Apinion 1 is driving a gear 3 (moderate shock machinery) through an idler 2. the lines between the centers of 1-2 and 3-2 make an angle of 135e. the diameter of the pinion is 4" and it has 24 teeth. the mounting is accurate with low clearances and high precision gears. the pinion is powered by a 20 hp uniform motor running at 400 rpm, in a direction that minimizes the force on the idler shaft. the idler has 32 teeth. the required speed of rotation of gear 3 is 300 rpm. all gears are full depth spur gears, precision shaved and ground, with a pressure angle of 25-deg, face width 2" and made from the same steel. assuming that the power losses are negligible: (a) what are the maximum bending stresses at the idler and pinion gears? (b) what is the required minimum material strength for a fatigue strength reliability of 98.7%? (c) what is the force on the idler shaft?