What is the weighted-average distance of the two initial weights (10 pounds at 4 feet aft and 5 pounds at 2 feet aft) from the CG?

What is the weighted-average distance of the two initial weights (10 pounds at 4 feet aft and 5 pounds at 2 feet aft) from the CG?

• A. 3.000 ft
• B. 3.333 ft
• C. 3.500 ft
• D. 4.000 ft

Answer: (B)

Center of gravity is found by averaging the positions of all weights weighted by their forces. In other words, you take each weight times its arm (distance from the reference), add those moments, and divide by the total weight.

Here, the total weight is 10 + 5 = 15 lb. The moments are 10×4 = 40 ft-lb and 5×2 = 10 ft-lb, for a total moment of 50 ft-lb. The CG location from the reference is 50 / 15 = 3.333 ft aft.

So the weighted-average distance of the weights (the CG) is about 3.333 ft aft of the datum. The CG lies between the two weights, closer to the heavier one, as expected.