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The conservation of momentum is probably one of the most commonly laws of physics that is ignored for the sake of theatrics. The truth is that if someone is shot and completely absorbs the momentum of the bullet, they will be pushed back with the same force as the gun pushed back on the person that fired the weapon (ignoring momentum loss due to wind resistance).
The movie Eraser wildly ignores this law of physics especially surrounding the railgun featured in the movie. In order to calculate the relevant quatities we need to make some estimates about the gun and its victims. We don’t get to see the projectile, but we do get to see the cartrage that loads them into the gun. Looking at this and using the actor’s hand and other know cartrages as references; we can estimate (conservatively) that the projectile is 2 inches long and ½ inch in diameter. The movie also tells us that the projectile is aluminum. Using the density of aluminum (2.7g/cm3) we can calculate the mass of the projectile to be 17g. The movie aslo says that the projectile is fired at near the speed of light. This will give astronomical values so we’ll do the calculations both with c/2 and the velocity of the navy’s version.
With a mass of 0.017 Kg and a velocity of 1.5×108 M/s, the projectile would have a momentum of 2.6 million KgM/s! If this momentum was completely absorbed by a stationary freely moving 80 Kg man, he would then be moving backwards at 32,000 M/s. This is with the characterization of the weapon provided by the movie. This is absurd not only because of the uncontrollable recoil of such a weapon, but the energy envolved would probably just vaporize a human.
A more probable railgun muzzel velocity would be 3500 M/s. With this velocty, the same projectile would have a momuntum of 60 KgM/s. If this was absorbed by a stationary freely moving 80 Kg man, he would then be moving back at 0.75 M/s. This calculation makes the recoil of a handheld gun manageable, but not the impact on a victim. In the first scene where someone is shot, the ex-boyfriend is sent back about 20 ft in less than 1 second. We’ll aproximate this to 10 M/s. This is much faster than the momentum of the round can provide.
This problem is based on Newton’s third law of motion which basically says that for every action there is an equal and opposite reaction. As a gun is fired, the bullet pushes on the gun and on the person firing the gun. This is the recoil and is due to starting the bullet in motion. The equal force of stopping the bullet is shown in pushing on the victim. In short, if you shoot someone, the force of the bullet hitting them will equal the force of the gun’s recoil on you as you fire it.
