problem $4.(8$ points$)q,$

A $20$ pressure angle spur pinion having $16$ teeth is driving a $48-$tooth gear. The pinion speed is $300re\frac{v}{m}in,$ the face width is $5$ cm $,$ and the module is $5$ mm $.$ Both gears are grade $1$ steel, through$-$hardened at $200$ Brinell, made to No$.6$ quality standards. Assuming a pinion life of ${10}^7$ cycles, a reliability of $0\mathrm{.}99,$ a load distribution factor of $1\mathrm{.}2$ and smooth driving conditions, determine the maximum power that can be transmitted based on wear in the pinion.