Some archers are obsessed with light arrows, arrow speed, and kinetic energy numbers, but this is only the initial speed and energy leaving your bow. As hunters, we care more about retained energy (and more so, momentum) as the arrow hits the animal and goes through the animal hitting flesh and bone).

The Kenetic Energy equation means you have to put in much more energy to get an increase in speed for a given mass. And the speed returns are diminishing as they increase with the square root of the energy increase.

In archery, a bow has a given amount of energy it can impart to an arrow. As you increase the mass of the arrow, the initial velocity will drop proportional to the square root of the mass.

V = SQRT(2*KE/M)

Now just remember this. Drag on anything moving through air (car, rocket, or arrow) is quadratic with the velocity. That means the faster something goes, the drag on that thing increases more than with the square of the velocity. This is why it is so difficult for cars, motorcycles, jets to go really fast without lots of wind drag elimination and tons of energy going behind propulsion.

So the faster an arrow starts out of your bow, the faster it will lose that speed (and energy).

Now when it hits the animal, what matters is momentum. Momentum is simply mass times velocity. This velocity is the velocity at impact - not the same as initial velocity out of your bow.

When there is a collision (say between your arrow and a deer), there is some transfer of momentum (ask anyone who has been hit by an arrow while wearing a bullet proof vest - like that idiot on YouTube). If the point is sharp, like with a good broadhead or if the flesh is soft and easily punctured, there will be little transfer of momentum and instead the arrow will pass right through the animal. If it hits bone, or if the arrow broadhead is mechanical and must use up some energy to open, or if the broadhead is dull, more momentum will transfer, and energy in the arrow will be lost, thus decreasing the arrows momentum dramatically - depending on how solid the connection.

Also, as an arrow gets lighter, it is less efficient in absorbing the energy from your bow. This is one reason why a heavier arrow quiets your bow shot. Be reasonable when selecting an arrow weight.