$16\mathrm{.}15$ The helical gear reducer represented in Figure P$16\mathrm{.}15$ is driven at $1000$ rpm by a motor developing $15$ kW $.$ The teeth have $\backslash (\backslash$psi$=0\mathrm{.}50\backslash$mathrm$\{$rad$\}\backslash )$ and $\backslash (\backslash$phi$\_\{$n$\}=0\mathrm{.}35\backslash )$ rad. Pitch diameters are $70$ mm and $210$ mm for pinion and gear. Determine the magnitude and direction of the three components of the gear$-$tooth force. Make a sketch like the one in the figure except with the shafts separated vertically, and show all tooth force components acting on both gears.