Two boxes weighing 10 lbs and 5 lbs are placed in an airplane so that their distance aft from the CG are 4 ft and 2 ft respectively. How far forward of the CG should a third box weighing 20 lbs be placed so that the CG will not be changed?

Two boxes weighing 10 lbs and 5 lbs are placed in an airplane so that their distance aft from the CG are 4 ft and 2 ft respectively. How far forward of the CG should a third box weighing 20 lbs be placed so that the CG will not be changed?

• A. 2.5 feet
• B. 5.0 feet
• C. -2.5 feet
• D. 1.0 feet

Answer: (A)

Balancing moments about the original CG is what keeps the CG from shifting when you add a new weight. The two boxes behind the CG create aft moments: 10 lb × 4 ft = 40 ft-lb and 5 lb × 2 ft = 10 ft-lb, for a total aft moment of 50 ft-lb. To keep the CG in the same place, the new 20-lb box must produce an equal forward moment: 20 lb × distance = 50 ft-lb, so distance = 50/20 = 2.5 ft forward of the CG. Any other placement would not cancel the aft moment (2.5 ft forward is the exact distance to balance), so the correct placement is 2.5 feet forward of the CG.

Balancing moments about the original CG is what keeps the CG from shifting when you add a new weight. The two boxes behind the CG create aft moments: 10 lb × 4 ft = 40 ft-lb and 5 lb × 2 ft = 10 ft-lb, for a total aft moment of 50 ft-lb. To keep the CG in the same place, the new 20-lb box must produce an equal forward moment: 20 lb × distance = 50 ft-lb, so distance = 50/20 = 2.5 ft forward of the CG. Any other placement would not cancel the aft moment (2.5 ft forward is the exact distance to balance), so the correct placement is 2.5 feet forward of the CG.