Conservation of Momentum Calculator
Analyze collisions and momentum conservation in two-object systems
Collision Parameters
Object 1
Object 2
Momentum Conservation Results
Momentum Conservation
Kinetic Energy
Collision Type Analysis
Conservation Formula: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Total momentum must be conserved in isolated systems with no external forces
Example Calculation
Billiard Ball Collision
Object 1: Mass = 8 kg, Initial velocity = 10 m/s
Object 2: Mass = 4 kg, Initial velocity = 0 m/s (at rest)
After collision: Object 1 slows to 4 m/s
Find: Final velocity of object 2
Solution Steps
1. Initial momentum: p₁ = 8 kg × 10 m/s + 4 kg × 0 m/s = 80 kg⋅m/s
2. Final momentum of object 1: p₁f = 8 kg × 4 m/s = 32 kg⋅m/s
3. Required momentum for object 2: p₂f = 80 - 32 = 48 kg⋅m/s
4. Final velocity of object 2: v₂f = 48 kg⋅m/s ÷ 4 kg = 12 m/s
Answer: Object 2 moves at 12 m/s after collision
Types of Collisions
Perfectly Elastic
Both momentum and kinetic energy conserved
Example: Billiard balls, gas molecules
Partially Elastic
Momentum conserved, some KE lost
Example: Car crashes, most real collisions
Perfectly Inelastic
Objects stick together after collision
Example: Bullet hitting wooden block
Real-World Examples
Gun Recoil
Bullet forward → Gun backward
Rocket Propulsion
Hot gas expelled → Rocket moves forward
Ice Skaters
Push apart → Move in opposite directions
Pool/Billiards
Cue ball transfers momentum to target ball
Physics Tips
Momentum is always conserved in isolated systems
Kinetic energy is only conserved in elastic collisions
Total energy is always conserved (includes heat, sound)
Momentum is a vector quantity (has direction)
Understanding Conservation of Momentum
The Fundamental Principle
The law of conservation of momentum states that in an isolated system (no external forces), the total momentum before collision equals the total momentum after collision. This is one of the most fundamental principles in physics.
Mathematical Formula
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where:
m = mass, u = initial velocity, v = final velocity
subscripts 1,2 refer to objects 1 and 2
Key Concepts
- •Momentum: Product of mass and velocity (p = mv)
- •Isolated System: No external forces acting on the system
- •Vector Quantity: Momentum has both magnitude and direction
- •Newton's Laws: Conservation follows from Newton's third law
Remember: Momentum is always conserved, but kinetic energy is only conserved in perfectly elastic collisions. In real-world scenarios, some energy is usually converted to heat, sound, or deformation.
Types of Collision Analysis
Elastic Collision
Both momentum and kinetic energy are conserved. Objects bounce off each other completely.
Examples: Billiard balls, gas molecules
Inelastic Collision
Momentum is conserved but kinetic energy is lost to other forms like heat and sound.
Examples: Car crashes, clay balls
Perfectly Inelastic
Objects stick together after collision and move with common velocity.
Examples: Bullet in wood, train coupling