Inelastic Collision

Introduction

An inelastic collision is one in which two objects collide and some kinetic energy is lost, typically converted to heat, sound, or deformation. Unlike elastic collisions, the objects don't bounce apart cleanly — they may stick together completely (perfectly inelastic) or separate with reduced speeds. While kinetic energy is not conserved, momentum is always conserved in inelastic collisions. This makes them particularly useful for understanding real-world impacts where energy dissipation is significant.

The physics explained

In any collision, momentum is conserved due to Newton's third law. When object A pushes on object B, object B pushes back with equal and opposite force. These internal forces cancel out, leaving the total momentum of the system unchanged. This fundamental principle holds regardless of whether the collision is elastic or inelastic.

What distinguishes inelastic collisions is the loss of kinetic energy. Some of the initial kinetic energy gets converted into other forms: heat from friction, sound from the impact, or energy used to deform the objects. In a perfectly inelastic collision, the maximum possible kinetic energy is lost while still conserving momentum — the objects stick together and move as one unit after impact.

The coefficient of restitution quantifies how elastic a collision is, ranging from 0 (perfectly inelastic) to 1 (perfectly elastic). Most real collisions fall somewhere in between, with rubber balls having high restitution and clay balls having very low restitution. Understanding this spectrum helps predict the outcomes of practical collisions.

Key equations

Conservation of momentum: m1*v1 + m2*v2 = m1*v1' + m2*v2'

Perfectly inelastic collision: v1' = v2' = vf

Final velocity (perfectly inelastic): vf = (m1*v1 + m2*v2) / (m1 + m2)

Energy lost: Delta_KE = KE_initial - KE_final

Coefficient of restitution: e = (v2' - v1') / (v1 - v2)

Key variables

Symbol	Unit	Description
m1, m2	kg	Masses of the colliding objects
v1, v2	m/s	Initial velocities before collision
v1', v2'	m/s	Final velocities after collision
vf	m/s	Combined velocity in perfectly inelastic collision
p	kg*m/s	Momentum, always conserved in collisions
KE	J	Kinetic energy, partially lost in inelastic collisions
Delta_KE	J	Amount of kinetic energy lost during collision
e	dimensionless	Coefficient of restitution (0 to 1)

Real world examples

Car crashes: Modern vehicles are designed to undergo controlled inelastic collisions, with crumple zones absorbing kinetic energy to protect passengers. The more energy converted to deformation, the less energy transferred to occupants.
Ballistic pendulum: A classic physics demonstration where a bullet embeds in a wooden block suspended by strings. The perfectly inelastic collision allows measurement of bullet velocity by observing the combined motion afterward.
Asteroid impacts: When meteors strike Earth's atmosphere or surface, the collisions are highly inelastic. Most kinetic energy converts to heat, creating the bright streaks we see and potentially forming craters.
Sports collisions: A football tackle or hockey check represents an inelastic collision where players may move together after impact, with significant energy lost to sound, heat, and player movement.

How the simulation works

The simulation allows you to control the masses and initial velocities of two objects on a frictionless track. You can set the coefficient of restitution to create different types of collisions: 0 for perfectly inelastic (objects stick together), 1 for perfectly elastic (maximum bounce), or values in between for partially inelastic collisions. When objects collide, the simulation calculates final velocities using conservation of momentum and the restitution equation. Real-time displays show momentum before and after collision (always equal) and kinetic energy before and after (demonstrating energy loss). This visual approach helps you understand how mass ratios and collision types affect the outcome.