One of my posts form a previous thread:
Ofcourse there is proof, stemming from Newton's second law of motion. Force equals mass time acceleration. Acceleration is the rate of change of velocity, or its first derivative in calculus terms. If you double velocity, you get a greater result of force than if you double mass.
Your bullet analogy doesn't apply. A 44 mag uses a 10.9 mm diameter bullet. It is phsyically larger, so it will do more phsyical damage in terms of area.
A 180 grain bullet traveling at 1610 feet per second has 1036 ft lb of energy. A 240 grain bullet traveling at 1180 feet per second as only 741 ft lb of energy. Both are plenty high enough to tear flesh. A larger bullet will do more physical damage.
A cue ball weighs the same, regardless of what cue hits it. The only thing that increases the energy of the cueball is a higher velocity of the cueball. There is probably a relative maxima (again, calculus talk) for every person in terms of force created when breaking. Too heavy of a cue, and the person will not be able to generate enough stick speed to get maximum results. If the cue is too light, then the force is reduced, because the players muscle fibers can fire only so fast. There is a peak speed someone can achieve using a certain weight cue, and if the cue is any lighter, the speed will be the same with less mass, so less force. That optimum cue weight is a little different for everyone, depending on their weight, their strength, and how fast they can physically move. Ofcourse throw in inconsistent hits, not hitting center, too much stick speed and control is not optimum, and it all greatly becomes a personal preference.
Why do you think it is against the rules for baseball players to cork bats? A corked bat weighs less, but the increase velocity of swinging the bat more than makes up for the less mass, so the baseball goes farther (as long as the bat doesn't shatter).
Old thread:
http://forums.azbilliards.com/showthread.php?t=73988&highlight=derivative
