The World's Greatest Detective (Not Physicist)

I love Batman. I really do. There's no way to precisely articulate how much of a fanboy I am over Batman. An introductory paragraph in a class blog certainly won't do it justice. Anyway, I was extremely excited to hear we were doing a comic book themed blog this week, and even though I love the Avengers and Marvel, I prefer my comic books and films with far less levity and more austerity. They don't call him The Dark Knight for nothing.

Keeping in line with the "film" part in the class title, I'm going to analyze some scenes throughout the newest Christopher Nolan movie trilogy.

• Chinese Take-Out

One of the most notable attributes about Batman is that he, well, dresses like a bat. In doing so, this gives him one of his prime abilities -- to glide around with his bat-cape. Now the question I'm not asking issn't whether or not it is possible for him to glide around with a material (I'm going to assume it's possible), but if it's possible or not that his arms would be able to take the force after an extended fall.

In the above scene, Batman attempts to retrieve the mob's accountant in Hong Kong and use him as a major witness to testify against the Joker in court. To do this, he needs to penetrate Lau's corporate building, which he does by gliding in from a taller, adjacent building to its side.

Bruce Wayne jumps off the building for 4 seconds, and using our old kinematic equations, we know that his final velocity at the point before spreading his wings was 39.2 m/s. After this, he does a circle maneuver, where go goes from completely vertical to completely horizontal. This circular motion makes it a centripetal force. To prevent his arms from giving way or buckling, Bruce Wayne would have to exert the same force back onto the air as it is pushing onto him, a la Newton's 3rd law.

We're assuming Batman's mass is 80 kg, and that the radius of the circular path to be about 20 m. With the knowledge that a centripetal force is involved, we can plug it into one of those equations.

F = mg + mv^2
                     r
m = 80kg
g = 9.8 m/s^2
v = 39.2 m/s
r = 20m

F = (80)(9.8) + (80)(39.2^2)  =   6930.56 N
                                   20
6930.56 newtons turns out to be 1558 pounds, so Batman would have to withstand 779 pounds on each of his arms. And since Batman doesn't have super strength, I don't think that can happen. 

• Truck Derby

Another good scene in The Dark Knight is when Batman is on the Batpod chasing the Joker in a semi truck. To stop him, the Bat attaches some cables into the ground which halt the truck, making it flip in spectacular fashion. But the question is, can the cables Batman attached withstand the force its being put under?

Let's assume that the entirety of the truck has a mass at about 15, 000 kg and is traveling at a speed of 22 m/s (50 mph). The forward motion also looks to be stopped at around 0.1 s. 

F = (m)(Δv)
            Δt
m = 15, 000 kg
Δv = 22 m/s
Δt = 0.1 s

F = (15, 000)(22)  = 3, 300, 000 N
                0.1
The truck experiences 3, 300, 000 newtons of force, and using Newton's 3rd law, the cable would have had to withstand just the same amount of force as well -- 3, 300, 000 newtons or 741,869 pounds of force. Since I love Batman so much, I'm going to let him slide this time and assume Luscious Fox gave him some super wire that can withstand that crazy amount of force. 

• Conclusion

So I still love Batman. I always will. Forcing me prove that the physics in the movies aren't up to par with reality was soul crushing, so paging Dr. Fragile to save the day and come up with some cool-yet-accurate movie scenarios to make Batman credible once more.

We need you.

IT'S COMPRESSED OF IRON-IRON!

     Iron ferrite, probably the funniest oxymoron ever coined in existence. This really has nothing to do with the analysis at hand, but it was just so funny I couldn't leave it unmentioned. Guess they had space dementia when they wrote that line.

     So let's get back on track. Although there are many things wrong with the NASA plan in the film, given some leniency, the real problem boils down to their "Zero Barrier" theory -- the point at which the two asteroid pieces would have enough distance to spread out far enough not to hit earth. The earth has a diameter of 12,742,000 meters and according to the plan in the movie, the asteroid would have spread out a whopping... 253meters.

It's okay Ben. I'm upset at that number, too.

     So, assuming there's no other way to construct a more explosive bomb, the "Zero Barrier" is really the only thing that needs to be changed in this scenario. So let's see what the newly modified barrier would have to be for this crazy Michael Bay plan to work.

t = Δy/Vf

Δy = 12, 742, 000m

Vf = 0.0246 m/s

t = 517, 967, 479.7 seconds

    So, we have the time in seconds, and since we know the initial velocity of the crazy fog asteroid of doom, we can plug that into the distance formula to calculate the new "Zero Barrier". 

d = (t)(Vi)

t = 517, 967, 479.7 seconds

Vi = 9834 m/s

d = 50,900,000,000 m

 

      In retrospect, the Chinese space probe Chang'e-2, which was launched in 2010, just reached this distance (50 million km) in outer space in July, marking it as a record in deep space exploration.  

China is at it again.

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?