Elastic Collision Simulation Documentation

This document provides an overview and guide for the Elastic Collision Simulation. The simulation demonstrates the principles of elastic collisions between two balls by applying conservation of momentum and kinetic energy.

Overview

The simulation features an interactive canvas where two balls (one red and one blue) move and collide elastically. When the balls collide, the simulation calculates their new velocities based on the energy and momentum conservation laws. In parallel, a dynamic graph displays real-time data such as kinetic energy, momentum, and the total number of collisions throughout the simulation.

How to Use the Simulation

Upon launching the simulation, you will encounter several sections:

  • Simulation Area: The main canvas (with a dark background) shows the red and blue balls in motion. An overlay in the corner displays the current frames per second (FPS) to help monitor performance.
  • Graph Panel: Alongside the simulation, a graph (powered by Chart.js) plots chosen parameters over time. Use the dropdown menus to select which quantities appear on the x- and y-axes (e.g., Time vs Kinetic Energy, Momentum, or Collision Count).
  • Controls Panel: The bottom section provides adjustable inputs for both balls. For Ball 1 (red) and Ball 2 (blue), you can modify parameters such as mass, initial velocities (X and Y components), and radius. Additionally, you have buttons to Start, Pause, or Reset the simulation.

Physics Behind the Simulation

In an elastic collision, both momentum and kinetic energy are preserved. The simulation relies on these conservation laws:

\[ m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{v}'_1 + m_2\vec{v}'_2 \]
\[ \frac{1}{2}m_1\|\vec{v}_1\|^2 + \frac{1}{2}m_2\|\vec{v}_2\|^2 = \frac{1}{2}m_1\|\vec{v}'_1\|^2 + \frac{1}{2}m_2\|\vec{v}'_2\|^2 \]

During a collision, these equations determine the adjusted velocities of the balls. The simulation continuously computes the instantaneous kinetic energy and net momentum, while also keeping track of the number of collisions, and updates the graph accordingly.

Educational Insights

This simulation is an effective tool for learning about:

  • Conservation Laws: Visualize how momentum and kinetic energy remain conserved during interactions.
  • Dynamic Parameter Testing: Experiment with varying the masses, velocities, and sizes of the balls to see how different physical properties influence collision outcomes.
  • Real-Time Data Analysis: The live graph enhances understanding by showing how kinetic energy and momentum evolve over time, reinforcing theoretical principles through practical observation.
  • Collision Counting: Monitoring the collision count helps illustrate repeated dynamic interactions in a closed system.

Conclusion

The Elastic Collision Simulation is a powerful, interactive tool designed to help users explore and understand the physics behind elastic collisions. By experimenting with various parameters and observing the resulting data in real time, learners can deepen their understanding of how momentum and energy are managed during collisions.

Enjoy exploring the dynamics of elastic collisions and gaining insights into the fundamental principles of physics!