Elastic Collision Calculator
Calculate final velocities for elastic and inelastic collisions between two objects
System Configuration
Enter masses and initial velocities for collision calculation
Derivation Steps
Real-Time Simulation
Interactive visual 1D collision track and vector monitors
Kinematic Laws
Momentum is conserved in all collisions (m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f).
Kinetic energy is conserved only in **elastic** collisions, where objects rebound without permanent shape modifications or thermal/acoustic energy dissipation.
Collision Formulas
Elastic Collision (1D)
v1f = ((m1 - m2) / (m1 + m2)) * v1i + ((2 * m2) / (m1 + m2)) * v2i v2f = ((2 * m1) / (m1 + m2)) * v1i + ((m2 - m1) / (m1 + m2)) * v2i
Inelastic Collision (1D)
vf = (m1 * v1i + m2 * v2i) / (m1 + m2)
Elastic Collision
Both momentum and kinetic energy are conserved. Objects bounce apart clean.
Inelastic Collision
Momentum conserved, energy partially lost to sound, heat, or internal deformation.
Perfectly Inelastic
Objects stick completely together after impact, traveling with a single unified final speed.
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.
🔹 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
Academic & Scientific References
For further understanding and validation of the formulas used above, we recommend exploring these authoritative resources: