Since Kinetic energy in a .223 is significantly higher than a .45 acp yet they both are similiar in momentum (both in the 20s) where does the kinetic energy of the .223 go so that energy is conserved?
Conservation of energy and conservation of momentum are not actually closely related at all, from a layman's perspective. When you get into relativity and string theory and unified field theory, I suppose they are though.
But conservation of momentum means that, if a bullet hits something and doesn't exit, 100% of the bullet's momentum is "transferred" to the target, thus accelerating it in the direction the bullet was going.
Conservation of energy only means that energy cannot be created or destroyed (except by nuclear reactions and the annihilation or creation of antimatter
), it can only change form. And that's what happens with any process. Eventually, 100% of the bullet's energy (really, the gunpowder's energy) turns into heat.
Like a .223 with 1,000 ft-lbs, the gunpowder will probably have about 3,000 ft-lbs of energy in it. When it's burned, 2,000 of that goes to the bullet, and the other 2,000 ft-lbs are used to heat various parts of the gun, and make a loud sound and bright flash, and propel bits of powder and smoke at high speed. But eventually, all of that energy turns inot heat. Like the flash heats things up a bit from the light; everyone knows strong lasers can burn things. And the sound heats things, too. You could boil a cup of water by yelling at it for a few decades, if it were well insulated enough.
Then the bullet hits the target. It's force, or more accurately strain, which does damage, not "energy." Though force will correlate somewhat with energy, it doesn't tell you the whole picture, as less force is necessary to destroy tissue which the bullet directly contacts, which is why a .45 makes a bigger hole than a 9mm, even though they both have the same energy. For a given amount of energy, a larger and heavier bullet makes more efficient use of it (however, don't make the mistake of confusing efficiency with effectiveness).
But most rifles 1,000 ft-lbs and up can, with a softpoint bullet, exert enough force on an organic target to make a big temporary cavity (the so-called hydrostatic shock effect), which stretches and tears and shreds tissue, making a hole many times larger than the bullet.
In any case, some of the energy is used to make a hole, some of it remains as kinetic energy for awhile, moving tissue around, some of it goes straight to heat, some to sound, etc. But eventually, 100% of the bullet's energy turns into heat, as well.