In the large scale manufacturing of Jaguar Bold Blue Bouncy Balls (JB4) for children, it is important that their material properties be sufficiently uniform. One way to detect gross differences in their material properties is to observe how a ball rebounds when dropped on a hard strike plate (see the figure below). Assuming that each ball has a radius R of 23.0 mm, design a sorting device to select the balls with 0.900 < e < 0.925, where e is the coefficient of restitution, which is sometimes written as COR. These balls have a density of 0.95 g/cm3. The device consists of an incline defined by the angle and length L. The strike plate is placed at the bottom of a well with depth h and width w2. Finally, at a distance w1 from the end of the incline, there is a trap with a diameter d. By releasing a ball from rest at the top of the incline and assuming that the ball slides with negligible friction, the ball will reach the bottom of the incline with a speed v0, rebound off the strike plate, and then fall directly in the trap.
In your design, choose appropriate values of L, ?, h, w1, w2, and d to accomplish the desired task while ensuring that the overall dimensions of the device do not exceed 2.0 meter in both the horizontal and vertical directions. The values for inclined angle should not exceed 45°.
It is not absolutely necessary for this stage of the design, but you may want to:
• Consider adding a design element that prevents balls from simply rolling into the trap if the actual trajectory doesn’t match the desired trajectory.
• Allow your analysis to handle a different radius (R) value for the ball.