Problem $3$: You are designing a shaft with a helical gear supported by two tapered bearings

directly mounted on either end of the shaft. The helical gear generates a radial load of

$1500$ lbf directly between the two bearings and an axial load of $900$ lbf $.$ The shaft is

to operate for $3000$ hr at $400$ RPM with $95\%$ reliability. Find a suitable tapered rolling

bearing for the design. Use Figure $11-15$ to select your bearing $($Note the $L_{10}$ value$).$