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GIVEN:
- Weight A: 135 pounds at 15 inches aft of datum
- Weight B: 205 pounds at 127 inches aft of datum
- Weight C: 85 pounds at 195 inches aft of datum

Based on this information, how far aft of the datum would the center of gravity (CG) be located?

Answer :

Final answer:

To determine the center of gravity (CG) location aft of the datum, calculate the sum of the moments due to individual weights about the datum and divide by the total weight. The CG is found to be 105.02 inches aft of the datum.

Explanation:

To find the center of gravity (CG) location aft of the datum, one must use the moment method in which the sum of moments due to individual weights about the datum is divided by the total weight. The moment is calculated by multiplying each weight by its distance from the datum. Using the provided weights and distances, the calculation is as follows:

  • Moment for Weight A = 135 pounds * 15 inches = 2025 inch-pounds
  • Moment for Weight B = 205 pounds * 127 inches = 26035 inch-pounds
  • Moment for Weight C = 85 pounds * 195 inches = 16575 inch-pounds
  • Total Moment = 2025 + 26035 + 16575 = 44635 inch-pounds
  • Total Weight = 135 + 205 + 85 = 425 pounds

Now, to find the CG:

CG = Total Moment / Total Weight = 44635 inch-pounds / 425 pounds = 105.02 inches

Therefore, the CG is located 105.02 inches aft of the datum.

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