Problem

In the manufacture of steel balls of the type used for ball bearings, it is important that...

In the manufacture of steel balls of the type used for ball bearings, 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. Assuming that each ball has a radius R = 0.3 in., design a sorting device to select the balls with 0.900 < COR < 0.925. The device consists of an incline defined by the angle θ and length L. The strike plate is placed at the bottom of a well with depth h and width w. Finally, at a distance ℓ 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 υ0, rebound off the strike plate, and then fall directly in the trap (you may want to add a design element that prevents balls from simply rolling into the trap). In your design, choose appropriate values of L, θ < 45°, h, w, d, and ℓ to accomplish the desired task while ensuring that the overall dimensions of the device do not exceed 4 ft in both the horizontal and vertical directions.