Trebuchet Calculations

Calculate the counterweights mass  English - 250 lb. / 32.2 ft./s2 = 7.76 slugs  Calculate the mass of the projectile  English – 6lb /32.2 ft./s2 = .19 slugs

Calculate the torque on the counterweight T = F x L English - 250lb x 4.5ft = 1125 lb.ft Calculate the torque of the projectile T= F x L English – 6lb x 8ft = 48 lb.ft

Calculate the potential energy of the counter weight EP = w x h EP = m x g x h English EP = 250lb x 4.5ft = 1125 lb

Calculate the potential energy of the projectile EP = w x h EP = w x g x h English EP = 6lb x 6.5ft = 39 lb

Calculate the velocity of the projectile English v = d/t so v = ft./t so 32.8ft / 1.75 sec = 18.74 ft./s   Calculate the acceleration of the projectile English aave = vf – vi / t2 – t1 or a = 18.74 ft./s – 0ft/s / 1.75s – 0s =10.71 ft./s

Calculate the kinetic energy of the pumpkin English EK = ½ w/g v2 English ( .5 x (6lb / 32.2ft/s2)) x (18.74 ft./s)2 = 32.72 lb

Calculate the efficiency of the trebuchet Efficiency = Workout / Workin x 100% Work = T x Ɵ T= torque Ɵ = Angle moved through x 0.0175 radians English Workout = projectile torque x (degrees x 0.0175 rads) Workin = Counterweight torque x (degrees moved x 0.0175 rads) Wout = 48lb.ft x (60°x 0.0175 rads) = 50.4 lb.ft Win. = 1125lb.ft x (60° x 0.0175 rads) = 1181.25 lb.ft Eff = 50.4 lb.ft / 1181.25 lb.ft x 100% = 4.26%