Question $2.(20$ points$)$

Select a deep$-$groove ball bearing for a life $($L$10)$ of $500$ million revolutions and specified loading as follows:

The radial load: $P_r=1032lb$ and the axial load: $P_a=800lb.$

Question $3.(20$ points$)$

Two spur gears $($Grade $2$ through$-$hardened steel with Brinell Hardness of $250$ HB each, $20$ pressure angle$)$ are in contact. The pinion has $12$ teeth with a diametral pitch $(Pd)$ of $8$ teeth$/$in and the gear has $48$ teeth. The pinion speed is $4000$ rpm and $3100ft-l\frac{b}{s}$ is transmitted. The pinion minimum life is $5$ million revelations. The gears have a face width of $0\mathrm{.}75$ in $.$ The electric power source is uniform, but the machine loading results in occasional light shock. Find the safety factor against failure due to excessive bending stresses.