Elastic Collisions: 2D Billiards & Maxwell-Boltzmann Distribution

What Elastic Collisions Are

An elastic collision is one where both momentum and kinetic energy are conserved. In a 2D space, particles can move in any direction until they collide with another particle or the boundary.

These collisions mimic real-world interactions between molecules in gases, which helps us understand macroscopic properties like temperature and pressure.

Why It Happens

The conservation of momentum and kinetic energy ensures that during a collision, the total momentum and kinetic energy before and after the collision remain constant.

This is due to Newton's laws of motion and the principle of conservation of mechanical energy.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution describes the statistical distribution of speeds among particles in a gas at a given temperature.

In the simulation, as collisions occur, the speed histogram converges to this distribution, illustrating how particle velocities are distributed statistically.

Equipartition Theorem

The equipartition theorem states that each degree of freedom in a system contributes equally to its internal energy.

In the simulation, adjusting the mass ratio slider allows you to observe how kinetic energies are shared among particles, demonstrating this principle.

Frequently asked questions

Try it live

Everything above runs in your browser — open Elastic Collisions — 2D Billiards & Maxwell-Boltzmann (2D) and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.