๐ก Conservation of Momentum
p = mv โ In an isolated system with no external forces, total momentum before collision equals total momentum after: mโuโ + mโuโ = mโvโ + mโvโ
Momentum Calculator
Configure collision parameters
โ๏ธMass (m)
๐Velocity (v)
Momentum
50.00 kgยทm/s
Total Before
50.00 kgยทm/s
Total After
50.00 kgยทm/s
KE Lost
0.00 J
๐ Try These Examples
Car Crash
1000kg + 800kg
Billiard Balls
Elastic collision
Bouncing Ball
e = 0.8
Train Coupling
Perfectly inelastic
๐ฅ Collision Visualization
pโ = 50 kgยทm/s
pโ = -15 kgยทm/s
ฮฃp = 35 kgยทm/s
๐ Momentum Formulas
p = mv
Momentum
J = Fฮt = ฮp
Impulse
ฮฃp = const
Conservation
e = -(vโ-vโ)/(uโ-uโ)
Restitution
๐งฎStep-by-Step Solutionโผ Show
Understanding Momentum and Collisions
Momentum is the product of an object's mass and velocity. It's a vector quantity, meaning it has both magnitude and direction. The law of conservation of momentum states that in an isolated system, the total momentum remains constant.
Types of Collisions
- Elastic Collision (e = 1): Both momentum AND kinetic energy are conserved. Objects bounce off each other (billiard balls).
- Inelastic Collision (0 < e < 1): Momentum is conserved but some kinetic energy is lost (most real-world collisions).
- Perfectly Inelastic (e = 0): Objects stick together after collision. Maximum kinetic energy loss while momentum is still conserved.
Impulse-Momentum Theorem
Impulse (J) equals the change in momentum: J = Fฮt = ฮp = m(v - u). This explains why airbags work โ they increase collision time, reducing the force on passengers.
Real-World Applications
- Vehicle Safety: Crumple zones and airbags extend collision time
- Sports: Follow-through in golf, tennis, and baseball maximizes impulse
- Rockets: Propulsion based on conservation of momentum
- Ballistics: Bullet and recoil momentum analysis