8 teeth 42 teeth 10 teeth 55 teeth 3. In the gear train shown, gear 1 has 14 tee

Question

8 teeth 42 teeth 10 teeth 55 teeth 3. In the gear train shown, gear 1 has 14 teeth, gear 2 has 43 teeth, gear 3 has 22 teeth, and gear 4 has 92 teeth. Arope carrying a weight ofw#300b is being wound at a constant rate onto a spool with a radius of r ift, The spool is directly attached to gear 4 Gears 2 and 3 are rigidly connected to each other. Assuming 100% efficient gears, what is the torque supplied by the output shaftof the motor? 23 36 1-lbf Hint: Remember, you can relate torque through the gear train using the gear ratios discussed in class 6. You can also calculate torgue by as Force x Distance. This expression may give you a starting point GEAR 3 GEAR MoToR 0 2 Wt

Explanation / Answer

Weight on the rope = 300lbs.

Number of teeth:

T1 = 14

T2 = 43

T3 = 22

T4 = 92

Torque generated on spool Torque4 = Weight x radius of spool = 300 x 1 = 300 ft-bf

As Gear 4 and spool are on same axis, Torque on Gear 4 = Torque4

Number of teeth and torque are directly related (directly proportional)

Torque on gear 3, Torque 3 = (T3 / T4) * Torque4 = (22 / 92) * 300 = 71.73 ft-lbf.

As Gear 2 and Gear 3 are on same axis,Torque on Gear2 = Torque 3

So, Torque on gear 1, Torque1 = (T1 / T2) * Torque 3 = ( 14 / 43 ) * 71.73 = 23.353 ft-lbf.

As Gear 1 and Motor are on same axis, torque supplied by output shaft of motor = 23.353 ft-lbf.

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