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Answer :
The maximum weight that could be added at Station 150.0 without exceeding the aft CG limit, for an aircraft with a weight of 5,000 lb and a CG location at Station 80.0, is 35.9 pounds. This was determined by using the moment formula account for the specified aft CG limit of Station 80.5. The correct option is c.
To determine the maximum weight (load) that could be added at Station 150.0 without exceeding the aft CG limit of an aircraft given the following data:
- Aircraft weight: 5,000 lb
- CG location: Station 80.0
- Aft CG limit: Station 80.5
We can use the moment formula to find the weight balance: Moment = Weight x Arm.
The current moment of the aircraft is its weight multiplied by its CG location; therefore, it's 5,000 lb x 80.0 Station = 400,000 lb-station. The maximum additional moment that can be achieved without exceeding the aft CG limit is calculated by multiplying the aft CG limit with the total weight after adding the extra load.
Moment after adding load = Aircraft weight + Additional Load x Aft CG limit Station
Therefore, the calculation would be:
400,000 lb-station + Additional Load x 150.0 Station = (5,000 lb + Additional Load) x 80.5 Station
After algebraic manipulation, we solve for the Additional Load:
Additional Load x 150.0 Station - Additional Load x 80.5 Station = (5,000 lb x 80.5 Station) - 400,000 lb-station
Additional Load (150.0 Station - 80.5 Station) = (5,000 lb x 80.5 Station) - 400,000 lb-station
Additional Load x 69.5 Station = 402,500 lb-station - 400,000 lb-station
Additional Load = 2,500 lb-station / 69.5 Station
Additional Load \< 36.0 lb (rounded from 35.9712)
Based on the calculation, the maximum additional load without exceeding the aft CG limit is just under 36.0 pounds, which rounds to option c) 35.9 pounds. Options a) and b) would exceed the aft CG limit.
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