Collision Calculator
Calculate final velocities for elastic and inelastic collisions between two objects
System Configuration
Enter masses and initial velocities for collision calculation
Results
Enter parameters and calculate to see results
Properties
Momentum is conserved in all collisions. Kinetic energy is conserved only in elastic collisions.
Total momentum before collision equals total momentum after collision.
Collision Formulas
Elastic Collision
v1f = (m1 - m2)/(m1 + m2) * v1i + (2m2)/(m1 + m2) * v2i v2f = (2m1)/(m1 + m2) * v1i + (m2 - m1)/(m1 + m2) * v2i
Inelastic Collision
vf = (m1 * v1i + m2 * v2i) / (m1 + m2)
Elastic
Energy conserved
Inelastic
Energy lost
Perfectly Inelastic
Objects stick together
Collision Calculator – Calculate Final Velocities in Elastic and Inelastic Collisions
Collisions are fundamental to understanding momentum and energy conservation in physics. Our Collision Calculator helps you compute the final velocities of two objects after elastic or inelastic collisions, providing insights into conservation laws and real-world applications.
🔹 What are Elastic and Inelastic Collisions?
A collision occurs when two objects interact briefly, exchanging momentum and possibly energy.
Elastic Collision: Both momentum and kinetic energy are conserved. No energy is lost to heat, sound, or deformation. Objects bounce off each other.
Inelastic Collision: Momentum is conserved, but kinetic energy is not. Some energy is converted to other forms like heat or sound. Objects may stick together in perfectly inelastic collisions.
Most real-world collisions are inelastic, while elastic collisions are ideal for atomic or subatomic interactions.
🔹 Collision Formulas
The formulas depend on the collision type and assume one-dimensional motion for simplicity.
Elastic Collision (1D): v₁f = ((m₁ - m₂) / (m₁ + m₂)) * v₁i + ((2m₂) / (m₁ + m₂)) * v₂i v₂f = ((2m₁) / (m₁ + m₂)) * v₁i + ((m₂ - m₁) / (m₁ + m₂)) * v₂i Inelastic Collision (1D): v_f = (m₁ * v₁i + m₂ * v₂i) / (m₁ + m₂) Perfectly Inelastic Collision: Objects stick together with velocity v_f above. Where: m₁, m₂ = masses of objects 1 and 2 v₁i, v₂i = initial velocities v₁f, v₂f = final velocities v_f = final velocity (combined)
🔹 Features of Our Collision Calculator
- Calculate elastic or inelastic collisions
- Input masses and initial velocities
- Quick presets for common scenarios:
- Equal masses head-on
- Stationary target
- Heavy vs light masses
- Light vs heavy masses
- Real-time calculation with step-by-step results
- Conservation law verification
🔹 Example Calculations
Example 1: Elastic Collision - Equal Masses
Mass 1 = 1 kg, Velocity 1 = 5 m/s
Mass 2 = 1 kg, Velocity 2 = -3 m/s
v₁f = ((1-1)/(1+1))*5 + ((2*1)/(1+1))*(-3) = 0 + 1*(-3) = -3 m/s
v₂f = ((2*1)/(1+1))*5 + ((1-1)/(1+1))*(-3) = 1*5 + 0*(-3) = 5 m/s
👉 Velocities are exchanged: Object 1 ends at -3 m/s, Object 2 at 5 m/s.
Example 2: Inelastic Collision - Stationary Target
Mass 1 = 2 kg, Velocity 1 = 4 m/s
Mass 2 = 3 kg, Velocity 2 = 0 m/s
v_f = (2*4 + 3*0) / (2 + 3) = 8 / 5 = 1.6 m/s
👉 Combined velocity = 1.6 m/s
🔹 Applications of Collision Physics
- 🚗 Automotive Safety – Designing crumple zones and airbags
- ⚽ Sports Science – Understanding ball trajectories and impacts
- 🔬 Particle Physics – Analyzing subatomic collisions
- 🏗️ Engineering – Structural impact analysis
- 🎮 Game Physics – Realistic simulations in video games
🔹 Frequently Asked Questions (FAQs)
Q1. What's the difference between elastic and inelastic collisions?
Elastic collisions conserve both momentum and kinetic energy. Inelastic collisions conserve momentum but not kinetic energy.
Q2. Can objects stick together in a collision?
Yes, in perfectly inelastic collisions, objects stick together and move with a common final velocity.
Q3. Are real-world collisions elastic or inelastic?
Most real-world collisions are inelastic, with some energy lost to heat, sound, or deformation.
Q4. How does mass ratio affect collision outcomes?
In elastic collisions, lighter objects bounce back more, while heavier objects barely change velocity.
Q5. What is coefficient of restitution?
The coefficient of restitution (e) measures elasticity: e = 1 for perfectly elastic, e = 0 for perfectly inelastic.
Academic & Scientific References
For further understanding and validation of the formulas used above, we recommend exploring these authoritative resources: