ORIGINAL: GMMAT
My whole point revolved around the fact that they arent traveling the same speeds. The lighter of the two will go faster, but it also wont knock the person down, meaning its travel path is stopped more easily...the heavier bat, will knock the guy out of the way and continue its path of swinging through. You are exerting the same amount of force with each swing, the speed is determined by the weight of the object...not how hard you are swinging.
Each side can come up with scenarios to make their points. Would you rather be hit with the bat traveling 10mph or the lighter pipe traveling 60mph.....if both have the same amount of force required to produce said speeds (which would hold true)? THAT'S getting closer to the hunting arrow scenario. It takes the same amount of force (DW/DL) to propel the lighter arrow at greater speeds as it does the heavier arrow at slower speeds. If we could propel heavier objects with no more force required.....hell we'd all be shooting logs. When speaking in hunting arrow terms (which is all I'm interested in, really).....you give up speed when you add weight....every time.
but the speed you give up is less than the weight you gain, up to a point....a heavier arrow absorbs more of the bows potential energy, instead of it passing into limbs and riser......this is why heavier arrows tend to be quieter on the shot.
This increase in initial energy for heavier arrows is why going up slightly in weight slightly increases your KE AND Momentum....again only up to a point before the advantage diminishes.
The energy exerted on the arrow isnt technically the same for every arrow from the same bow, it depends on the mass or weight of that arrow.