Mark Christian’s Physics in Film Blog

I found this assignment hard to do because it is difficult to try to examine your favorite superheroes in a realistic way.  I mean, they are superheroes because they have powers that are unreal and thus, only can be taken at face value.  Like, the advanced Superman can fly instead of just leap tall buildings because, well, he’s Superman.  Or, Spiderman can heroically swing down and catch most falling people right before they hit the ground without the physical principle of impulse destroying his damsel because he’s Spiderman and that’s what he does.  I believe a hero like Iron Man is a nice choice for this assignment because he himself doesn’t have super powers – his armor is a super entity, if you will.  So, I”m going to point out a few things from the movie version of Iron Man that deal with the abilities given to Tony Stark by his armor.

-  The obvious thing that we would want to look at first would be Iron Man’s ability to fly.  In the movie, we see 3 different versions of the suit of armor with improvements from one version to the next: clunky cave armor, pre-paint, freezable armor, and badass awesome armor.  The flying capabilities of the first suit would have been very limited even if it hadn’t fallen apart immediately after lift-off.  The need for the rocket boots in that suit was so he could escape a situation, not maintain flight.  He wouldn’t have been able to go far because there was only rocket blasts from the feet and no support elsewhere that would even out the propulsion from the thrusters.  I believe that the second he leaned forward after take off would be the second his flight started on a parabolic trajectory that would cause him to fly straight into the ground just like his first test flight in his lab of the new suit sent him rocketing straight backwards.  That problem was fixed in the next stage of the armor when Stark added thrusters to his hands.  This enabled him to stabilize his body during flight, it actually gave Stark the ability to have controlled flight, and it provided a pulsating weapon that he could use.  In the first flight, the armor freezes at a high altitude, so his solution is to make the suit out of a gold-titanium alloy which not only helps defend from ice, but also bullets, missles, and running into fighter jets.  The final suit is the one made of the gold-titanium allow with a very sleek look and ran a spectacular test flight mission.  There is one thing, though, that must be present for Stark to use the thrusters for flight and the arm thrusters as a weapon, ’super’ strength provide by the armor.

- The bionic exoskeleton that makes up the interior of the suit allows Tony Stark to have an incredibly large amount of strength.  This is needed because, for example, if he was flying without this added strength with a high amount of thrust, he wouldn’t be strong enough to keep his hands from staying straight up in the air the entire time.  Also, he might not be strong enough to keep his legs together, so he could thrust-split himself in half.  The director did a good job in pointing out this need for advanced strength (just like he did a good job pointing out the necessity for arm thrusters) when Tony was testing the arms as pulse weapons without his suit on.  The first shot flung his arm back and the next shots showed him bracing his arm with the other one to maintain a straight shot.  Obviously, the strength provided by the suit was used in other ways, like hanging on to a fighter jet, lifting a car, etc, but it is nice to see that the need for the super strength was adequetly portrayed first.

- The last thing that I wanted to comment on was the arc reactor.  Obviously, this invention is fictional, but it is rather intriguing.  I read that the arc reactor Stark built at home could provide 12 Gigawatts of power, or more power than a nuclear power plant produces.  This incredibly efficicient tiny thing made out of leftover missile parts causes one to hope it could actually be a real development to solve our energy problems.  The only thing that isn’t really explained is what the actual fuel supply is, so until we solve that problem, this is entirely fictional.  The physically accurate thing with the arc reactor is that it is not a never-ending power supply.  Even though it is so efficient and capable of expelling so much power, it is not an infinite amount.  This not only makes the device more realistic, but of course, it adds to the drama of the final climactic fight because we don’t know if Iron Man will be able to fly high enough to freeze Iron Monger.

I found Iron Man to be a greatly enjoyable movie in theaters and was brought the same joy with this second viewing.  It is a nice blend of action and comic relief and Iron Man is a good example of a ‘normal’ person who uses his intelligence to create a suit that allows him to be super.  I call him ‘normal’ because not many vastly intellectual people are billionares.

I know I sighed about watching Contact again when it was first announced that it was a feature film, but I’m glad I decided to sit down and watch it all the way through again.  It had been a few years since watching it in every high school science class, and the movie is a lot better now that I have a larger fascination with science then I did back then.

The twin paradox idea that the movie gets wrong is the mission times from the perspective of Jodie Foster’s character (in the pod) and the outside observers at misssion control.  The director got the idea of time dilation backwards.  The pod was moving at a speed that was close to the speed of light, so Jodie Foster would have experienced a shorter time period then the outside observers.  This didn’t happen because she experienced an 18 hour long event while everyone else witnessed a seconds long event.

If I were to rewrite the script to make it follow the laws of special relativity, I would have to change the time that the observers in mission control observe.  I wouldn’t want to shorten the trip for Jodie Foster’s character because I believe she would deserve as much scripted time allowed in space, so I have to change the outside observer time.  If we assume that the pod travels at a velcity, v= .998 c, we can plug into the time dilation formula (using 18 hours as the proper time) to find that the correct time that should be observed by mission control of the mission would be about 285 hours or almost 12 days.  This could’ve been very suspenseful and would work in the movie.  They could show everyone waiting up all hours of the night drinking coffee waiting for her to make contact again.  Matthew McConaughey could have been the last one awake after 12 days and hear her static-filled first recontact.  It would work and we could be spared from the last hearing where she has to sit there and say she has no proof for what she saw and begin to doubt her own sanity.

I had never watched anything all the way through that related to Star Trek until now.  I remember as a kid walking in as my dad watched The Wrath of Khan and thinking about how scary the bad guy was.  I’m familiar with some stuff from Star Trek, but not a whole lot, so I am basing my response on just what can be observed in Star Trek IV: The Voyage Home.

I think the two technologies that were the most necessary to drive the entire plot were the warp drive on the ship and the transporting device.  You could argue that the cloaking device on the ship was necessary to keep it hidden during the crew’s entire mission on Earth, but they could have managed without that somehow.

In the movie, the warp drive was necessary to get the ship to go fast enough to go back in time.  Also, they would need the warp drive in order to do interplanetary travel.  In order to time travel and easily travel around the galaxy, the ship would need to travel at a velocity that exceeds the speed of light.  We have shown in class that this is theoretically impossible (since it is theoretically impossible to go the speed of light), but Star Trek, as I know it, could not really be possible without the warp drive technology that would allow the crew to travel faster than the speed of light.  The biggest thing that confused me in the use of the warp drive was the time travel.  I was confused because they used a sling shot trajectory around the sun in warp speed to not only travel back in time, but to also travel forward in time once they were done tooling around in the 1980’s.  I stumbled upon a website that dives deeper into the discussion of the temporal anomalies in Star Trek IV: http://www.mjyoung.net/time/stvoyage.html.  This talks about a lot of the questions I had regarding the time travel aspect of the movie.  I don’t think that a warp drive could ever really be invented, but the development of it in fiction allows for a lot of exploration into a realm we cannot experience ourselves.

The teleporting device, or the “Beam me up Scotty” device, is the thing I was most familiar about before watching the movie.  I don’t know if the technology is completely explained throughout the series, but I am under the impression that it dematerializes matter into a beam that is sent somewhere to rematerialize.  The thought of that process being successful a majority of the time (consistent enough to be used as a main means of casual transportation in Star Trek) is outrageous.  I can remember cartoons and movies, like The Fly, where someone gets transported and something else gets picked up too, and the two objects mutate together in the rematerialization process or the person gets sent away and then doesn’t reappear.  The teleporter technology was incredibly important for this movie because they had to sneak into a nuclear reactor (”We’ll beam in, then beam out.  They won’t even know we were there”), escape from the cops at the hospital, and, oh yeah, get two humpback whales (and enough water to keep them alive in a ship) from the ocean into a makeshift aquarium on their space ship.  Something would have had to go wrong during that process.  There should have at least been more stuff transported than just water and whales, but nope, a clean aquarium with just those in it was the result. Physically, I don’t know if a teleporter like that can be made.  How can you dematerialize someone in a controlled way, transfer them safely, and then rematerialize them and have control over it?

I found that there is a physicist named Michio Kaku who wrote a book called Physics of the Impossible where he claims that technologies like interplanetary travel and teleportation are real life possibilities.  Perhaps if I get my hand on this book, he could turn me into a believer, but for now, I believe these technologies are incredibly useful and necessary in the world of Star Trek, but in reality, we cannot replicate them and (in my opinion) they aren’t that necessary to drive our plot.

I decided to go to the Festa lecture by Dr. Doug Roble because I am a fan of the behind the scenes things that come in special edition DVDs and thought that it’d be cool to see a behind the scenes person talk about what he does.  If anybody in the class likes those extra features on DVDs and didn’t go to the talk, they missed out.  This was a nice interactive way to learn about what goes on behind the scenes.

Most of the talk was about computer generated fluid dynamics.  To start out with, he examined a huge river flood scene his company worked on in the movie Dante’s Peak that came out in the mid-90’s.  To make the flood look real, they had to build a huge set that was a 1/3 scale model of a large river and then create the flood and film it from all sorts of angles.  If you see the movie, you see that they succeeded in making a realistic looking flood, but the tons of effort that were put into that small part of the movie made special effects artists start to look towards simulating these types of scenes in a different way.  Thanks to Dr. Roble and his colleagues, computer simulation technology for fluid dynamics was developed.  They simply utilized the Navier-Stokes equations to develop a program that simulates fluid motion.  This program allows designers to alter variables such as drag and velocity to create different effects in the fluids they are creating in the computer.  The program creates a ‘wire-frame’ to control the movement of the fluid.  Once the movement frame is created, artists paint on and add effects to it in order to make it appear real as well.

One of the coolest things that was shared in the lecture were the demo reels of some of the movies his company, Digital Domain, has worked on.  These showed the scenes Dr. Fragile spoke about in class from Lord of the Rings and The Day After Tomorrow and also scenes from The Pirates of the Caribbean at World’s End, Stealth, and Speed Racer.  In most of these reels, they showed scenes in a split screen format that showed what was filmed with live cameras and real people and what was completely computer-generated.  It was pretty incredible to see some of the stuff that was not real at all and to realize that I’ve been tricked by some of the effects.

This was a good lecture to go to for our Physics in Film class because we are learning in class to be skeptical about what we see on the screen and Dr. Roble pointed out some more things to question while watching a movie.  Dr. Roble mentioned that some of the movies he works on are crap, but the things he works on look cool and he actually uses correct science to get his part of the job done.  I wish the talk had been longer because there was probably tons more he could have showed us and given me a ton more to share.

He also mentioned the movie The Curious Case of Benjamin Button and how it will change the way you look at special effects.  He didn’t say anything other than to go see it when it comes out in theatres.  So, I just wanted to pass that along because I’ve been interested in seeing the movie since I first saw a preview for it, and now I’m really excited about seeing it.

I have always had a hard time coming up with a firm stance on nuclear power. When we look at the pros of relatively cheap energy and energy independence, it looks like a no-brainer, especially this day and age. Energy costs are rising and natural resources are being depleted, so this source of energy is an incredibly ideal thought until you look at the potentially large risks involved in focusing on adopting nuclear power as a large source of our energy. My biggest concern is the waste that will be produced by the nuclear materials used in nuclear power plants: uranium and plutonium. We have spoken in class about the length of time it takes for uranium to decay (a half life of hundreds of millions of years) and I looked up plutonium’s half life to be over 20,000 years. These numbers are before any reactions happen, though. According to the EPA, it could be an excess of 10,000 years before spent nuclear fuel is no longer deemed a threat to public health and safety¹. This is a scary thought. If we continue to make nuclear power plants and rely heavily on them, there will be a lot of nuclear waste to deal with, and what we can do with it is a huge problem. We cannot just keep stuffing waste in mountain ranges, but what do we do? I remember the first thing that scared me about radioactive waste from nuclear power plants: The Simpsons. Three-eyed fishes and glowing people never really seemed like a good thing to me, but at least we have explained in class that B-movie monsters will not destroy our major metropolitan areas. When it comes to nuclear power, I do not know too much. When I become more informed about how the whole process works and how waste is handled, I will be able to formulate a more honest and educated opinion about the subject.

I do have a stance on nuclear warfare, though. I am a person who is very much against war in general, so it is easy to conclude that I am against nuclear weaponry. Unfortunately, countries go to war and countries have nuclear weapons at their disposal. Since the existence of nuclear weapons is inevitable, I feel as though the development of ‘tactical’ nuclear weapons would be a much better idea to start with than the weapons of mass destruction, like the bombings on Japan. I think, though, that battlefield technology can and should advance without the use of nuclear weaponry. The question that was posed about the development of low-yield devices providing further impetus for other countries to develop and use weapons is very intriguing. I think that it would entice other countries to start developing these types of tactical weapons because once the technology is developed, it will probably be a lot cheaper to make these weapons than the large weapons of mass destruction that are currently being developed and held. In the long run, though, there might be a large number of these smaller tactical nuclear weapons that will be used by a large number of countries in a large number of wars and the damaging effects could add up to the effects of just a couple of attacks utilizing the larger weapons. There is no doubt in my mind that a nuclear holocaust is a possibility in the future. Everyone said that The Holocaust could not have happened, but it did. If someone gets the idea that an entire nation of people should disappear from this Earth, they would easily be able to carry out that plan a lot quicker than Hitler did. If this happens, then there would be repercussion bombings from somewhere, and that could spark a greater chain reaction. I believe that this is a possibility. This is a very scary thought and it is one of the big reasons why I do not like the idea of war.

1. (www.epa.gov/ocir/hearings/testimony/110_2007_2008/2008_0715_rjm.pdf)

I think that disaster movies such as The Day After Tomorrow and even Armageddon are both good and bad releases into the public. Though these movies are mostly produced in order to cash in on big box-office numbers, they also help raise a sense of awareness about things that many people do not think about. I do not believe many people thought about the possibility of an asteroid hitting Earth and possibly altering the existence of humanity until Armageddon and Deep Impact came out. Same thing goes with The Day After Tomorrow. It brought a huge sense of awareness to the topic of global warming and it made many more people begin to ponder about the topic and ask if this could really happen. I know that the three movies I have brought up are examples of movies that take a small scientific idea and blow it out of proportion, and that is one of the biggest flaws these movies have in being helpful in raising awareness. While some people will wonder if the scenarios brought up in these moves are real life possibilities, many others will probably discard the thought entirely since these movies are so far-fetched and have many physical inaccuracies. So, I am sure there are people who just look at these movies and say, “not a chance that anything like this would happen to our perfect existence.”

I do believe the movie An Inconvenient Truth was a wonderful tool of propaganda to raise awareness and a sense of urgency regarding global warming. It was also a great example of how effective an impressive Powerpoint presentation can be. The topics brought up in this documentary were picked up by a massive amount of people and even earned Al Gore a new sense of celebrity. We see all around us the trend of “Going Green” and I believe the urgency to do something now to protect our not so distant future was greatly fueled by An Inconvenient Truth and other films like it.

Since we are talking about the general public’s reaction to these movies, there is one important thing that we must think about: ignorance. Many people who watch these movies (disaster and documentaries) only have that one source as a basis for formulating an opinion about the severity or reality of some of these issues. A lot of people can be swayed easily and if two people just see The Day After Tomorrow and that is the only exposure they have to the idea of global warming, one could go crazy and become radical at stopping this impending doom from happening and the other could say that the movie was such a farce that there is no way any of it being true.

Like I said at the beginning, I think that these movies are good and bad. I believe that when movies like this come out, people should at least pay attention to the general message and independently try to find out more about the subject. There is no way that people should take these movies in a completely literal sense. I believe that as long as people do not get completely lost in the magic of Hollywood, I am completely fine with directors putting out movies like this to get people to start talking about things that are real.

This was my first time ever watching The Core.  Usually when a group of people get together and someone says “That movie was ridiculous,” everyone in the group that saw the movie nods their heads in agreement.  Even the person who disagrees nods generously with the crowd.  This was the situation I thought I was getting into with The Core.  When it was mentioned on the first day of class as being ridiculous, there was a large agreement by the members of the class that had obviously seen the movie.  I thought everyone was agreeing just so they were not outcast.  After seeing the movie myself and reading a ‘Goofs’ page that had the quote “Since almost all of the ’science’ in the movie is entirely erroneous, we are prepared to accept that the movie’s universe *must* have entirely different rules – it’s the only possible explanation. It’s just for fun.”, I will nod along with everyone else if I am ever in a room where someone mentions The Core as ridiculous.  I will however, remind them that Stanley Tucci has a great freakout monologue before he gets punched in the face.

I have compiled a list of some things that I had some disbelief in throughout the movie. I couldn’t have made a list of every flaw because I may have gotten distracted by the movie and gotten tired of questioning everything that was presented to me by the director of “The Man That Knew Too Little.”

My list of ?????:

- In the scene where the business man falls flat on his face at the beginning, it is hard to believe that he would fall and stick to the table like he does.  He should have broken the table, but if he was over a support, which it appears he was, it is plausible that the glass doesn’t break.  I just have a hard time believing he falls and immediately stops upon impact.  I do hope that his firm gets the $30 million, though.

- The birds scene was oh so entertaining.  Without getting into how the magnetic field of the Earth might make them freak out, I just want to question the birds’ ability to crash cleanly through office building windows.  I mean, I’ve seen birds hit windows pretty hard, but I’ve never seen one crash through one.

- The shuttle crash scene was pretty awkward I’d have to say.  They steered the shuttle away from the heart of the city within seconds of crashing.  I don’t know how Hilary Swank came up with her coordinates, but I’d love for that process to be explained to me.  Then, as they speed through the ‘river’ and try to slow down, they manage to not destroy the shuttle with every small collision they encounter.  The shuttle had to have been damaged severely once the landing gear was disengaged.  Then, they miraculously seem to stop right before taking out the lucky construction worker.  I think it would’ve taken them a much longer time to stop and that man should have died.

- This isn’t physics persay, but I think everyone who has been to school is familiar with the levels of the Earth: crust, mantle, inner/outer core.  Did Two-Face really need to explain that to those high and mighty military men?  Boy, do I hope that would not be needed with our leaders.

- I’m not entirely sure that our magnetic field is what blocks the radiation from the sun.  I thought that was the ozone layer.  So, that threat probably shouldn’t have been proposed and the ever doomed in this movie Pacific area would not have had boiling lakes and melted bridges.  Also, what amount of heat would require the Golden Gate Bridge to melt, a huge body of water to boil, or an instant 2nd degree sunburn?

- I’d like to look at one more thing from that Golden Gate Bridge scene.  Shouldn’t that piece of the bridge that hit that guy’s windshield just take off the whole top of the car instead of just smashing into the windshield?

- Unobtanium.  I’m just going to say that

- The lightning destruction of Rome was entertaining, but seriously?  There were explosions, fires, laser lightning.  It looked like someone had a constant laser aiming down the street trying to kill everyone.  It’s like someone was playing a God-sim.  I don’t think I’ve ever scene lightning that just stays in a constant stream of electricity like that did.  The guys on Mythbusters would’ve liked to recreate that when they were trying to make a water-powered stun gun.

- When they launch Virgil into the ocean, I kept wondering what made it fall straight down and not level off.  The whole decent was a straight shot down.  That just raised my eyebrows when I saw it.  I did like the idea of Virgil’s self leveling sections so the crew always felt upright.  That was cool and their spinning chairs.

-  The whole navigation through the Earth.  Just everything about the entire journey was obviously thought up by some scientist on a bad trip: diamonds, geodes, navigation images that look like a trip in the Magic Schoolbus through the body.  I couldn’t get the idea of how it was being propelled and how they were in fact constantly at a dive to the center.

- The scene where Bob falls into the, let’s call it ‘lava’, it shows him float up intact before he sinks back down again.  I think that with the hole in his helmet, his face wouldhave at least melted off if not his whole body melted.  I just don’t think that suit was that heat resistant.

-  I want to question the ideas of Braz’s ultrasonic lasers and the TRINITI weapon.  Would these ever be possible?

-  I liked that they recognized that the nuclear reactor would be really hot due to the constant motion in the scene where Keyes picks up the fuel rod.  I just want to know why his hands were the only things to get hurt in the scene.  There was a point when he was leaning against it and the part that hurt his hands was unfortunately pressed against his crotch.  I thought they were sparing him so he could have some ‘before we die’ sex with Hilary Swank, but nope.  He just got lucky in the fact that only his hands were burnt.

-  The last thing I wanted to point out was the scene where they set off the nukes and the earthquakes start happening on the surface.  If they were earthquakes, I don’t think the Earth would vibrate in a big ripple like they show in the desert.  Also, why didn’t all of the volcanoes of the world erupt with this huge magnitude of seismic activity all around the world?

This is the list that I was able to write down and the one that I wanted to share.  I hope that things I thought were bad physics weren’t the actual examples of good physics in this movie (are there any?).  I hope you enjoyed and if you want to leave any comments about the list, this is a good one to start a conversation about.

“So, I heard that movie The Core was ‘effing ridiculous”

*nods*

So, to do the Armageddon assignment, I picked an asteroid size and a time until impact and calculated to see if the Earth would be saved based on those values and then I looked at the problem from another angle.

I wanted to find a realistic sized asteroid and I found one in the asteroid known as 2002 NT7. This asteroid was on the NASA IMPACT RISK list. It is about 1.2 miles wide or about 2.0 km. Thus, we are going to determine the mass of the asteroid with this estimation and the density of Earth (5500 kg/m³) like we did in class.

We know m = d*V and V = 4/3*pi*(d/2)³

Thus, V = 4/3*pi*(2000 m/2)³ = 4.19 x 10⁹ m³

So, m = (5500 kg/m³)*(4.19 x 10⁹ m³) = 2.30 x 10¹³ kg

Now, we know what mass we are dealing with, so let’s go on.

When the 2002 NT7 was discovered, many predictions came out that it could hit Earth in the year 2019. I decided to see what would happen if we spend the next 10 years coming up with a plan to reach the asteroid and plant a 100 megaton nuclear bomb at a time of 30 days (2.6 x 10⁶ s) before impact. Remember, we are keeping the asteroid’s speed of 25000 mph (v_{towards earth} = 1.1 x 10⁴ m/s). That would put the asteroid at a distance = t * v_{towards earth} = (2.6 x 10⁶ s) *(1.1 x 10⁴ m/s) = 2.86 x 10¹⁰ meters away from Earth. That is a huge distance of about 74 times the distance from the Earth to the moon, but hopefully in the 10 years of developing the plan, we will learn how to send a drilling and nuclear bomb planting device that far.

So, let’s see if we could save the Earth by intercepting this particular asteroid 30 days before it hits Earth. We can do this by looking at conservation of energies.

Remember: ME_i = ME_f –> PE_i + KE_i = PE_f + KE_f

Looking at the 100 megaton nuclear bomb, we know that it has a potential energy of 100 megaton (4.2 x 10¹⁵ joules/megaton) = 4.2 x 10¹⁷ J

To do the calculation, we are going to assume that this bomb is 100% efficient, i.e. all potential energy is released, and we are going to assume that the asteroid is split into two identical halves after the explosion and we know that the asteroid is not moving apart before the blast:

(4.2 x 10¹⁷ J) + 1/2*m*v²_{towards Earth} = 0J + ½ (m/2)* v²_{towards Earth} + ½ (m/2)* v²_{towards Earth} + ½ (2.30 x 10¹³ kg/2)*v²_{split apart} + ½ (2.30 x 10¹³ kg/2)* v²_{split apart}

(4.2 x 10¹⁷ kg m/s) = 0 J + (2.30 x 10¹³ kg/ 2)* v²_{split apart}

v_{split apart} = 191 m/s

Now we know that with our blast, the asteroid halves will be travelling 191 m/s away from each other. Let’s see if we have saved Earth. Remember, we assumed that we were doing this 30 days before impact so we need to see how far the two halves travel in that amount of time.

Again, d = v*t = (191 m/s) * (2.6 x 10⁶ s) = 4.97 x 10⁸ m

We needed them to travel more than 6.38 x 10⁶ m to miss Earth, and it looks like we did it.

Looking at this problem I noticed that we could just look at the conservation of energy equation and find out what the smallest amount of time we could do this at in order to save the Earth since our velocity of the split only depends on the mass of the asteroid and the energy of our bomb.

So, we could use 191 m/s as our v and find a t that satisfies (191 m/s)*t > 6.38 x 10⁶ m and that t would be any     t > 33403 seconds (9 hours) . So, if I haven’t had a brain fart of sorts, we could save the Earth from this asteroid if we can blow it up if it is more than 9 hours away from us. So, if we chose to intercept it 10 hours before impact, it would be 3.96e8 meters away from Earth which is close to the distance from the Earth to the moon.  We know how to send things that far.

Eraser was another movie that I could only remember certain parts of when first reading the assignment.  I remembered x-ray guns, Arnold, and the dock explosions, but not so much about the plot (I mean I was 9 years old when this one came out).  As an adult, I found this to be entertaining and the plot to be predictable, but engaging.

I would like to analyze the rail gun scene that immediately follows Arnold bursting through the floor in the warehouse and wields a rail gun in each hand.  At this moment, two baddies that are about 35 yards (32 m) away from Arnold both get blasted with simultaneous shots from both rail guns and fly backwards.  Since both guys are about the same size and distance away from Arnold and they both fly back the same distance, I’ll just show calculations for one guy getting shot.

The way I am going to analyze the shot is by trying find out (1) Arnold’s final velocity (v_Ai) after shooting the gun and then, (2)the velocity of one of the baddies who gets shot after being pierced by the projectile launched by the rail gun.

(1)To get started with the first question we need to know a few quantities to use the Law of Conservation of Momentum: Arnold’s mass (m_A), Arnold’s initial velocity (v_Ai), the mass of the projectile (m_p), and the initial and final velocities of the projectile (v_Pi, v_Pf).

We can estimate Arnold as weighing about 235 lbs (m_A = 107 kg) in the movie.  Since he was standing still when he shot the gun, v_Ai = 0 m/s.

To find the mass of the projectile, I used the fact that it was made of aluminum (stated earlier in the movie) and I estimated some values to find its volume. I took the projectile to be a cylinder with a diameter of about .5 inches (.0127 m) and a length of 2 inches (.0508 m).  I used the formula for the volume of a cylinder to find that the volume of the projectile would be about .000003 m³.  The density of aluminum is 2.7 g/cm³ (2700 kg/m³).  Density = mass/volume, thus m_p = (2700 kg/m³)(.000006 m³) = .017 kg.

We know that the initial velocity of the projectile, v_pi = 0 m/s.  Like I said before, the projectile travelled 32 m and it did it in about .1 s, so v_pf =(32 m – 0 m)/(.1 s) = 320 m/s.

Now we have all of the values we need to see what would happen to Arnold in a frictionless world.

Remember p_initial = m_A­v_Ai + m_p­v_pi and p_final = m_A­v_Af + m_p­v_pf

The initial momentum of the system is 0 kg m/s because both the initial velocity of Arnold and the initial velocity of the projectile are 0 m/s.  The Law of Conservation of Momentum states that p_i = p_f, so we know that p_f = 0.

So, to find V_Af, we just have the equation V_Af = (-m_pv_pf)/(m_A) = (-.017 kg * 320 m/s) / (107 kg) = -.051 m/s.

So we found that Arnold would be thrust backwards at a speed of about 2 inches/second if there was no friction. I should also note that since Arnold shot two guns at the same time with basically the same conditions, he would be traveling at about twice the speed or 4 inches/second without friction.  He doesn’t move in the scene, but he’s got friction on his side and the fact that he is in a hole in the floor to help him stay put.

(2) Now we want to look at what happens when the baddy gets shot.  We already know all of the quantities for the projectile since it hits the guy going 320 m/s and goes right through him without slowing down, but I’m going to go with Mike’s idea and look at this as if the projectile lost 50% of its speed.  So, v_bi = 320 m/s and v_bf = 160 m/s.

Let’s get some values for the baddy.  I’d say the guy is about 160 lbs (m_b = 73 kg).  He is standing still when he gets hit, so v_ib = 0 m/s.  We now have everything we need to know to find out how fast and in what direction he would fly backwards when he gets struck.

Remember p_initial = m_b­v_bi + m_p­v_pi and p_final = m_b v_bf + m_p­v_pf

p_initial = 0 kg m/s + (.017 kg)(320 m/s) = 5.44 kg m/s

We know that p_initial = p_final , so p_final = m_b v_bf + m_p­v_pf = 5.44 kg m/s

So the final velocity of the guy would be:

v_bf = [5.44 m/s - (m_pv_pf)]/(m_b) = [5.44 kg m/s - (.017 kg)(160 m/s)]/(73 kg) = +.037 m/s

Thus, we find that the baddy only moves .037 m/s or 1.46 inches /second (slower than Arnold).

So we’ve shown with some math that if directors didn’t want to spend money on stunt men and extensive cable systems that pull the actors back with great velocity, they can just say that they wanted their film to look more realistic and have the actors just stay still when shooting or being shot.

I’d like to say that I greatly enjoyed analyzing this scene because I got to watch Arnold break through the floor about ten times in a row.

When it was first mentioned that we were going to watch Speed 2: Cruise Control, I remembered watching it as a kid and thinking I enjoyed it.  Then, after thinking about it more, I could only remember that it involved Sandra Bullock, a cruise ship, and a creepy guy who liked leeches, so it must not have been that great.  I’m glad I thought about it and didn’t set myself up for disappointment for my first viewing of the movie since I was ten.

Well, on with the assignment!

The first scene that I would like to examine is the scene where Willem Dafoe knocks the captain off of the ship.  I would like to know how high above the ocean the captain fell from. This can be calculated by using the kinematic equation d = v_i*t + ½ a*t².

We can assume that the initial velocity, v_i, is 0 m/s since the captain did not push off towards the ocean, but was just pushed off of a cruise ship.

The acceleration, a, is the constant downward acceleration due to gravity: 9.8 m/s².

Finally, I estimated the time it took for the captain to fall from the ship to the ocean to be about 3 seconds.

Putting these together we can see that d = 0 m/s*3s + ½ (9.8 m/s²)(3s)² = 44.1 m or approximately 145 ft

Additionally, in the scene where the lifeboats are being dropped into the water, it appears that they are on the same deck that the captain was pushed from and it seems to take the boat about 3 seconds to hit the water as well. Hooray for consistency!

The next scene I want to look at is the scene where the seaplane crashes into the oil tanker. An interesting thing to find out would be the force exerted on the plane, and subsequently Willem Dafoe when it goes from flying to stopping in a split second. Things we would need to know are the acceleration (deceleration in this case) and the mass of the plane.

We could find the acceleration by examining the change in the velocity over a time that we can estimate as 1.5 seconds. We know the final velocity, v_f, is 0 m/s, so all we need to do is come up with an estimation for the initial velocity. I’m not exactly sure how to do this, but I did try to find the slowest flying speed for a plane and found that the slowest the plane could have been going was in the 100-150 mph range (44.7 – 67.1 m/s). Then, using the average mass of a small plane, around 2500 kg, we can find the force exerted on the plane.

Finally, I would like to analyze the scene where the ship crashes into the dock and find out how much of the dock was directly damaged by the ship. To do this, we can find the distance the ship travelled through the dock and then use the width of the ship to find an approximate area affected.

We can find the distance travelled by using the kinematic equation d = (v_i + v_f)/2 * t.

The initial velocity, v_i, was stated as about 7 knots right before the impact. Converting this to m/s we find 7 knots is roughly 3.6 m/s.

The final velocity, v_f, is 0 m/s.

Using the time on the movie file I watched, the ship hit the dock at 1:37:04 and stopped at 1:40:10 for a duration of time, t, of 3 minutes 6 seconds or 186 s(econds).

So we find that d = (3.6 m/s + 0 m/s)/2 * 186 s = 334.8 m. This is the distance the front of the ship traveled. I want to note that when the ship is stopped, we see that the back of the ship is aligned with the end of the dock, suggesting the ship only traveled a distance of 135 m (length of the ship Seabourn Legend). I suppose it looked better on film stopping at that point.  Also, some of the shots we see of the crash are just different angles of the same instant in time, so the time it takes for the ship to stop would be not be as lengthy as the time we I used in my calculation.

So, we look at the width of the ship, 19.6 m, and the length it should have travelled, 335 m, and find that it would have struck an approximate area of a = 19.6 m * 335 m = 6566 m².