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].
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. A collision between to particles is said to be elastic if it involves no change in their internal state. Accordingly, when the law of conservation of energy is applied to such a collision, the internal energy of the particles may be neglected.[^2]
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., _[PLAYING POOL WITH π (THE NUMBER π FROM A BILLIARD POINT OF VIEW)](http://rcd.ics.org.ru/RD2003v008n04ABEH000252/)_, _Regular and Chaotic Dynamics_, 2003, Volume 8, Number 4, pp. 375-394.
[^2]: Landau, L.D. and Lifshitz, E.M., _Course of Theoretical Physics_, vol. 1: _Mechanics_, Elsevier Science, 1982.