Calculate various fuel quantities for Flight 143. The plane already had 7,682 L

Question

Calculate various fuel quantities for Flight 143. The plane already had 7,682 L of fuel on board prior to the flight, and the tanks were to be filled so that a total of 22,300 kg were present at take-off.

(a) Using the incorrect conversion factor of 1.77 kg/L, calculate in units of kg the amount of fuel that was added to the plane.

(b) Using the correct factor of 1.77 lb/L, calculate in units of kg the amount of fuel that should have been added.

(c) By what percent would the plane have been under-fueled for its journey? Be sure to distinguish between weight and mass quantities in your calculations. (read chapter 3 from Wickert)

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Explanation / Answer

(a) The plane already had 7,682 L of fuel,

conversion factor given here is 1.77 kg/L

this mean 1 L = 1.77 Kg

therefore 7682 L = 1.77*7682 Kg = 13597.14 Kg

this mean initially plane had 13597.14 Kg of fuel, and tanks were to be filled so that it had 22,300 kg of fuel finally.

The amount of fuel that was added to the plane

= final amount -initial amount

= 22300-13597.14

= 8702.86 Kg.

(b) here the conversion factor is 1.77 lb/L

this mean 1 L = 1.77 lb

initial amount of fuel the plane had

= 7682 L

= 7682*1.77 lb

= 13597.14 lb

now we will use the conversion factor 1 lb = 0.45 Kg

therefore,

initial amount of fuel the plane had = 13597.14 lb = 13597.14*0.45 Kg = 6118.713 Kg

final amount of fuel in the plane = 22300 Kg

the amount of fuel that should have been added

= final amount - initial amount

= 22300-6118.713 = 16181.287 Kg

(c) In part (a) we used the incorrect conversion factor to calculate the initial amount of fuel and we calculated how much amount of fuel had been added to make the final amount of fuel to be 22300 Kg. In part (b) we used correct conversion factor to calculate the initial amount and the amoun of fuel that should have been added.

The amount of fuel that was added to the plane = 8702.86 Kg.

the amount of fuel that should have been added = 16181.287 Kg

The plane have been under-fueled by amount = 16181.287 Kg - 8702.86 Kg = 7478.427 Kg

percentage of the amount by which the plane has been under-fueled = 7478.427*100/22300 = 33.54 %

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