$($Total $37$ pts$.)($Clearly show the steps and the necessary calculations.$)$

The figure shows a two$-$stage gear reducer. The input shaft A is driven by $7\mathrm{.}2$ kW single cylinder engine at a constant speed of $1800$ rpm counterclockwise $($as shown$).$ Output shaft C drives a small concrete mixer $($moderate shock$).$ The gears have a module of $4$ mm and a $20$ pressure angle. If gear $3$ has a tooth bending fatigue strength of $S_{tbf}=160$MPa $($fully modified$)$ and a face width of $50$ mm $,$ what is the safety factor guarding it against bending fatigue failure?

You must take into account the following criteria for estimating the safety factor.

The mountings are less rigid. Assume lower precision gearing. Assume $100\%$ efficiency for power transmission between shafts. Assume gearing quality factor $Q_v=8.$ All gears are made of steel. $(37$ pts$.)$