RE: Who said that physics wasn't fun?
Bowhunter44, Thanks for the terminology...it's all coming back to me...lol
So the KE would have to be a parabola since it is the integral of the draw force curve or the area under the curve. Just trying to refresh here, so how would the momentum graph reach a vertex (which we both agree that it must) since it is a linear function. I guess my thoughts are leading me to the fact that in this situation of dealing with bow performance, momentum would have to be graphed in relation to KE. As I stated before, when we get to the vertex of the KE graph, we are dealing with the maximum efficiency of the bow in the test. Once this is fixed, velocity decreases exponentially as weight goes up. So would this mean that the graph of the momentum be a " / " with half of an upside down parabola following it and connecting at the highest point? The 2nd half would resemble y= 1/x ?
What I am attepting to prove with out the math proplems or actual test results is that momentum and KE are so closely related that they would maximize at the same point. If infact, velocity is decreasing "exponetially" once the bow has maximized efficiency and KE is maximized, then momentum would have to decrease exponentially at that point as well.
Maybe you can actually come up with the proper formulas to prove or disprove this. You seem to have the technical math and physics on the front of your mind. I had 3 physics classes, Calculus I, II, III, and Differential Equations by my sophomore year in college which was 8 years ago. I remember bits and pieces....but maybe I just crammed it all in too short a period of time...lol
P.S...I had a physics and chemistry teacher simular to you in HS....he's the one that got me so interested in this stuff. We had a lab every week and it was all real life scenerios. We would spend Monday learning the physics and the rest of the week performing the physics that we learned...Lab report was due by end of class on Friday for a grade. He never taught from a book and never helped with the Labs...you had to listen on Monday very closely and figure it out on your own. He was the BEST DAMN TEACHER I ever had!!!!