FAA Aviation Mechanic General (AMG)Physics, Math and Fluid LinesHard
An aircraft component assembly has three weights positioned along a beam: 100 lb at station 20, 150 lb at station 60, and 50 lb at station 100. What is the location of the combined center of gravity (CG)?
- AStation 50.0
- BStation 53.3
- CStation 60.0
- DStation 46.7
Show answer & explanationAnswer & explanation
Correct answer: B. Station 53.3
Total moment = (100×20) + (150×60) + (50×100) = 2,000 + 9,000 + 5,000 = 16,000. Total weight = 100+150+50 = 300 lb. CG = total moment ÷ total weight = 16,000 / 300 = 53.3. The CG is the weighted average location of all moments divided by total weight.
Why the other options are wrong
- A. This is a simple average of the stations, ignoring the different weights.
- C. This is only the station of the heaviest weight, not the combined CG.
- D. This results from a moment arithmetic error, understating the true CG.
Center of Gravity (CG) Calculation
CG location is found by dividing the sum of all individual moments (weight × arm) by the total weight of all items.
- Moment = weight × arm (distance from reference datum)
- CG = total moment ÷ total weight
- Heavier weights and greater arms pull CG further from the datum
Memory trick: 'Sum the pulls, divide by total weight' finds the balance point.