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Firing a Gun

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Recently I was watching Point of Interest, a TV show, and I was thinking about what kind of physics are behind firing a gun.  I concluded that when the shooter shoots a gun, the force on the bullet is equal to that on the gun-shooter. This is due to Newton's third law of motion (for every action, there is an equal and opposite reaction).  The force of the bullet is equal to the gun-shooter due to the law of conservation of momentum.  A person with a gun have a combined mass M and the bullet has a mass m. When the gun is fired, the two systems move away from one another with new velocities V and v respectively.  Also, the person with a gun moves in the opposite direction of the bullet.  Therefore, the initial momentum is equal to the final momentum due to the law of conservation of momentum.  Since the net force is equal to the change of momentum, the initial change of momentum of the person and gun is equal to the final bullet's momentum.  Therefore, the person with a gun has a equal force and a opposite direction of the bullet.  

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As a person who does a good amount of shooting, it is really cool to see this relationship play out.  Especially when you shoot guns of the same power, but with different masses, it is easy to see how the lack of mass of the gun is made up for by the increased velocity the gun hits your shoulder with.

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Absolutely.  I can remember going to a class where we were on the range and a little old lady was learning to shoot and thought she'd be fine because she had a small little "pocket revolver," and was surprised how tough it was to control.  Giving her a much larger semi-automatic, she found hitting the target was a piece of cake.  Larger mass, smaller acceleration, easier to control!

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