$(24$ points$)$ You are working as a design engineer at an amusement park. You have been tasked with

designing a compound gear train to drive a rollercoaster up a hill. A two stage compound gear train

powered by spur gears is to be used. Using your knowledge of physics, you have calculated that the

required output shaft torque is $6260$ Nm to drive the rollercoaster up the hill. To meet the daily output

of the amusement park $($number of riders processed per day$),$ the output shaft must rotate at $125$

RPM$.$ Your gear train is to be powered by a $110$ horsepower motor operating at $3000$ RPM$.$ The

available gears have a face width of $2$ inches and the minimum number of teeth on any gear is $12.$

a$)(5$ points$)$ Sketch your compound gear train. Specify the number of teeth on each gear. Calculate

the overall gear ratio and verify that it will produce the required speed of the output shaft.

b$)(16$ points$)$ Select a material, pressure angle and diametral pitch for your gears. Show that the

resulting gears will be strong enough for the application $($can compare torques or tooth loads$).$

c$)(3$ points$)$ What is the safety factor on your weakest gear? Are you comfortable with this result? If

not, what would you like it to be$?$