This is great stuff By Dr. Ed Ashby. Check it out and read the whole thing there is a lot of great info there that can be applied outside of archery.
“Given two arrows of equal momentum, but with one deriving a greater portion of its momentum from mass than the other, the heavier arrow will change velocity (decelerate) at a slower rate as it passes through the tissues. In other words, the heavier arrow will retain a higher percentage of its impact velocity at any given time period during its passage through the animal’s tissues, thus it also retains a higher momentum at any given point during the time required for the arrow to penetrate.
Another way of saying this would be that, though the heavier arrow is traveling slower, it takes a longer time to stop. The result is that the heavier arrow will have a greater impulse of force than does the light arrow.
It is momentum that gives an object in motion the tendency to STAY in motion. The greater the contribution of the object’s mass is to the resultant momentum the harder it will be to stop the forward progression of a moving object. Anyone who has pushed a car in neutral and then tried to stop it will understand this. The more of a moving object’s momentum that is derived from its mass, the more TIME it takes to stop it with any given resistance force.
It is common for proponents of light and fast arrows to counter that the faster arrow will have traveled a greater distance through the tissues in the same time period than will the heavier, and slower, arrow. This would be valid were it not for the nature of resistance forces.
As the arrow’s velocity is increased the resistance does not increase equivalently. The resistance increases exponentially. The resistance of a medium to penetration is reliant on the square of the object’s velocity (assuming objects of a given coefficient of drag; i.e., using arrows with the same external profile, material and finish). In other words, if the arrow’s impact velocity doubles, the resistance increases by a factor of four. If the impact velocity quadruples, the resistance to penetration increases 16 times!”