The See Saw Trebuchet
The See Saw trebuchet is fairly simple. The angle q is the angle between the support and the short arm of the beam. If the beam is massless, the net torque is tnet=McwL1gsinq-MprojL2gsinq. The moment of inertia is given by I=McwL12+MprojL22. And since t=Ia, a=g(M1-M2)/(M12-M22)sinq=gksinq. Where k is a constant. The angular velocity, w can be found by the equation w2=w02+2aDq (when a is constant). Since the initial angular velocity is zero, w2=òadq. This can be solved, using the a found earlier. When solved, it yields w=-gk(cos(qf)-cos(qi)). Since Vproj=wL2, the range of this model is R=2(-k(cos(qf)-cos(qi)L2)2sin(qf)cos(qf). The maximum range is acheived not at q=45º, but at q=38º. The efficiency of this model is about 11%.
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