Recently, the recommendation system of a video hosting site suggested me to watch a video of several cubes colliding. It appeared to be an intriguing concept. After viewing the video, I was inspired to create a simulation of that process and explain its underlying principles.
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.
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, vol. 8, no. 4, pp. 375-394.