exchange velocities if one is initially stationary.
Impulse is the change in momentum of an object when a force is applied over time. It equals force multiplied by time (J = FΔt) and is also equal to the change in momentum (Δp).
Yes, momentum is a vector quantity, so it has both magnitude and direction. Negative momentum simply indicates motion in the opposite direction of your defined positive direction.