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I'm no hunter, but there is something that come around the butt of the arrow and releases it causing it to shoot. This means that the potential energy is stored in the elastic/rubber/string thing that launches the arrow

Actually the energy is stored in the bow, all the string provides is tension. as you pull the string back, the distance between the bow tips gets pulled in, spreading the potential evenly around the entire bow. Upon pulling the trigger, the bow is allowed to relax back into shape, pulling the string taught, and forcing the arrow forward.

If you were to try and use the string as a store (IE. a rubberised string), there would be much less area to hold potential, and as a result you would have to pull the string considerably further back than the tip spacing of a crossbow (think slingshot).

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Q: What part of the crossbow stores the potential energy?
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