The vertical shaft shown is set up as means of an overspeed trip to an older...

  

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The vertical shaft shown is set up as means of an overspeed trip to an older hit-miss engine. Currently as shown, it will shutdown the engine when the DC and BA are at an angle of 90° forced up by the oil pressure of the engine on collar J. This currently occurs at a RPM of *1133. However, we need the speed to be changed to 1800 rpm. A solution was proposed of adding two brass spheres to the end of rods DC and BA, where the edge of the sphere would be brazed to the end of the rod. The current design is as follows: When the vertical shaft is rotating 60 RPM rods DC and BA are at 0'. The mass of the rods are Skg. Lengths DC and BA are 0.3m. The lengths of DE, EC, BG, and GA are all equal. Dimension CA is 0,1 m. The spheres that will be machined and added will be made of brass 60/40 (p=8520 kg/m^3). What vill the mass and radius of the spheres be? Ignore the mass of rods EF and GH. Ignore the mass of component CA. PART A (1 point) Draw a freebody and kinetic diagram showing the before and after conditions of the system. Part B (2 Points) Set up mass moment of inertia equations of all elements for the before and after conditions using parallel axis theorem. You will need to note that the parallel axis theorem used for the mass moment of inertia of the spheres is dependent on the radius, and can be rewritten to be dependent on the mass of the sphere. (Do not substitute any values in at this point) Part C (2 Points) Set up conservation of angular momentum equations for the two conditions, and substitute the mass moment of inertia equations in found in part B. Part D (2 Points) Substitute values from the design into your equations for Part C to find the mass of the spheres. With the mass now known determine the radius of the spheres. The vertical shaft shown is set up as means of an overspeed trip to an older hit-miss engine. Currently as shown, it will shutdown the engine when the DC and BA are at an angle of 90° forced up by the oil pressure of the engine on collar J. This currently occurs at a RPM of *1133. However, we need the speed to be changed to 1800 rpm. A solution was proposed of adding two brass spheres to the end of rods DC and BA, where the edge of the sphere would be brazed to the end of the rod. The current design is as follows: When the vertical shaft is rotating 60 RPM rods DC and BA are at 0'. The mass of the rods are Skg. Lengths DC and BA are 0.3m. The lengths of DE, EC, BG, and GA are all equal. Dimension CA is 0,1 m. The spheres that will be machined and added will be made of brass 60/40 (p=8520 kg/m^3). What vill the mass and radius of the spheres be? Ignore the mass of rods EF and GH. Ignore the mass of component CA. PART A (1 point) Draw a freebody and kinetic diagram showing the before and after conditions of the system. Part B (2 Points) Set up mass moment of inertia equations of all elements for the before and after conditions using parallel axis theorem. You will need to note that the parallel axis theorem used for the mass moment of inertia of the spheres is dependent on the radius, and can be rewritten to be dependent on the mass of the sphere. (Do not substitute any values in at this point) Part C (2 Points) Set up conservation of angular momentum equations for the two conditions, and substitute the mass moment of inertia equations in found in part B. Part D (2 Points) Substitute values from the design into your equations for Part C to find the mass of the spheres. With the mass now known determine the radius of the spheres.

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