Sunday, September 8, 2013

AHNULD, GET TO DA HARBAH

     Confession: this past week, I've been saying "you've been erased" nonstop. And with good reason -- Eraser was one of the best "worst" movies I've ever seen, starring the big Austrian himself, Arnold Schwarzenegger. 

So many muscles.
     If those two guns in Arnold's hands don't look familiar, it's because they aren't -- they're "rail guns", high tech weapons that shoot aluminium rounds "close to the speed of light". If the premise of the gun sounded wacky, then the payoff must be insane; men are lifted off their feet and flung back multiple meters. And that's exactly the draw of the movie.

Simply beautiful.
     But no matter how beautiful that looks, it just can't be because of a little thing called the Law of the Conservation of Momentum. In this, it states that the final momentum and the initial momentum must be equal to each other. Meaning, that our dear friend Arnold should have flown back just as far as his victims. 

     But that scene isn't the one I'm analyzing today. The scene I'm going to dissect is when the audience is first introduced to the rail gun at the damsel-in-distress's house. 

Ain't no party like a rail gun party.
     This scene is golden because up until then, the film seems to be a pretty standard action movie, but then they completely jump the shark with the firing of the rail gun. As seen above, poor Darryl, the heroine's ex-boyfriend, is completely obliterated by the weapon. He flies back and smashes into the wall. It looks hilariously impossible, because it really is once you look at the numbers. Let's do just that. 

Whoops, wrong movie.
  • Important Values
--Average mass of an adult male = 70 kg
--Average mass of an assault rifle = 10 kg
--Speed of light = 299 792 458 m/s
--Mass of an aluminium round = 0.00023 kg

  • Gun + Bullet
Initial
--Vg = 0 m/s
--Vb = 0 m/s
--Pi = 0 kgm/s

Final
--Pb = (Mb)(Vb)
--Pb = (.00023 kg)(299 792 458 m/s) ---> 68,952.27 kgm/s
--Pf = Pg + Pb = Pi
--Pg = -Pb
--(Mg)(Vg) = -68,952.27 kgm/s
--(10kg)(Vg) =  -68,952.27 kgm/s
--Vg = -6,852.23 m/s

  • Shooter + Gun
Ps = (70kg)(-6,852.23 m/s) ---> 479,656.1 kgm/s
  • Bullet + Victim
Initial
--Vb = 299 792 458 m/s
--Vv = 0 m/s
--Mb = .00023 kg
--Mv = 70 kg
--Pb = 68,952.27 kgm/s
--Pv = 0 m/s
--Pi = Pb + Pv ---> 68,952.27 kgm/s

Final
--Vb = 0 m/s
--Pf = Pbf + Pvf
--Pf = Pbf + (Mg)(Vvf)
--Vvf =  68,952.27 kgm/s    ---> 985.03 m/s
                     70kg
--Pv = (Mv)(Vvf) ---> 68, 952.27 kgm/s


     Well, the numbers don't lie. The film didn't really pay attention to the Law of the Conservation of Momentum. But then again, if they did, it wouldn't be as hilariously bad as it was. And for that, I am thankful. Rock on, Schwarzenegger.

When are we watching this one?
 

1 comment:

  1. Be careful. In collisions, it is the momentum that gets transferred from one object to another, not the velocity. Just because the gun by itself would recoil at 6,800 m/s, that does not mean the shooter would. He's 8 times more massive than the gun, so his velocity will be 8 times less for the same amount of momentum.

    Love the animation of the twin guns firing, though!

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