Physics of a bullet

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A bullet flies through the air and hits its target due to three aspects of phyics: Force, Velocity and Energy.

Force

    If both the shooter and gun are not moving or at rest, then the force on both the shooter and the bullet are equal.  This comes from Newton's third law; for every action, there is an equal and opposite reaction.  If we consider a system where the gun and shooter combine for a mass M and the bullet has a mass m.  Then when the bullet is fired from the gun it moves in the opposite direction with velocity v, as the gun/shooter withwith new velocity V.  However, due to the law of conservation of momentum we get the equation MV + mv = 0 (1) since the magnitudes of their momenta must be equal to each other. And since force is equal to the rate of change in momentum and the systems initial momentum are both 0, the force that is acted on the bullet is the same as the force acted on the shooter.  Having said this it brings up the point of people being flung 20 feet in the air and through windows in the movies.  Although this makes the movies interesting and fun to watch it is simply not true.  If it were the case then the shooter would also be flung off their feet equally as the person being shot.


Velocity

    After looking at equation 1 we can come up with an equation for the velocity of the shooter: V = mv/M.  Showing that desipte the bullet traveling at a very high velocity, the small mass of it campared to the much larger mass of the shooter gives a low recoil velocity (V) even though both force and momentum are equal.

Kinetic Energy

The small mass of the bullet, compared to that of the shooter, allows for significantly more kinetic energy to be passed on to the bullet than to the shooter. The kinetic energy for the two systems are ½ MV2 for the shooter and ½ mv2 for the bullet. The energy passed on to the shooter can be written as:

½ MV2 = 1/2M (mv/M)2  = (m/M) (½ mv2)

    Since the mass of the bullet is so much smaller than the shooter much more kinetic energy is transfered to the bullet than the shooter.  Once a bullet is shot out of the gun its energy immediately starts to drop until it hits the target where it transfers what is left.