Brief Description: In a ball bearing manufacturing plant, the manufactured steel balls are to be sorted according to the coefficient of restitution (e) using an oblique impact test setup shown in Fig. 1. The steel balls (one at a time) are released from rest at a height $h_1$ above an inclined plane (with an angle of inclination of $\theta$). It is required to design the setup such that balls with $e<0.8$ are to be separated using a barrier of height $h_2$ placed at a distance $d_1$ from the point of impact B and are collected in a bin placed underneath the barrier. The balls with a specified range of $e$, ($0.8 < e < 0.9$) are to be collected in a bin placed at a distance $d_2$ from the bottom edge of the barrier. The width of the collecting bin is to be decided such that balls with $e > 0.9$ are to be collected in another bin placed accordingly.
The project has the following requirements:
1. Analyze the motion of the balls in 3 separate parts: (a) Free fall between points A and B, (b) impact at point B, and (c) projectile motion after impact (BC, BC')
2. Show details of analysis for each of the above parts with equations in parametric forms (in terms of inputs $h_1$, $\theta$ and $e$).
3. Find expressions for the design variables $d_1$, $h_2$, $d_2$, and $d_3$.
4. Create a computer code in Matlab/C++/Java/Python to analyze the motion. Your code should be general enough to accommodate a range of inputs and give all the design variables.
5. Demonstrate the operation of the code.
6. Submit a report for the project- with sections for Abstract, Introduction, Method of Analysis, Code Development (and computer code listing), Results, Sketch of the design and Conclusions.
Test data $h_1$= 0.75-1 m, $\theta$= 35-45°, 0.8 < e < 0.9
