Inelastic Collision Calculator

Enter the masses and initial velocities of two objects to calculate their common final velocity, kinetic energy lost, and momentum after a perfectly inelastic collision.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter Mass 1 (kg)
Input the mass of the first object in kilograms.
2
Provide Velocity 1 (m/s)
Enter the initial velocity of the first object in meters per second. Use negative values for motion in the opposite direction.
3
Specify Mass 2 (kg)
Input the mass of the second object in kilograms.
4
Enter Velocity 2 (m/s)
Enter the initial velocity of the second object in meters per second. Use negative values for motion in the opposite direction.
5
Review final velocity and energy metrics
The calculator will display the final velocity of the combined mass, kinetic energy lost, and initial momentum.

Example Calculation

A physics student is analyzing a perfectly inelastic collision where a 2 kg object moving at 5 m/s collides with a 3 kg object moving at -2 m/s.

Mass 1

2 kg

Velocity 1

5 m/s

Mass 2

3 kg

Velocity 2

-2 m/s

Results

0.8 m/s

Tips

Momentum is Always Conserved

In any collision, whether elastic or inelastic, the total momentum of the system before the collision is equal to the total momentum after. This is a fundamental law of physics.

Kinetic Energy is Lost in Inelastic Collisions

A perfectly inelastic collision is defined by the maximum possible loss of kinetic energy, as the objects stick together. This lost energy is converted into other forms, such as heat, sound, or deformation.

Direction Matters for Velocity

Always use positive and negative signs consistently to denote direction for velocities. For example, if motion to the right is positive, then motion to the left must be negative.

Analyzing Impact: An Inelastic Collision Calculator for Physics Problems

Understanding inelastic collisions is fundamental to classical mechanics, illustrating how momentum is conserved even when kinetic energy is not. This Inelastic Collision Calculator allows you to determine the final velocity of combined masses, the kinetic energy lost, and initial momentum in a one-dimensional, perfectly inelastic collision. For instance, if a 2 kg object moving at 5 m/s collides with a 3 kg object moving at -2 m/s, they will stick together and move at a final velocity of 0.8 m/s, demonstrating significant energy dissipation in 2025.

Real-World Inelastic Collisions

Perfectly inelastic collisions are common occurrences in the real world, though often simplified for analysis. They are characterized by the colliding objects sticking together after impact, moving as a single unit. A classic example is a car crash where two vehicles crumple and become entangled, moving together after the impact. Another instance is a bullet embedding itself in a block of wood, where the bullet and block then move as one system. In these scenarios, while kinetic energy is not conserved (it's converted into heat, sound, and deformation), the total momentum of the system is conserved. This principle allows physicists and engineers to analyze the outcomes of such impacts, even when the internal forces and energy transformations are complex. The study of these collisions is crucial for understanding material science, vehicle safety, and even astronomical events where objects merge.

The Conservation of Momentum in Inelastic Collisions

The core principle governing inelastic collisions is the conservation of momentum. While kinetic energy is lost due to deformation, heat, and sound, the total momentum of the system remains constant before and after the collision, assuming no external forces act on the system.

The formulas used are:

Total Mass (M_total):

Total Mass (kg) = Mass 1 (kg) + Mass 2 (kg)

Initial Momentum (P_initial):

Initial Momentum (kg·m/s) = (Mass 1 (kg) × Velocity 1 (m/s)) + (Mass 2 (kg) × Velocity 2 (m/s))

Final Velocity (V_final):

Final Velocity (m/s) = Initial Momentum (kg·m/s) / Total Mass (kg)

Initial Kinetic Energy (KE_initial):

Initial KE (J) = 0.5 × Mass 1 (kg) × (Velocity 1 (m/s))² + 0.5 × Mass 2 (kg) × (Velocity 2 (m/s))²

Final Kinetic Energy (KE_final):

Final KE (J) = 0.5 × Total Mass (kg) × (Final Velocity (m/s))²

Energy Lost (E_lost):

Energy Lost (J) = Initial KE (J) - Final KE (J)

These equations provide a complete picture of the momentum and energy transformations during an inelastic collision.

💡 To delve deeper into the impact of mass and velocity on an object's motion, our Bullet Momentum Calculator can help analyze similar principles for projectiles.

Analyzing a Two-Object Inelastic Collision

Consider a perfectly inelastic collision scenario:

Object 1: Mass (m1) = 2 kg, Initial Velocity (v1) = 5 m/s
Object 2: Mass (m2) = 3 kg, Initial Velocity (v2) = -2 m/s (moving in the opposite direction)

Let's calculate the outcome:

Calculate Total Mass:
```
M_total = 2 kg + 3 kg = 5 kg
```

Calculate Initial Momentum:

P_initial = (2 kg × 5 m/s) + (3 kg × -2 m/s) = 10 kg·m/s - 6 kg·m/s = 4 kg·m/s

Calculate Final Velocity:
```
V_final = 4 kg·m/s / 5 kg = 0.8 m/s
```

Calculate Initial Kinetic Energy:

KE_initial = (0.5 × 2 kg × (5 m/s)²) + (0.5 × 3 kg × (-2 m/s)²) = (0.5 × 2 × 25) + (0.5 × 3 × 4) = 25 J + 6 J = 31 J

Calculate Final Kinetic Energy:

KE_final = 0.5 × 5 kg × (0.8 m/s)² = 0.5 × 5 × 0.64 = 1.6 J

Calculate Energy Lost:
```
E_lost = 31 J - 1.6 J = 29.4 J
```

After the collision, the combined 5 kg mass moves at 0.8 m/s. A significant 29.4 J of kinetic energy was lost, converted into other forms of energy during the impact.

💡 To explore how velocity changes over distance for a projectile, our Bullet Velocity at Distance Calculator can provide further insights into related physics problems.

Analyzing Collision Outcomes in Engineering and Safety

Professionals in fields like automotive engineering, forensic science, and sports equipment design heavily rely on collision physics to analyze impact outcomes. In automotive safety, engineers use inelastic collision principles to design vehicles with crumple zones that absorb kinetic energy during a crash, reducing the force transferred to occupants. The goal is not to have an elastic collision (where kinetic energy is conserved and objects bounce off rapidly), but rather a controlled inelastic one that dissipates energy through deformation, minimizing injury. For instance, in a front-end collision, a car's crumple zone might be designed to dissipate 80% of the kinetic energy, slowing the passenger compartment more gradually.

Forensic experts use these calculations in accident reconstructions, determining initial velocities and impact forces from post-collision wreckage and skid marks. In sports, understanding inelastic impacts helps in designing helmets and protective gear that absorb energy from blows, preventing head injuries. These experts look for the amount of kinetic energy lost and the final velocity to understand the severity of an impact and the effectiveness of protective measures, translating theoretical physics into practical safety applications.

Frequently Asked Questions

What is a perfectly inelastic collision?

A perfectly inelastic collision is a type of collision in which the colliding objects stick together after impact and move as a single combined mass. In such collisions, kinetic energy is not conserved; it is converted into other forms of energy like heat, sound, or deformation, representing the maximum possible loss of kinetic energy.

Is momentum conserved in an inelastic collision?

Yes, momentum is always conserved in any type of collision, including perfectly inelastic collisions, as long as no external forces act on the system. The total momentum of the system before the collision is equal to the total momentum of the combined mass after the collision.

Why is kinetic energy lost in an inelastic collision?

Kinetic energy is lost in an inelastic collision because some of the initial kinetic energy is converted into other forms of energy during the impact. This conversion occurs due to deformation of the objects, generation of heat and sound, and internal friction as the objects stick together, rather than being transferred as kinetic energy.

What is the final velocity of objects after a perfectly inelastic collision?

The final velocity of objects after a perfectly inelastic collision is the single velocity at which the combined mass moves together. It is calculated by dividing the total initial momentum of the system by the total mass of the combined objects, reflecting the conservation of momentum principle.