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Total energy of an airplane, work done against air resistance

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data

    An airliner of mass 300 tonnes is powered by four engines, each developing 15 000 kW. Its speed at take-off is 75 m(s^1), and it takes 11 minutes to reach its cruising speed of 210 m(s^1) at a height of 10 000 metres. Calculate the work done against air resistance during the climb.




    2. Relevant equations



    3. The attempt at a solution

    Alright so I have reasoned that (total energy at take-off)+(work done by engines)+(W, work done against air resistance)=(total energy at 10 000 metres) and that:
    Total energy at take-off = PE +KE = 0 + (0.5 x 300 000 x (75^2))
    Work done by engines (in 11 minutes) = (60 000 000)/(660)
    Total energy at 10 000 metres = PE + KE = (10 000 x 300 000g) + (0.5 x 300 000 x (210^2))
    G=10

    Which makes W (work done against air resistance) = ((10 000 x 300 000 x 10) + (0.5 x 300 000 x ((210^2)) – (0.5 x 300 000 x (75^2)) – ((60 000 000)/(660))) = 3.58 x (10^10) J correct to 3 s.f.

    However, the correct answer is 3.83 x (10^9) J.
    What mistake(s) did I make?
     
  2. jcsd
  3. Oct 26, 2011 #2
    I think that the above equation must be

    (total energy at take-off)+(work done by engines) = (W, work done against air resistance) + (total energy at 10 000 metres)
     
  4. Oct 26, 2011 #3
    Note that Energy = Power x time
     
  5. Oct 27, 2011 #4
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