Kinetic Energy vs. Momentum in Projectile collisions

[gearhead]

I'm trying to figure out the role that kinetic energy and momentum play in projectile collisions. there are two cases: 1.) when the projectile becomes completely embedded in the target and 2.)When the projectile completely passes through the target and flys out the other end.
If the collision is completely inelastic in situation 1, then wouldn't the impact force just be impulse? given by the equation: Force*delta(t)=change in momentum. If this is true, then isn't the destructive force a projectile related solely to it's momentum and not it's kinetic energy? The only situation i see where having a high kinetic and low mometum is better than having really high momentum and low energy, is situation 2.

I shoot bow and arrow, and my bow shoots a 25.7gram arrow 46.4m/sec, giving it a momentum of 1.19 kg*m/s. The energy is only 27.66J. Now compare this with a .22lr: 2.6 grams moving @ 330m/sec., which gives it only 0.858kg*m/s. But it has an energy of 141.5J.
Although my intuition tells me the bullet will do more damage, i don't understand why.

 

[LightHero]

Is it the higher energy or momentum? The destructive force of a projectile is related to both its kinetic energy and momentum. In a collision, the kinetic energy of the projectile is converted to potential energy and is then dissipated in the form of heat, sound, and other forms of energy. This energy is ultimately responsible for the damage done. However, the momentum of the projectile also plays a role. Momentum determines how much force is being applied to the target and can have an effect on its structural integrity. Therefore, in the case of the bow and arrow and the .22lr, the higher energy of the .22lr will likely result in more damage due to the greater amount of energy that is released upon impact.