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?
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