@newfalguy101 - yes, the physics (algebraic formulas) in this case are ridiculously simple:
Momentum is conserved, so we know the momentum of the rifle is equal to the momentum of the ejecta, then knowing the momentum of the rifle tells us its velocity, which then gives us its free recoil energy.
Momentum of the total ejecta:
Pe = [(muzzle velocity)*[(bullet weight) + 1.75*(powder charge weight)]]/7000
That gets you to a kinda silly set of units, but it doesn’t really matter, we’re simply in transition here.
The momentum of the rifle, Pr, is equal to the Momentum of the ejecta, Pe, so we can determine the recoil velocity of the rifle: rifle weight in pounds.
(Recoil Velocity) = Pe / (Rifle weight)
Then Free Recoil Energy is simply the kinetic energy of the rifle mass at that velocity:
FRE = (Rifle weight in lbs) * 7000 * (recoil velocity)^2 / 450380
• note: the 7000 multiplier converts the Rifle weight in pounds back to grains, then the divisor 450380 is the product of the 1/2 from 1/2 m v^2, then 1/7000 converting grains back to pounds, and 1/32.17 gravitational constant, such our FRE comes out unit converted to ft.lbf.
Quick and easy math.