What Is an Inelastic Collision?
An inelastic collision is an impact where total momentum is conserved, but kinetic energy is not fully conserved. Some of the initial kinetic energy is transformed into other forms such as heat, sound, deformation, or internal energy. In the most extreme case, a perfectly inelastic collision, the colliding objects stick together and move with a common final velocity.
This inelastic collision calculator is designed for one-dimensional motion, where both objects move along the same straight line. It provides practical outputs for students, teachers, and engineers: final velocities of both objects, momentum before and after the collision, kinetic energy change, and percentage energy loss.
How the Inelastic Collision Calculator Works
The calculator uses two core equations from classical mechanics:
- Conservation of linear momentum
- Coefficient of restitution equation
By combining these equations, the calculator solves for final velocities after impact. You can enter masses, initial velocities, and a restitution value between 0 and 1. A lower restitution value means a more inelastic collision and typically a larger kinetic energy loss.
Coefficient of Restitution (e)
The coefficient of restitution describes how “bouncy” a collision is:
- e = 1: perfectly elastic collision (no kinetic energy loss in ideal model)
- 0 < e < 1: partially inelastic collision
- e = 0: perfectly inelastic collision (objects leave with same velocity)
Real-world impacts are often partially inelastic. Material type, surface conditions, and deformation all influence restitution.
Step-by-Step Usage
- Enter mass of object 1 and mass of object 2.
- Enter initial velocities. Use negative values if an object is moving in the opposite direction.
- Enter a coefficient of restitution or choose a preset.
- Click Calculate to get final velocities and energy results.
Make sure your units are consistent. If mass is in kilograms and velocity in meters per second, momentum will be in kg·m/s and energy in joules.
Why Momentum Is Conserved but Kinetic Energy Changes
In an isolated system with negligible external force during the short collision interval, total momentum remains constant. However, kinetic energy can decrease because some translational motion converts into deformation, thermal energy, sound waves, and microscopic internal motion. This is why inelastic impacts are extremely common in practical engineering and safety analysis.
Applications of Inelastic Collision Calculations
- Vehicle crash reconstruction and safety studies
- Sports science (bat-ball or body impacts)
- Manufacturing and material testing
- Robotics and machine collision response
- Physics education and exam preparation
Perfectly Inelastic Collision Special Case
In a perfectly inelastic collision, both bodies move together after impact, so final velocities are equal:
v = (m₁u₁ + m₂u₂) / (m₁ + m₂)
This case corresponds to e = 0 and usually produces the largest kinetic energy loss for the given masses and initial speeds. Use the preset selector to apply this condition instantly.
Common Mistakes to Avoid
- Using inconsistent units for mass and velocity
- Entering coefficient of restitution outside 0 to 1
- Forgetting that direction matters (sign of velocity)
- Assuming kinetic energy is always conserved
Frequently Asked Questions
Can this calculator handle opposite directions?
Yes. Enter a negative velocity for one object if it moves opposite to the positive direction.
Is this calculator for 2D or 3D collisions?
This page solves one-dimensional collisions. For 2D or 3D collisions, momentum must be resolved component-wise.
What if e = 1?
That is an elastic collision in this model. Momentum and kinetic energy are both conserved in ideal conditions.
Can kinetic energy increase after collision?
In ordinary passive impacts, no. In special cases involving stored internal energy release (like explosions), effective outcomes can differ and require a different model.