Sunday, September 13, 2015

Eraser Homework

Some people believe that certain weapons only exist in science fiction novels and shows. After all, a rail gun seems like a ridiculous notion even in SciFi movies, but it's real. The United States Navy has been developing rail guns for the last thirty or so years, and they've been very successful, even mounting two such weapons to a ship that will be tested later next year. The concept of a rail gun is relatively simple. More so than an actual gun that we use today. Much like bullets we all know about, the rail gun uses a force behind the projectile down a long and form-fitting barrel around the round to propel it past the speed of sound and hit a target accurately from a distance, but unlike the smokeless powder used in bullets today, its not an explosive decomposition of a substance that generates the force, it's electric current.

In the movie Eraser, John Kruger (Schwarzenegger) is a US Marshal assigned to protecting high-value individuals by 'killing' them and then hiding them away from those who aimed to do them harm. This is shown in the movie when Kruger stops a mob hit. He takes pictures of the already tied up couple with fake blood splattered all over them and sticks those pictures in the pockets of dead mobsters outside. Then he puts a gun in both of the mobster's hands to make it look like they turned on each other. He sets the house on fire and eliminates all other evidence, thus erasing that couple from existence as far as anyone else knows.

Later, Kruger is assigned to protect a woman who stole two copies of data about a top secret rail gun from an independent weapons manufacturer who sells to the Army. Plans are uncovered about the weapons being sold on the black market and the CEO of the company shoots himself in the head to avoid being arrested. Later, hired thugs use one of the rail guns to try and assassinate the woman who stole the data, but Kruger manages to arrive in time to stop them.

The rail gun in the movie is described as being able to fire an aluminum rod "close to the speed of light." The rail gun also has the apparent ability to knock humans hit by the projectile back a ludicrous distance. Something that would in no way be possible with any standard weapons and modern bullets. To prove this theory, we can use the law of conservation of momentum.

p = mv     or     Momentum = Mass x Velocity.

If we find the change in velocity of the gun when the bullet is being fired, (using the speed of light for reference, 299,792,458 m/s), we'd find that the gun would be shot backwards at -29,929,245.8 m/s. Now, I don't know about you, but I don't think any human could handle that kind of recoil. Not even Arnold. But just to make sure, let's calculate the change in momentum between the gun and Arnold. After calculations, a man of Arnold's size would be shooting back at -1,324,302.9 m/s. Even if Arnold is Mr. Olympia, he can't handle that kind of force. Now. On to the fun part. Would the victim being shot by this aluminum rod be shot back a ridiculous distance? After the initial calculations, it's extremely likely that's true. Let's put it to the test. After calculations, the man would be shot back at the velocity of -187,057 m/s. Now that is significantly less than what Arnold will have to deal with, but it's still enough to throw him back an enormous distance. Now the real question is.. Is momentum conserved? I think the answer is more than a little obvious. Not even close.

1 comment:

  1. I loved the commentary on the movie and the reality of the rail gun, but there are some problems with your calculations. First, you don't provide any of the masses you assumed. This is crucial since mass enters into the calculation of momentum (other than in the rare case where every object in the problem has the same mass). I also don't understand how Arnold could be knocked back at almost 10 times the velocity of the bad guy. Where did the rest of the momentum go?