Please show all your work and write cleanly. Box or highlight intermediate steps as necessary to

produce a professional report.

Problem 1 (10 points): The input shaft of a gear reducer is supported by two bearings at location A

and B while transmitting 240 lbf-in torque. The distance AB is 2.5 inches. The gear G₁ is shown

without the teeth for simplicity. It has a pitch radius of 0.75 inches and pressure angle = 20°. It is

mounted 1.5 inches away from the bearing B.

(a) Draw the free-body diagram for the shaft AB and determine the net reaction forces and

moments at the location where G1 is mounted.

(b) If the shaft is rotating at 300 rpm, what is the motor HP needed to run this application?

CE

5 in

7,240 lbf-in

AC

F

N

N

α

F

B

Please note that a gear experiences a tangential force (F) that transmits the torque and a radial force

(N) that is inevitable due to tooth geometry. The radial force, N = F tan ø.