The whole physics discussion is interesting but really when we are talking about KE vs. Momentum there really is no "vs." aspect to it. Both kinetic energy and momentum are resultant of motion / acceleration of a particle. Since both KE and momentum have the same variables in their equations, we are really talking about the same thing but different aspects of the motion of the same particle.
Newtons laws of motion in a nutshell state that momentum, energy, or angular momentum cannot be created or destroyed. That being said, KE and momentum
push through an object in the same way. A comment was made that momentum wins at longer distances and that really isn't all that relevant. An object that slows down, in this case an arrow, it both looses kinetic energy and momentum. Granted since in the kinetic energy equation, the velocity component is squared, means that the value of kinetic energy dissipates at a faster rate than momentum does. However, they are both describing the energy of the same particle (arrow).
A rifle is a little easier to explain than a bow but I will try. When you shoot a rifle, the cartridge explodes, accelerating the projectile down the barrel. Force is a resultant of the acceleration of a particle and every force has the same force in an equal and opposite direction according to Newton. The opposite force that you feel, is the kick of the rifle. That force is the energy that is put into the bullet while the gasses expand and accelerate it down the barrel. At this point, the same kinetic energy and momentum that the bullet contains after it leaves the barrel has acted upon your body and the rifle. (This is why knockdown power is somewhat a misunderstood concept as in movies, people appear to be blown away by a large caliber weapon. The projectile or projectiles cannot impart more force to an object or person than the shooter has already taken in the recoil. This is merely dramatic action in the movies.)
Now to the collision of the bullet with an object. The collision between the bullet and the deer, target, etc... is the exact same concept. The KE and momentum that is transferred to the object is equal to the frictional forces and the inertial forces of the object that is in the way. So bone, tissue, and fluids need to move in order for the bullet / arrow to pass through an animal. This is a transfer of energy (KE and momentum) since these particles of bone, tissue, and fluid accelerate out of the way of the projectile, thus giving them their own motion and components of kinetic energy and momentum which is robbed from the projectile.
In bowhunting and archery, we look at the bow and arrow system. The energy you put into your bow when you draw it back is the total energy you have available. As many of you have probably experienced, shooting a heavier arrow makes your bow quieter and reduces the shock felt by your hand. This is because the bow can transfer more energy efficiently to a heavier arrow than a light one. When you shoot very light arrows, much of the energy is left in the limbs, cams, string, etc... (this is why 5 grains per lb. is as light as you can go because that energy has to go somewhere and it goes right into your cams and limbs and nearly simulates a dry fire) the shock you feel is the transfer of that energy to move the riser. The limbs and cams all have their own inertia (inertia is a particle's ability to resist motion FYI) and that inertia in the case of light arrows keeps the limbs and cams from accelerating as fast as the arrow does resulting in a lagging energy transfer.
In short, it is best to find the balance of the speed in which you are comfortable with the trajectory and the weight of your projectile which best suits your bow and arrow system.
I don't know what I just said... I blacked out. Hope it helps someone understand the concepts involved if you bother to read it.
I need a beer. :drink1:
