There are numerous reasons why this project is relevant, as well as a wide range of potential applications. The following will outline the primary reasons and applications:
- It can be used in the educational process. For instance, it can be used to illustrate some principles of mechanics to students and to visualize some physics problems.
- It can be used to simulate some physical experiments. For instance, it can be used to simulate the one described in _G. A. Galperin's work_[^1].
- It can be used as a foundation for future projects.[^2]
Firstly, it is essential to comprehend how the velocity of the particles after collision is calculated. We will solve the problem in the elastic collision model (one-dimensional Newtonian).
Consider two particles, designated as particles `1` and `2`, with respective masses $m_1$ and $m_2$. Before the collision, the velocities of particles 1 and 2 are $v_1$ and $v_2$, respectively. After the collision, the velocities of particles 1 and 2 are $v_1'$ and $v_2'$, respectively.
In any collision, momentum is conserved. An elastic collision is an collision, as a result of which the total kinetic energy of the colliding particles is conserved.
Consider particle and a wall with respective masses $m$ and $m_w \rightarrow \infty$. Before the collision, the velocities of the particle and the wall are $v$ and $v_w = 0$, respectively. After the collision, the velocities of the particle and the wall are $v'$ and $v_w'$, respectively.
In order to proceed, we will utilize the formulas derived in section **3.1**.
The velocity of the particle will take the following form:
[^1]: Galperin G. A. (9 December 2003). ["PLAYING POOL WITH π (THE NUMBER π FROM A BILLIARD POINT OF VIEW)"](http://rcd.ics.org.ru/upload/iblock/007/RCD080402.pdf). DOI: [10.1070/RD2003v008n04ABEH000252](http://rcd.ics.org.ru/RD2003v008n04ABEH000252/)
[^2]: Please be aware that the project is distributed under the MIT license. However, if you decide to use it as the basis of your project, it would be advisable to contact me first.