https://github.com/alejo1630/colliding_blocks

This Python code computes the kinematics data (linear momentum and kinetic energy) for the 2D collission between 2 blocks and a rigid wall taking into account the coefficient of restitution but ignoring the friction.
https://github.com/alejo1630/colliding_blocks

colliding-blocks collision compute-pi python vpython

Last synced: 5 months ago
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This Python code computes the kinematics data (linear momentum and kinetic energy) for the 2D collission between 2 blocks and a rigid wall taking into account the coefficient of restitution but ignoring the friction.

• Host: GitHub
• URL: https://github.com/alejo1630/colliding_blocks
• Owner: alejo1630
• Created: 2023-01-19T22:50:41.000Z (about 3 years ago)
• Default Branch: main
• Last Pushed: 2023-01-20T00:05:42.000Z (about 3 years ago)
• Last Synced: 2025-05-31T13:08:54.814Z (9 months ago)
• Topics: colliding-blocks, collision, compute-pi, python, vpython
• Language: Python
• Homepage:
• Size: 106 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
# Colliding Blocks

This Python code computes the kinematics data (linear momentum and kinetic energy) for the 2D collission between 2 blocks and a rigid wall taking into account the [coefficient of restitution](https://en.wikipedia.org/wiki/Coefficient_of_restitution) but ignoring the friction. 

## 🔰 How does it work?

- The code uses [VPython](https://vpython.org/) library to create the 2D-3D interactive environment and the physics interactions.

  



- Letter A is set for the red block and the letter B is set for the green block.

- User has to enter the following parameters

  - Blocks' mass.

  - Initial velocity of the blocks (in the main case the red block doesn't have initial velocity).

  - Coefficient of restitution between the red and the green block.

  - Coefficient of restitution between the red block and the rigid wall.

- After each collision the kinematic data is computed using the following equations (Notation: 1-Before collision, 2-After collision):

  - Conservation of momentum:

  $$m_A (v_A)_1 + m_B (v_B)_1  = m_A (v_A)_2 + m_B (v_B)_2$$

  

  - Conservation of energy:

  $$\frac{1}{2} m_A {(v_A)_1}^2 + \frac{1}{2} m_B {(v_B)_1}^2  = \frac{1}{2} m_A {(v_A)_2}^2 + \frac{1}{2} m_B {(v_B)_2}^2 $$

  

  - Coefficien of restitution between blocks:

  $$e = \frac{(v_B)_2 - (v_A)_2}{(v_B)_1 - (v_A)_1}$$

  

  - Coefficient of restitution between the red block and the rigid wall:

  $$e = -\frac{(v_A)_2}{(v_A)_1}$$

- Kinematic data for both blocks is computed for each step of time during the simulation:

  - Linear momentum

  

  

  

  - Kinetic energy

  

  

  

- There is an special set of parameters which could be used to calculated the digits of Pi $(\pi)$.

  - All the coefficients of restitution muts be equal to 1 (perfectly elastic)

  - Mass' A must be equal to 1.

  - Mass' B bust be equal to $100^{n-1}$, where $n$ is the number of digits of Pi computed based on the number of collision between all the bodies during the simulation. For example:

    - If $n = 1$ $(m_B = 1 kg)$, the number of collision would be $3$

    

    - If $n = 2$ $(m_B = 100 kg)$, the number of collision would be $31$

    

    - If $n = 3$ $(m_B = 10000 kg)$, the number of collision would be $314$

    

 - An explanation of this peculiar phenomenon is described by [G.Galperin](https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf) with a lot of math, but there is an incredible and illustrative explanation in the [3Blue1Browm Youtube Channel](https://www.youtube.com/watch?v=jsYwFizhncE)

 

    

## 🔶 What is next?

- Increase the number of blocks and rigid walls.