Friday, September 25, 2015

Here comes the Spider-Man.

The book I chose to do research on is The Physics of Superheroes and the chapter being "Can He Swing From a Thread? - Centripetal Acceleration"  In this chapter, author James Kakalios challenges the comic book minds on if Spider-Man can actually swing from a thread at the speed that he does, would it be able to accommodate for his weight and possibly the weight of others that he may be carrying?  To solve this he looked at the following factors.  Newton's second law of motion shows us that force is needed to change an object's motion.  A change in motion or acceleration is made evident by a change in magnitude or change in direction.  The force that would be acting on Spider-Man while he is swinging in a parabolic arc or semi-circles would be the force of gravity and the force from the tension in the webbing.  Due to these forces he is constantly changing acceleration during the swing.  Since the webbing is providing some of the force acting on Spider-Man it must be incredibly strong in order to hold his weight and the weight of others while providing an outside force.  If the webbing were to snap mid swing, Spider-Man would go falling in the direction at which he was pointing when the web line snapped.  The acceleration acting on Spider-Man provided by the web is identical to that of the acceleration of the moon by Earth's gravity.  If there was no gravity acting on the moon then it would simply fly off with the same velocity that it had initially, just like Spider-Man falling off of his thread.  The author provided us with an equation to show the acceleration of an object being constantly directed onto a circular orbit with a velocity ((v * v)/R = v^2/R) with "R" being the radius of the circle.  The webbing must provide a force (mv^2/R) in order to change the direction of the swing and to support his weight.  The faster he swings, the greater the centripetal acceleration will be (v^2/R).   For example, when Spider-Man swings from a web 200 feet long at a speed of 50 mph the acceleration would be 27 feet/sec^2 as well as the acceleration of gravity (32 feet/sec^2).  With Spider-Man weighing approximately 160 pounds and the force needed to change his motion being 135 pounds, the webbing would have to hold nearly 300 pounds and then other possible passengers on top of that.  Kakalios then states that real spider silk is actually five times stronger per pound than steel cables and even more elastic than nylon.  The webbing is made of thousands of rigid filaments that are a few billionths of a meter wide with fluid-filled channels that distribute out the tensile force along the webbing instead of just on one strand.  The high tensile strength of real spider silk can support a weight of more than 20,000 pounds per square centimeter.  Even a thinner webbing could hold 6,000 pounds, so 3,000 pounds, or even a runaway train, would be no problem for Spider-Man's webbing.

Friday, September 18, 2015

Save us NASA... and Gravity

This week we watched another great hit from the 90's, Armageddon.  The premise of the film is that there is a large, Texas-sized asteroid hurdling towards Earth at 25,000 mph and in 18 days it will impact Earth, destroying all life on the planet.  NASA's great plan to stop this "global killer" from reaching Earth... some drillers and a nuke.  In the film the plan is a complete success but in reality... not so much.  Putting aside the drillers becoming astronauts in 18 days with absolutely no qualifications, the physics behind the whole plan just does not hold up.  However, addressing the film itself is not the objective this week, I am, instead, tasked with finding an actual working plan that could save the Earth from impending destruction if need be.

The plan I found to be the most interesting and that actually had some tests done was the "Tractor Pulling" plan.  The plan in itself is simple and almost sounds ludicrous but with some more thought given in to it, might just work but at an extremely high cost.  This plan could go two ways, one is cheap and possibly beneficial to the planet but more risky and the other is expensive but overall more safe than the previous.  The first plan is not really a defense plan but could act as one if the initial test is successful.  NASA plans to sends a probe or probes out to an asteroid headed in our general direction and see if they can alter the gravity of the object and ultimately alter the trajectory of the space rock.  To do this, the probe will fly alongside the asteroid and slowly remove chunks of the rock in hope of changing the objects gravitational field.  The original application of this plan was to be used to bring small asteroids into orbit of the moon so that astronauts could use it as a pit stop on their way to Mars in 2030.  The physics for this plan would be tricky but possible and since this plan is already on schedule to be tested it may very well be the best solution we have to date.  Things to consider when going with this plan would be the mass of the object, the force of gravity of the asteroid (which we need the mass and the radius of the asteroid), how dense the asteroid is and how fast it is traveling towards Earth.  Given the quantities that are needed to be known we can see that changing the asteroid mass would affect the overall gravitational force of the object, possibly changing its course.  For example, all of the planets in the solar system revolve around the sun because of gravity and the huge amount of gravitational pull the sun has, since gravity depends on mass these planets must be at an exact and constant mass to maintain their orbit.  If Earth suddenly became less massive its orbit would change.  The same could be said about an asteroid going towards Earth, since it is also caught in the sun's gravitational field.  The proof is in Newton's equation for the gravity of two objects (Fgrav -proportional to- m1*m2/d^2) whereas the mass of the two objects is directly proportional to the final gravity.  The only problem I see with this plan is that it could possibly put the Earth in more danger, especially in its testing phase.  This is due to the fact that they would be bringing in an asteroid closer to Earth instead of redirecting it away from Earth.  The second plan is quite similar but could prove to be safer, if it is even possible.  For the second defense technique NASA wishes to send one big probe or several probes to throw the asteroid off course using gravity.  This could be a possible solution but only if they could gather enough force to counteract the asteroid's gravity (which could be large depending on the asteroid's mass and radius) and even if this amount of force needed to transmit the required impulse can be harnessed it still must be directed at the rock and forced upon it for quite sometime for the change to be effective enough.  In short, NASA would need to deploy this plan as early as possible to ensure success.  Basically this plan is to change the objects momentum in general.  Quantities needed in this plan would be the mass, acceleration, radius, and overall velocity.

Friday, September 11, 2015

Arnold... There is No Way

The 90's were chock full of classic action movies and Eraser is sort of one of those.  Big name action star, female co-star, multiple action scenes, minimal plot, cheesy one-liners, it's all here.  Another thing that Eraser stays true to is the undoubtedly broken movie physics.  The scene I am analyzing happens at the movie's climax, the bad guys have just brought down the warehouse that Arnold was hiding out in, thanks to his quick thinking he tosses his gun to a nearby enemy.  The fool picks it up and is then targeted by his own teammate who mistakes him for Arnold.  The bad guy fires at his comrade as he screams "NOOOOO", he is then struck by the aluminum round and sent flying to the far wall of the remaining warehouse.  Right away you can tell there is seriously something fishy about the physics in this scene, an EM gun firing aluminum rounds at nearly light-speed having virtually no recoil?  As said in an earlier scene, the gun fires rounds at nearly light-speed so let's just assume it is at light-speed. The aluminum rounds seemed to the size of a 50. caliber round, take into account its less massive element I estimated that the rounds would weigh as much as two empty cans or 0.026 kg.  As for the shooter and victim I used the average mass of a North American male so about 80.7 kg.  The gun itself looked like a sniper rifle so I took the average mass of a military sniper rifle so about 12.9 kg.  Add the mass of the gun to the mass of the shooter and you get the shooter's final mass at 93.6 kg.  Finally the velocity at which the round would be going 299,792 km/s or the speed of light.  Taking all this into account I have written out and solved the following momentum equations accounting for the shooter and the victim to see if momentum was, in fact, conserved.
    As you can see, momentum was definitely not conserved in this scene, let alone any in this film where an EM gun was being used.  According to the math and physics behind it, the shooter and the victims would have flown back much farther and faster than portrayed in the film and shooter would not have been able to fire a round off with no recoil at all.  This film is, in fact, scientifically broken. As instructed by Dr. Fragile we were to assume that the round stayed inside of the victim, carrying him off but if we look at the scenes in a different way we can see that this would be impossible.  The rounds traveling at this speed pass through walls with virtually no resistance, this would be the same with the human body but instead the round gets stuck inside them somehow.

Friday, September 4, 2015

Mission Impossible 3, Questions That Should Be Asked.

This is my third time watching MI3 but the first time I have seen it in a new light, from a more physics oriented point of view.  Throughout the viewing, I was watching scenes as if for the first time, analyzing each and every aspect to form questions based around physics and if the physics of the film were plausible or standard Hollywood flare. I would like to start off with the scene during the second heist of the movie, the Shanghai sky-rise. Ethan Hunt must procure the mysterious item known only as "The Rabbit's Foot", if he does not acquire this item in the next two hours his wife will be killed by the film's antagonist, Owen Davian.  "The Rabbit's Foot" is being held in a 162 meter tall building with armed guards on the roof, Ethan's only solution is to swing from the neighboring building, which is 226 meters tall, using a fulcrum.  The buildings are 47.55 meters apart and against his team's warnings, Ethan plans to attempt this swing.  My question to this scene is, "Would he actually make the swing or fall to his death after bouncing off of the building?"  To analyze this scene we must look at the different quantities in play, luckily the movie provides us with the heights of the buildings and the distance between them.  More information that would be helpful is the length  of the rope, how high Ethan was from the top of the target building, and how far he fell before the swing took place.  To find the length of the rope I subtracted the two building's heights to get a rope with a length of 64 meters at least but with enough extra rope to swing with so I say about 69 meters long.  Next is how far Ethan fell before the swing began can be seen in the planning of the jump, he jumps at an angle equal to the height of the target building, putting the distance at 64 meters.  As for finding the height of Ethan at the end of the swing I analyzed the movie scene multiple times looking at the distance he fell and how long it took him to hit the glass, from what I could surmise he fell approximately 3 meters.

The next stunt scene in question for me is the infamous bridge scene.  I chose to question 2 specific stunts from this high octane action oriented scene.  It opens up with Ethan and his team escorting Owen Davian to custody when they are ambushed by an unmanned drone armed with rockets.  Many cars are destroyed and even a portion of the bridge.  Tactical teams come in by helicopter to get Owen Davian out of C.I.A. custody.  After their S.U.V. is flipped Ethan must scramble to retrieve the automatic weapon in the back.  As he is getting the gun the drone fires a rocket at him, without a second to lose he grabs the gun and flees from the truck only seconds before it is destroyed, he is close enough  to the blast that it knocks him sideways into a nearby car.  My question is, would it be possible for him to be knocked to the side of the blast instead of forward towards the camera?  Quantities needed to answer would be as follows, how far was he away from the exploding truck, how far was Ethan from the car, and the angle at which the missile hit.  To find out how far he was I took his height (5'7 or 1.72 meters) and multiplied it by 1.35 (average runner's stride) to get 2.32 meters per stride, multiply that by 8 (the number of strides he took and you get 18.56 meters away from the truck.  After analyzing the film clip further I can estimate that Ethan was about 2 meters away from the car that he slammed into, I came to this conclusion when looking at Ethan's height and using it for measurement between his initial position and the car.  As for the angle that the missile struck the S.U.V. I rewound the clip to when Ethan spotted the missile then watched the impact in slow motion.  The missile was heading straight on towards the drivers front door at about a 55 degree angle judging from the base of the bridge.  Taking all this into account, Ethan should not have been thrown sideways into the car but instead forward, this can also be concluded by watching the debris surrounding him going in a completely different direction.

The final action clip I will be questioning is contained in the same scene as the previous, Ethan is now chasing after Davian's helicopter with the automatic weapon but there is a large hole in the bridge that he must cross, he tosses his gun, sprints and then takes a daring leap across the gap just barely making it across.  My question is, could he have really made that jump?  A quantity to take into consideration would be the distance of the gap.  To find out how wide the gap was I used the overturned car in the background as reference. from what we see in the clip the gap is about as wide as the vehicle, the vehicle appears to be another S.U.V. from this we can say that the gap that Ethan nearly cleared was about 5 meters.  This distance of a jump can be done by the average male if in pique physical condition.  I believe this jump could have been completed by Ethan Hunt.