Answer :
Final answer:
To correct the aircraft's center of gravity, a ballast of 114 lbs is necessary when placed at an arm of +162 inches, which aligns the CG to the minimum acceptable range. This is calculated using the principle of moments based on the current and desired CG positions.
Explanation:
To bring the aircraft's center of gravity (CG) within the acceptable range, we need to calculate the minimum weight of the ballast required. The aircraft's current CG is at +30.5 inches, which is outside the allowable range of +32.0 inches to +42.1 inches. The ballast is to be placed at an arm of +162 inches.
To shift the CG to the minimum acceptable range (+32.0 inches), we must determine the amount of weight needed at the ballast arm to achieve this.
We can use the principle of moments, where the moment is equal to the weight times the arm (distance from reference point):
Weight of Aircraft × Current CG Position = (Weight of Aircraft + Ballast) × New CG Position
To solve for the minimum ballast:
4954 lbs × 30.5 inches = (4954 lbs + Ballast) × 32.0 inches
Expanding the equation and simplifying:
Ballast = ((4954 lbs × 30.5 inches) - (4954 lbs × 32.0 inches)) / (162 inches - 32.0 inches)
After performing the calculations:
Ballast = 114 lbs (approximately)
Therefore, the minimum weight of the ballast necessary to bring the CG within the acceptable range is 114 lbs, which corresponds to option C.
