Problem $4(8$ points$)$: Compute the bending stress number, $S_t,$ using Equation $(9-16)$ for a pair of gears with $20,$ full$-$depth, involute teeth that transmits $40$ hp while the pinion rotates at $1150$ rpm $.$ The diametral pitch is $6,$ and the quality number is A$11.$ The pinion has $20$ teeth, and the gear has $48$ teeth. The face width is $2\mathrm{.}25$ in $.$ The input power is from an electric motor, and the drive is for a cement kiln. The drive is a commercial enclosed gear unit. Assume that the gear blank is solid.