Asingle-thread steel worm rotates at 180.64 rad/s, meshing with a 24-tooth worm gear trans mitting 0.7457 kw to the output shaft. the worm pitch diameter is 3 in and the tangential diametral pitch of the gear is 4 teeth/in. the normal pressure angle is 14.5. the ambient temperature is 294.26 k. the application factor is 1.25 and the design factor is ; gear face width is 12.7 mm, lateral case area 5483.86 cm2, and the gear is chill-cast bronze. (a) find the gear geometry (b) find the transmitted gear forces and the mesh efficiency (c) is the mesh sufficient to handle the loading? (d) estimate the lubricant sump temperature.