Trebuchet Efficiency

  1. 1. The problem statement, all variables and given/known data
    I've calculated the time, the distance, the height of the counterweight before launch, the mass/weight, and I need to calculate the energy efficiency.
    How to go about it?

    h = 0.71 m
    m = 1.445 kg
    g = 9.8 m/s^2
    t = 0.7 s
    x = 4.44 m

    2. Relevant equations

    Eg = mgh
    Vix = x/t
    y = Viy(t) + (1/2) a(t)^2
    Ek = (mv^2)/2

    3. The attempt at a solution

    THEORETICAL YIELD:
    h = 0.71 m
    m = 1.445 kg
    g = 9.8 m/s^2
    Eg = mgh
    = (1.445 kg)(9.8 m/s2)(0.71 m)
    = 10.05 J

    ACTUAL YIELD:
    t = 0.7 s
    x = 4.44 m
    Vix = x/t
    = (4.44 m)/(0.7 s)
    = 6.34 m/s

    y = Viy(t) + (1/2) a(t)^2
    0.71 m = Viy(0.7 s) + (1/2) (-9.8 m/s2)(0.7 s)^2
    Viy = 4.44 m/s

    Vi^2 = (Vx)^2 + (Viy)^2
    Vi^ = (6.34 m/s)^2 + (4.44 m/s)^2
    Vi= 7.74 m/s

    Ek = (1/2) mv^2
    = (1/2) (1.445 kg)(7.74 m/s)^2
    = 43.28 J

    43.28 J / 10.05 J = 430%

    I don't think my trebuchet is 430% efficient.
    What did I do wrong?
     
    Last edited: Jan 15, 2007
  2. jcsd
  3. Efficiency is work in/work out
     
  4. An easier way to find trebuchet efficiency (all credit goes to Rom Toms http://www.trebuchet.com/):
    Actual measured range in meters /theoretical range= efficiency

    theoretical range in meters= 2 * (counterweight in kg * counterweight drop in meters)/ weight of projectile in kg
     
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