In the solution of this problem, use singularity functions. Clearly state the boundary conditions and the solution of the integration constants. Find the slope at the location of the bearings, i.e., ( = 0) and ( = 11), and at the location of the gear, i.e., ( = 9). Find the deflection at the location of the gear, i.e., ( = 11). If the safety factor is given by.

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Problem 2 (10 points)Slopes and deflections: Determine the slope at the locations of the bearings and the deflection at the location of the gear. Using Table 7-2, determine if the design of the shaft is adequate. In your analysis, consider that the diameter of the shaft between the two bearing is constant and equal to 1.875 in. The increase in the diameter's shoulder or the reduction in diameter at the bearing will have an insignificant effect on the results. The spur gear has a diametral pitch P = 6 and 24 teeth. Table 7-2 Typical Maximum Ranges for Slopes and Transverse Deflections Slopes Tapered roller 0.0005-0.0012 rad Cylindrical roller 0.0008-0.0012 rad Deep-groove ball 0.001-0.003 rad Spherical ball 0.026-0.052 rad Self-align ball 0.026-0.052 rad Uncrowned spur gear