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momentum is not changed by how the gun is held.
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The laws of the Conservation of Momentum still apply and are greatly affected by forces imparted upon the body in motion.
It is changed. Once you grip the gun, you become a part of that system. That is why we have shooting stances to manage the momentum of shooting. It's the difference between holding a 12 gauge buttstock 6 inches from your face and having it firmly planted in your shoulder.
That will give a good demonstrations of how the acceleration affects that conservation of momentum.
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As soon as the two masses are unequal, so is the energy.
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Unclenick, some people might be confused in that you talk about Kinetic Energy and then switch to blanket term Energy. Energy can change forms but it must equal and is subject to the laws of physics.
Energy must be equal.
Higher mass has more potential energy always. Potential energy has a direct relationship to mass.
Your last portion nicely illustrates how that conversion of Kinetic back to Potential relates to our recoil problem.
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The previous example: A forward-moving mass, 2M, is twice the oppositely directed mass, M, when an equal but oppositely directed force, F, and -F, is applied. The first accelerates to a speed of V, while the second accelerates to a speed of -2V. The signs are important because these are vectors, so something has to indicate their relative directions. As to energy, for the heavier mass, KE=½×2M×V²=1 unit of energy, and for the lighter mass, KE=½×M×2V²=2 units of energy. The kinetic energies of the two masses have proportions of 1:2 and are not equal. Note that squaring V eliminates any minus sign that might be associated with (minus times minus is plus), and thus, KE has no direction associated with it. It is just a quantity.
Often, when someone asks why, given equal and oppositely directed force, the shooter is not injured as badly as the recipient of the bullet. Usually, someone will say it is because the bullet has a smaller contact area with its target than the gun does with the shooter, but a bit of thought will reveal that this doesn't begin to account for it. Especially not for elephant guns and the like. Instead, it is the fact the bullet energy is much higher than that of the gun in contact with the body that accounts for the lion's share of the difference at the shooter's receiving end. Reduce the mass of the gun to the mass of the bullet so the energy becomes equal on the shooter's end, and then, despite the bigger contact area, it will damage the shooter, too.
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