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What is the efficiency of the engines?

  1. Dec 12, 2007 #1
    1. The problem statement, all variables and given/known data
    A 3250 km aircraft takes 12.5 minutes to achieve its cruising altitude of 10 km and cruising speed of 850 km/h. If the plane's engines deliver, on the average, 1500 hp of power during this time, what is the efficiency of the engines?


    2. Relevant equations
    Efficiency = Power output / Power input x 100
    P = W/t --> P= mgh/t, P=Fdcos(theta)/t



    3. The attempt at a solution
    m = 3250 kg
    t = 12.5 min --> 750 sec
    h = 10 km --> 10000 m
    Pin = 1500 hp --> 1119000 Watts
    v = 850 km/h --> 236.11 m/s

    vf = at +vi (attempt to find the velocity components but don't add up right)
    236.11 = a (750) + 0
    a = .315 m/s^2

    average v = vf/2
    = 236.11/2
    average v = 118 m/s

    Poutx = F(average v) = ma(average v)
    = 3250(.315)(118)
    = 120802.5 W

    Piny = Fd/t = mgh/t
    = 3250(9.81)(10000)/750
    = 425100 W

    The real answer is 4.091 x 10^8 J ; e = 48.7% but I don't know how to get that answer...
     
  2. jcsd
  3. Dec 12, 2007 #2

    rl.bhat

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    Homework Helper

    Acceleration can be found by v^2 = u^2 + 2as. This acceleration is in addition to the acceleration due to gravity. So the actual acceleration of the aircraft is a+g. Now find the work done.
     
  4. Dec 12, 2007 #3
    by u, do you mean initial velocity? or potential energy?
     
  5. Dec 12, 2007 #4

    rl.bhat

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    Homework Helper

    It is initial velocity, which is zero in this case.
     
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