Inelastic Collision Simulation Documentation

This document provides a comprehensive guide to the Inelastic Collision Simulation. In this simulation, two balls (one red and one blue) move within a confined area and, upon collision, merge into a single entity. The simulation demonstrates the conservation of momentum during inelastic collisions while also visualizing the loss of kinetic energy.

Overview

The Inelastic Collision Simulation is built to help you understand the fundamentals of inelastic collisions. In this type of collision, the two objects stick together after impact. While momentum is conserved, kinetic energy is not—some of it is transformed into other forms of energy (such as sound or deformation).

Key features of the simulation include:

  • Simulation Area: A large canvas displays the two balls moving over a ground with a specified height. An overlay shows the current frames per second (FPS) for performance monitoring.
  • Graph Panel: Using Chart.js, a graph dynamically plots real-time data such as time, kinetic energy, total momentum, and the number of collisions.
  • Controls Panel: Adjustable parameters let you modify the mass, initial velocity, and radius for each ball. Buttons provided allow you to start, pause, and reset the simulation.

How to Use the Simulation

When you run the simulation, you will observe the following:

  • Canvas and Ground: The simulation area features a black canvas with a ground region at the bottom. The balls can bounce off the walls, ceiling, and ground.
  • Motion and Collisions: Two balls (red and blue) are placed on opposite sides near the ground. They move based on the velocities you set. When the balls come into contact, they merge (indicated by a color change to purple) and continue with a common velocity.
  • Graph Controls: Dropdown menus allow you to choose which parameters are plotted on the x- and y-axes. Options include time, kinetic energy, momentum, and collision count.
  • User Input: Parameter inputs for both balls enable you to explore different scenarios. Adjust the mass, velocity, or radius to see how these changes influence the collision results.

Physics Behind the Simulation

In an inelastic collision, the following principles apply:

  • Conservation of Momentum: The momentum before and after the collision is conserved. Mathematically, this is expressed as:
\[ m_1v_1 + m_2v_2 = (m_1 + m_2)v' \]

where \( m_1 \) and \( m_2 \) are the masses of the balls, \( v_1 \) and \( v_2 \) are their velocities before collision, and \( v' \) is the common velocity after they merge.

  • Kinetic Energy Loss: Not all kinetic energy is conserved in an inelastic collision. Comparing the kinetic energy before and after the collision reveals that some energy is transformed into other forms (e.g., heat, sound).
\[ KE_{\text{initial}} = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 \]
\[ KE_{\text{final}} = \frac{1}{2}(m_1+m_2)v'^2 \]
  • Ground and Boundaries: The simulation includes a ground with a fixed height, ensuring the balls interact with the environment realistically by bouncing off walls and the ground.

Educational Insights

Through this simulation, users can learn about:

  • Momentum Conservation: Observe how, regardless of the collision, the total momentum of the system remains constant.
  • Energy Transformation: Even though momentum is conserved, notice that the kinetic energy after the collision is lower, demonstrating energy loss.
  • Impact of Parameters: Changing the mass, velocity, and size of the balls lets you see how these properties affect both the collision dynamics and the resulting merged motion.
  • Real-Time Analysis: With dynamic graphs, users can correlate the theoretical predictions with real-time simulation data.

Conclusion

The Inelastic Collision Simulation is an effective tool for exploring fundamental physics concepts. By adjusting simulation parameters and observing the effects on momentum and kinetic energy, users gain an intuitive understanding of how inelastic collisions work. Experiment with different configurations and watch as theoretical principles come to life in real time.

Enjoy your exploration of inelastic collisions and deep dive into the physics behind merging objects!