Sounds like you're still not real comfortable or familiar with the terms and definitions. I'll try to help make it less muddy, only way it'll make any sense is if you follow the logic line by line.
44_Amp said:
Energy is not equal to Energy.
Energy IS equal to energy. But energy can take many forms. For example, your 115 grain 9mm at 1085 FPS has 300 ft-lb of energy. If you weigh 150 pounds and stand on a 2 foot chair, you also have 300 ft-lb of energy. The AA alkaline battery in your TV remote has over 10 times as much, at about 3,700 ft-lb of energy. A gallon of gasoline has about 100,000,000 ft-lb of energy.
Since Energy = Energy, if you have a clever engineer to build you various mechanisms for utilizing each of these forms of energy to do Work, you will find that the AA battery can do about 10 times as much Work as the 9mm bullet or as you jumping off the chair. The gallon of gas can do about 300,000 times as much work.
If you use each type of energy to do the SAME amount of Work, the AA battery can do it 10 times as fast as the bullet or man jumping off the chair, while the gallon of gas could do it 300,000 times faster. Since Power = Work / Time, we would say that the AA battery has 10 times the Power of the bullet or man and the gallon of gasoline has 300,000 times the Power of the bullet or man.
44_Amp said:
Most of us should be using other terms to accurately describe the effect intended,
That is true. It makes it very confusing when I see someone post something that's the equivalent of "I took a frog from spaghetti to Los Angeles".
If I can't figure out that the poster thinks that "frog" and "airplane" are the same thing, and that "spaghetti" and "New York" are the same thing, it just goes downhill from there.
Energy is the ability to do Work. Doesn't matter what form it is in, 300 ft-lb of Kinetic Energy can do the same amount of Work as 300 ft-lb of Potential or Chemical or Electrical Energy.
Work is Force x Distance.
Power is Work / Time.
Force is Mass x Acceleration.
Momentum is Mass x Velocity.
Weight is Mass x Acceleration.
44_Amp said:
And, as I see it right now, with equal power cartridges (using ME as the measurement), and equal weight guns, recoil should be the same.
I believe that what you're trying to say is that it seems to you that given equal ENERGY cartridges in equal weight guns, then recoil should be the same.
Power has nothing to do with it unless you're using Power and Energy interchangeably.
44_Amp said:
but isn't, because ME should not be used to determine the available force, it should be momentum. ????
Now you're mixing Force and Energy. Momentum is used to determine Recoil Energy, which I think you're calling "available force".
However you are correct that Muzzle (Kinetic) Energy has no relation to Recoil (Kinetic) Energy because Kinetic Energy is NOT conserved in the reaction.
However, Momentum IS conserved, and through that we can calculate Recoil Energy.
I'll try an example, probably confuse you more.
How much Kinetic (Muzzle) Energy does a 115 grain 9mm at 1085 FPS have?
Kinetic Energy is Mass times Velocity squared divided by 2.
Easier to write it like this: KE = M * V^2 / 2
The ^2 means raised to the second power, which is the same thing as squared.
So, for the 9mm:
Weight = 115 grains / 7000 grains per pound = 0.0164 lb
But we need Mass, which the English system unit is the Slug.
Since we know that Weight = Mass x Acceleration, it's pretty easy to use basic algebra to figure out that:
Mass = Weight / Acceleration, and the acceleration due to gravity on Earth is 32.2 ft/sec^2.
So Mass of 115 grain bullet = 0.0164 / 32.2 = .0005102 Slugs
Now we can calculate Kinetic Energy:
KE = MV^2/2 = (0.0005102 x 1085 x 1085)/2 = 350 ft-lb
Now we can go through all the same calculations for a 230 grain 45 ACP slug at 770 FPS, or you can just plug in the weight and velocity into an online calculator like this one and let it do the ciphering.
https://billstclair.com/energy.html
Either way, you’ll find out that a 115 grain 9mm at 1085 FPS and a 230 grain 45acp ACP at 770 FPS have the same Muzzle (Kinetic) Energy: 300 ft-lb.
Now since we cleverly know that Kinetic Energy is NOT conserved, but Momentum IS conserved (per Problem 20.30 in the Schaum’s Outline problems above), we can use that knowledge to compute the Recoil (Kinetic) Energy of the gun.
Momentum of 9mm = Mass x Velocity
Weight = 115 grains: 115 grains/7000 grains/lb = .0164 pounds
.0164 pounds / 32.2 ft/sec^2 = .0005102 Slugs
Momentum = Mass x Velocity = 0.0005102 x 1085 = 0.554 Slug ft/sec
For the 45:
Momentum = 230/7000/32.2 x 770 = 0.786 slug ft/sec
THAT’S IMPORTANT STUFF ABOVE!!
You can see that although the two bullets have the same Muzzle Energy of 300 ft-lb, the 45 has 50% MORE Momentum, 0.786 slug ft-sec vs 0.554 slug ft-sec.
Again, we KNOW that Momentum is conserved, so the gun that fired it must have the same Momentum as the projectile.
In other words, Mass of 9mm bullet x Velocity of 9mm bullet = Mass of 9mm gun x Velocity of 9mm gun.
Let’s say we fire our bullets out of guns of equal weight as you stated above. We’ll use 3 pound guns for both bullets. What’s the Momentum of the 9mm gun?
Momentum of 9mm bullet = Momentum of 9mm gun = 0.554 Slug ft/sec (the units can be reduced to lbs-sec where it is sometimes called Recoil Impulse)
Since we know the Momentum of the 9mm gun, we can figure out the Velocity:
Momentum = Mass x Velocity, so Velocity = Momentum / Mass = 0.554 / (3/32.2) = 5.94 FPS
Now let’s figure out the velocity of the 3 pound gun that fired the 230 grain bullet at 770 FPS:
Momentum = Mass x Velocity, so Velocity = Momentum / Mass = 0.786 / (3/32.2) = 8.44 FPS
Even though they weigh the same and fired bullets of equal energy, the 9mm is recoiling at 5.94 FPS and the .45 is recoiling almost 50% faster at 8.44 FPS.
Now we remember that Kinetic Energy (also known as Recoil Energy) = Mass x Velocity^2 / 2
Obviously, since the guns weigh the same but the .45 gun is moving faster, the .45 gun is going to have more Recoil (Muzzle) Energy:
Kinetic Energy = Gun Mass x Velocity^2 /2
For 9mm Recoil Energy = (3/32.2) x (5.94 x 5.94) / 2 = 1.65 ft-lb
For the .45 Recoil Energy = (3/32.2) x (8.44 x 8.44) / 2 = 3.32 ft-lb
As you can see, even though they both fired bullets with the same amount of Kinetic (Muzzle) Energy from guns of equal weight, the Kinetic (Recoil) Energy of both guns is much less than the Kinetic (Muzzle) Energy of the bullet, and the .45 has about 50% more Momentum and twice as much Recoil Energy.
