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In writing your report, you should assume that the reader is scientifically literate but is totally unfamiliar with the problem. Provide narrative describing any equations that you list. The report should be presented using the following format:

Cover Page
At a minimum should include the title of the project, your name, class section, and date.

Abstract
A one-paragraph summary of the project stating the problem solved, method of solution used, and key results obtained. It appears first but should be written last.

Introduction
Give background and a detailed description of the problem to be solved.

Mathematical Statement
Present a figure showing the geometry. Describe equations to be solved and initial and boundary conditions and also elastic binary collision method.

Method of Solution
Give a detailed description of your solution algorithm.

Matlab Program
Provide a listing of your Matlab program.

Results
Print out representative frames of particles motion from your animation.

Discussion
Discuss what your results show. Describe any unusual behavior.

Conclusions
Give a summary of key results obtained.

Future Work
List any suggestion(s) for future work on this project in order to make it more general and realistic.
Papers bearing any resemblance to each other will receive a grade of negative 100% which will be averaged with your other grades.
The goal of the term project is to simulate rigid-body motion and impact of solid circular particles inside a box in the Cartesian coordinate. Consider a rigid solid particle with radius ?, location ?⃗ , and velocity ?⃗ as depicted in Fig. 1.
The particle moves with constant velocity in a straight line. The Newton’s second law of motion applies to the particle dynamic. If this particle is moving inside a rectangular box with width ? and height ? in the Cartesian coordinate, it can impact to the walls and change its direction and velocity based on the wall location (Fig. 2).
When the particle hits the wall, specular reflection (mirror-like reflection) is applied. Therefore, its velocity changes only the sign not the magnitude. Next, consider more than one particle (?? particles) moving inside the box. The difference in this case is that the particles may impact each other as well and change direction and velocity. The collision between particles is considered elastic binary collision meaning that only two particles can participate in a collision and there is no loss of kinetic energy in the collision (Fig. 3). Write a MATLAB program to simulate and animate motion of ?? rigid particles and their impact with wall and each other.

Consider the followings:
– Number of particles ??, box width ?, and box height ? should be asked from the user using input command.
– The initial position and velocity of the particles are random. Make sure the initial position of the particles resides within the box.
– The initial random velocity of each particle is between | ???| min ? ? 1 ?/? and | ?? | max ? ? 5 ?/?.
– Each particle has different initial velocity but it will remain the same during the simulation except during the impact in which it gets a new constant velocity.
– The initial position of each particle is inside the box and the distance between each particle pair is larger than 2?.

– The time step is 1 ?.
– Maximum number of particles ?? ?? is 10.
– At each time frame, the current position of particles should be plotted. Do not plot the particles at each time step which makes the plot unclear. Use getframe command to animate the particles.
– Use a random color for each particle to distinguish them from each other. Keep the colors unchanged during the simulation.
– In one case, consider right side of the box open (no wall) so the particles can leave the box. Estimate the total time until all particles leave the box.
– Add a toggle button inside the figure to STOP the animation.
– [Optional] consider rotation and angular velocity of the particles as well. Does it make a difference in particles dynamic?
– [Optional] consider inelastic binary collision which is more realistic.
– [Optional] consider a moving box in which the particles move inside a moving frame.
– [Optional] consider different particle-wall impact boundary conditions (nonspecular reflections).

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