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I'm currently doing a coursework assignment investigating the how the range of a model trebuchet varies according to the mass of the counterweight. Its pretty basic stuff (especially compared to a lot of whats on this forum), but i've spent the best part of today doing it and i'm still stuck.

Anyway, the problem:

Essentially i don't really know how to tackle the trebuchet in a mathematical model/equation. The trebuchet i'm using is pretty basic, it doesn't use a sling, the projectile (in this case, a marble) just sits in a slot on one arm and a counterweight is hung from the other. The beam is horizontal when the system is released. The arm with the projectile on it is considerably longer than the counterweight arm. The marble is released when the beam becomes vertical and is stopped by a metal bar. The problem I'm having is my limited physics knowledge can't get me from the force applied by the counterweight to the velocity the marble is released. I tried two approaches:

I looked at it in terms of moments/torque but in this case i don't know how to translate the torque in the system to the marble itself.

I also tried looking at in terms of energy. Ie. the counterweights GPE transferred to kinetic energy in the other arm. But I can't see how this accounts for the fact that the other arm is longer and that the projectile is positioned at the very end of this arm.

Sorry if this is very wordy and not very mathematical, I'm just trying to convey as much information about it as possible. Also, I'm not looking for someone to give me the answer, just a clue, or a point in the right direction will do.

Thankyou.