Question about transfer of Energy and Momentum in Ballistics

[Assaltwaffle]

You still seem to mix energy and momentum a bit. You should consider energy and momentum as two independent quantities that "just happens" to be related via mass and velocity. The momentum of the bullet (minus loss during flight) is transferred from the shooter to the target and, independently of this, some part of the energy released by the gun powder is first transferred to the bullet in the barrel and then transferred (except for loss during flight) to the target.

I think this was my misconception. It was my understanding that any motion undertaken by an object is a byproduct of energy and thus must be caused by energy. So the transfer of momentum causes the object to move accordingly, not the transfer of kinetic energy, and even though the kinetic energy transfer isn't zero (because kinetic energy and momentum both are a product of mass and velocity), the energy is not the cause of motion. Am I still misunderstanding?
So, then, how does work fit in?

 

[Drakkith]

So the transfer of momentum causes the object to move accordingly, not the transfer of kinetic energy, and even though the kinetic energy transfer isn't zero (because kinetic energy and momentum both are a product of mass and velocity), the energy is not the cause of motion. Am I still misunderstanding?

Movement requires BOTH energy and momentum. Your misunderstanding, in my opinion, centers around the idea that motion is related to one more fundamentally than the other. This is not true. Both are equally fundamental, they just behave and are transferred somewhat differently. Neither is the cause of motion.

 

[jbriggs444]

I think see now. It seems I had a fundamental misunderstanding about what determined the "impulse" and how what work the bullet did is determined.

So, if the round is fully stopped by a plate or fully capture by a body, the full momentum is transferred as an impulse. Energy does this work and transfers energy accordingly to make that impulse, but the rest of the energy of the projectile is lost through doing "damage", such as bending metal, breaking ceramic, or tearing flesh.

I would say "yes", you have this correct. Some small portion of the kinetic energy of the bullet is expended in the kinetic energy corresponding to the bulk motion of the target body. Energy is conserved. The remaining energy must be accounted for otherwise. As you put it, bending metal, breaking ceramic or tearing flesh. Or is retained as the bullet proceeds on and through the target.

If I understand it, it would seem to reason that if the plate failed because it could not resist the projectile and the object passed through the target, that the impulse would be less because the round still had energy and momentum remaining upon exit and did not transfer all of its momentum. Is that correct?

Yes. If the bullet carries on through the target, it retains some of its original momentum. Less has been transferred to the target.

 

[Filip Larsen]

So the transfer of momentum causes the object to move accordingly, not the transfer of kinetic energy

To the extend you mean that change in momentum of an isolated object causes change in its velocity, then you are correct. In classical mechanics Newtons 2nd law states that time rate change in momentum for an object equals the net force on that object, so if you can model what forces an object experiences as a function of its position and velocity then you can calculate how the object moves without directly having to consider the energy of anything.

However, for some dynamical models it can be much easier to derive the dynamics considering the energy flow between the interacting parts, especially so when the interactions can be modeled as frictionless. And in some cases, like for fully elastic collisions, you need to consider (conservation of) both momentum and energy at the same time to arrive at a solution.

Another reason why mass, momentum and energy are important (and independent) concepts in classical mechanics is that the sum of each of these quantities for the parts of an isolated system can be considered a conserved quantity (i.e. constant over time), with energy being conserved as the sum of kinetic energy and internal energy in case of friction.

 

[Herman Trivilino]

why, mechanically, is the person not knocked over despite such a high amount of energy striking the individual relative to a weaker force that can achieve this?

You made quite the leap there from energy to force. Just because something has more energy doesn't mean it exerts a larger force. You have to take into account the distance the object moves while it's slowing down.