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 6 and length L. The strike plate is placed at the bottom of a well with depth h and width w. Finally, at a distance & 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 vo. rebound off the strike plate, and then fall directly into 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, 0 < 45°, h, w, d, and e 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.

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3) Calculations for the red dog food can rolling down the slope in the Rube Goldberg design are as follows (we will name it Step 1): DO Step 1 (calculations are given): Coefficient of friction → μ = 0.14 Mass of the object → m = 368 gm = 0.368kg Initial height of the object (red can on top of books) → h=8.89, cm = 0.0889 m Slope of the file folder → 0 = 14° Travelling Distance by the object = 11.5 inch = 0.292 m And length that the object will travel = h/sin 0 = 0.0889/ sin14° = 0.367 m So, the radius of the object → R = 0.367 -0.292 = 0.075 m Initial Velocity of red can → u=0 Velocity and Force Calculations for Step 1: -From total mechanical energy conservation: → Initial mechanical energy = final mechanical energy → mg - In case of pure rolling, the velocity of the center of mass: →→V=Ro=0.075 x 14.28 = 1.07 m/s. -Hence the change in force acting on the object for the travel: →F=mgsine = 0.368 x 9.81 × sin14° =0.89 N Step 2: The Selective Step (Step 2) in this design and for the…

5) Calculations for the red dog food can rolling down the slope in the Rube Goldberg design are as follows (we will name it Step 1): Step 1 (calculations are given): Coefficient of friction → μ = 0.14 Mass of the object → m = 368 gm = 0.368kg Initial height of the object (red can on top of books) → h=8.89, cm = 0.0889 m Slope of the file folder → 0= 14° Travelling Distance by the object = 11.5 inch = 0.292 m And length that the object will travel = h/sin 0 = 0.0889/ sin14° = 0.367 m So, the radius of the object → R = 0.367 -0.292 = 0.075 m Initial Velocity of red can → u = 0 Velocity and Force Calculations for Step 1: -From total mechanical energy conservation: → Initial mechanical energy = final mechanical energy → mg - In case of pure rolling, the velocity of the center of mass: →V=Roo= 0.075 x 14.28 = 1.07 m/s. -Hence the change in force acting on the object for the travel: →F=mgsine = 0.368 x 9.81 × sin14° =0.89 N Step 2: The Selective Step (Step 2) in this design and for the…