Problem $1$

$(10$ points$)$ Shaft A in the figure has a power input of $75$ kW at a speed of $1000$ RPM in the counterclockwise direction. The gears have a module of $5$ mm and a $20$ degree pressure angle. Gear $3$ is an idler. $($This is problem $13-31$ in the text$)$

a$.(5$ points$)$ Find the force $F_{3b}$ that gear $3$ exerts against shaft b$.$

b$.(5$ points$)$ Find the torque $T_{4c}($magnitude and direction$)$ that gear $4$ exerts on shaft c $.$