MDM Practice Exam, #523

[el_carlito]

Is anyone else confused with the solution to #523 in the NCEES MDM practice exam?

To paraphrase the question: given a ring and pinion gear pair, what happens if you decrease the number of teeth on the ring gear?

A) The vehicle acceleration will increase

B) The vehicle speed at a given engine rpm will increase

C) Both A and B are true

D) Both A and B are false

The answer is (B). What I can't figure out is a comment in the solution that says that reducing the rear wheel torque reduces the car's acceleration.

The relationship between pinion/gear speed and number of gear teeth is pretty straightforward from MERM (eq. 59.25). But how is the torque on the output gear (the ring gear) reduced?

My thinking is based on eq. 54.45:

torque_gear * speed_gear = torque_pinion * speed_pinion

Since we have already established that the gear speed is reduced, and holding the torque and speed of the pinion constant, the only way to satisfy eq. 54.45 is for the gear torque to increase, not decrease. Meaning that (C) would be the correct answer.

 

[JHW 3d]

Is anyone else confused with the solution to #523 in the NCEES MDM practice exam?
To paraphrase the question: given a ring and pinion gear pair, what happens if you decrease the number of teeth on the ring gear?
A) The vehicle acceleration will increase
B) The vehicle speed at a given engine rpm will increase
C) Both A and B are true
D) Both A and B are false
The answer is (B). What I can't figure out is a comment in the solution that says that reducing the rear wheel torque reduces the car's acceleration.
The relationship between pinion/gear speed and number of gear teeth is pretty straightforward from MERM (eq. 59.25). But how is the torque on the output gear (the ring gear) reduced?
 
My thinking is based on eq. 54.45:
torque_gear * speed_gear = torque_pinion * speed_pinion
Since we have already established that the gear speed is reduced, and holding the torque and speed of the pinion constant, the only way to satisfy eq. 54.45 is for the gear torque to increase, not decrease. Meaning that © would be the correct answer.

Removing a tooth will increase the gear SPEED. Therefore gear TORQUE decreases to satisfy the power equation.

 

[Audi Driver P.E.]

Just think of the rear gearset on a bicycle. Smaller gear = faster; bigger gear = more torque (hills)