Question

part 9 - mechanical comprehension
what is the mechanical advantage of the gear train shown in the illustration?
a 3
b 4
c 6
d 8
click the button or type the letter next to your answer.

Explanation:

Step1: Recall Mechanical Advantage Formula for Gears

The mechanical advantage (MA) of a gear train is given by the ratio of the number of teeth on the driven gear to the number of teeth on the driver gear. So, \( MA=\frac{\text{Number of teeth on driven gear}}{\text{Number of teeth on driver gear}} \).

Step2: Substitute the Given Values

The driven gear has 60 teeth and the driver gear has 20 teeth. Substituting these values into the formula: \( MA = \frac{60}{20} \).

Step3: Calculate the Result

Simplifying \( \frac{60}{20} \) gives 3. Wait, no, wait. Wait, mechanical advantage for gears: when the driven gear is larger than the driver gear, the MA is driven teeth over driver teeth. Wait, 60 divided by 20 is 3? But wait, maybe I mixed up? Wait, no, let's check again. Wait, the formula for mechanical advantage in gears is \( MA=\frac{\text{Teeth on Driven}}{\text{Teeth on Driver}} \). So 60/20 = 3. But wait, the options have A as 3. But wait, maybe I made a mistake? Wait, no, let's confirm. The driver gear is B (20 teeth), driven is A (60 teeth). So MA = 60/20 = 3. So the answer should be A. 3. Wait, but let me check again. Wait, maybe the formula is different? No, mechanical advantage for a gear system (simple gear train with two gears) is the ratio of the number of teeth on the driven gear to the number of teeth on the driver gear. So yes, 60/20 = 3. So the mechanical advantage is 3.

Answer:

A. 3