⚖️ Conservation of Momentum Calculator
Calculate momentum conservation
How to Use This Calculator
Enter Object 1 Mass and Velocity
Input the mass (kg) and initial velocity (m/s) of the first object before collision. Use positive values for rightward motion, negative for leftward.
Enter Object 2 Mass and Velocity
Input the mass (kg) and initial velocity (m/s) of the second object before collision. The calculator assumes a perfectly inelastic collision (objects stick together).
Click Calculate
Press "Calculate" to determine the final velocity after collision, total momentum, and verify momentum conservation.
Formula
p₁ᵢ + p₂ᵢ = p₁f + p₂f (Conservation of Momentum)
For perfectly inelastic collision:
vf = (m₁v₁ᵢ + m₂v₂ᵢ) / (m₁ + m₂)
Where:
- m₁, m₂ = Masses of objects 1 and 2 (kg)
- v₁ᵢ, v₂ᵢ = Initial velocities before collision (m/s)
- vf = Final velocity after collision (m/s)
- p = Momentum = m × v (kg·m/s)
Example Calculation:
Two objects collide: m₁ = 5 kg moving at 10 m/s, m₂ = 3 kg moving at -5 m/s (opposite direction):
1. Total initial momentum: pᵢ = (5 × 10) + (3 × -5) = 50 - 15 = 35 kg·m/s
2. Final velocity: vf = 35 / (5 + 3) = 35 / 8 = 4.375 m/s
3. Total final momentum: pf = (5 + 3) × 4.375 = 35 kg·m/s ✓ (conserved!)
About Conservation of Momentum Calculator
The Conservation of Momentum Calculator determines the final velocity after a perfectly inelastic collision (where objects stick together) using the fundamental principle that total momentum is conserved in any collision where no external forces act.
What is Conservation of Momentum?
Momentum is always conserved in isolated systems (no external forces). This means the total momentum before a collision equals the total momentum after. This principle applies to all collisions, regardless of whether they're elastic or inelastic.
Types of Collisions
- Perfectly Inelastic: Objects stick together after collision. This calculator handles this type. Kinetic energy is not conserved (lost to heat/deformation).
- Elastic: Objects bounce apart. Both momentum and kinetic energy are conserved. Objects maintain their separate identities.
- Inelastic: Objects separate but lose kinetic energy. Momentum is conserved, but energy is partially lost.
Key Applications
- Physics Education: Understand collision dynamics and momentum conservation principles.
- Engineering: Design safety systems like car bumpers and airbags that absorb impact through inelastic collisions.
- Sports Science: Analyze collisions in contact sports, understanding how momentum transfer affects outcomes.
- Astronomy: Model galaxy collisions and interactions between celestial objects.
Understanding the Results
Final Velocity: The combined object's velocity after the perfectly inelastic collision. Direction is determined by which object had greater momentum initially.
Momentum Verification: The calculator confirms that initial and final total momenta are equal, demonstrating conservation of momentum.
Frequently Asked Questions
What is the difference between elastic and inelastic collisions?
In elastic collisions, objects bounce apart and kinetic energy is conserved. In perfectly inelastic collisions (this calculator), objects stick together and kinetic energy is lost to deformation/heat. Both types conserve momentum.
Why is momentum always conserved?
Momentum conservation comes from Newton's third law (action-reaction). When objects collide, their forces on each other are equal and opposite, so the total momentum change is zero. This holds true unless external forces act on the system.
What if one object is at rest before collision?
Simply enter 0 for its initial velocity. The calculator will work correctly. The final velocity will be in the direction of the moving object, but slower than its original speed.
Can I use this for objects moving in the same direction?
Yes! If both velocities are positive (same direction), the faster object catches up and collides. The final velocity will be between the two initial velocities, weighted by their masses.
How do I handle head-on collisions?
Enter one velocity as positive and the other as negative. This represents objects moving toward each other. The calculator will correctly determine the final direction based on which object has greater momentum.
Is kinetic energy conserved in these collisions?
No. Perfectly inelastic collisions lose kinetic energy to heat, sound, and deformation. Momentum is conserved, but energy is not. This is why the final velocity is less than you might expect from energy conservation alone.