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The Physics of Spiderman


Over this past weekend after I finished working on my homework, I decided to relax and watch a few movies before going asleep. Among the movies I watched was Spider-Man 3 from 2007 and despite the movie flaws I was interested by the scenes that showed Spider Man shooting through the sky with the use of his webs that come out of his wrists. Due to this, I decided to make my blog post about the physics of Spider-Man's slingshot. After doing some research, I discovered just how much information there is on the physics of Spider-Man and how elements of Spider-Man can be used as examples for most topics learned in mechanics.


For this investigation, I will not be using the horrible cliche and terrible CGI infested mess that Spider-Man 3 is but instead the all around superior Spider-Man movie of Spider-Man 2 to investigate the physics of Spider-Man's web propelled slingshot.  I want to talk about what happens in terms of physics when Spider-Man launches himself across a distance using a slingshot made out of his own web. In this particular scene, Spider-Man is attempting to save his Aunt May from Doctor Octopus on the side of a building. During the fight, Spider-Man is knocked across the street and has to get back quickly to save Aunt May. In order to do this, he launches webs at both sides of the window, then puts them under tension by walking backwards before jumping and being launched back across the street. This creates a Spider-Man slingshot that allows Spider-Man to return to the fight and save Aunt May from Doctor Octopus. A video of the relevant scene is attached below with the slingshot section starting around 1:40.


First off, this scene is clearly an example of both projectile motion and conservation of energy. Conservation of energy means that the total energy in the system is constant so that means that:
EI+W=EF
By looking at a simple picture, that of a regular slingshot it is easy to see that the energy initial would be elastic potential energy as Spiderman pulls back on the webs stretching them like an elastic band. If we ignore air resistance, then the only energy acting when Spider-Man flies out of the window is kinetic energy. This means that:
U+W=KEf 
Due to the work-energy theorem which says that the total change in the kinetic energy of an object must equal the net work done on an object. This means that:
Wspiderman = Uwebbing = KEflying-spiderman
The first step would be to solve for the elastic potential energy which first requires some approximations and estimations to get the necessary values. Let's assume that Spider-Man weighs 76 kg, he pulls himself 4 meters away from the window before jumping, the distance across the street is 33.5 meters, the angle at which he launches is 5 degrees, and that the k value of Spider-Man's webs are 800 N/m (1900N/m due their being two webs). The image shows the scene while Spider-Man is pulling back.


With these estimations, the elastic potential energy can be solved for using the equation and the above approximations:
Espr=1/2kx^2
Espr=1/2(1900)(4)^2
=15,200 J
This means that this is the total amount of energy in the system since we can't add any more without work which there is none after this point. This means that the second Spider-Man lets go of the webs his kinetic energy would have this much energy as well. However in order to achieve this amount of energy, Spider-Man had to do work by applying a force over a distance which means that:
W=FΔXcosϴ
F=W/ΔXcosϴ
F=15200/(4)cos5
=3819 N
This is roughly equivalent to about 850 pounds meaning that he is pulling a decent amount of weight, which explains the strange noises. By knowing the energy level of the kinetic energy after Spider-Man releases the webs, we can solve for Spider-Man's velocity across the street. 
KE=1/2mv^2
v=√ 2E/m
v=√ 30400/76
=20 m/s
This means that Spider-Man flew across the street at close to 45 mph which is not the smartest idea considering he is flying through the air with no means to control or stop his flight directly at his greatest foe on the other side of the street as seen in the below image.


While I did not do the projectile motion for Spider-Man in this situation it does not seem he will make it to the other side in the fashion depicted in the movie as the only force acting on him in the air is gravity which might put him lower than Doctor Octopus considering that he is starting a floor lower than Doctor Octopus. This could probably be rectified by getting a better angle of launch then 5 degrees but Spider-Man would have to be careful to avoid decapitation on the top of the window when he exits. This situation seems impossible to the sheer speed he is traveling and his seeming ability to instantly slow from that speed to avoid being punctured by the spike but maybe his Spidey magic has something to do with it. Even with this physics fallacy the movie is still incredible and I would recommend it.
Works Cited
https://cosmosmagazine.com/physics/the-science-of-spider
https://www.wired.com/2014/04/the-physics-of-spider-mans-webs/
https://hypertextbook.com/facts/2005/SpiderMan.shtml
https://www.popsci.com/article/2007-10/physics-spiderman-3
http://www.thescienceof.org/physics/physics-spider-man-slingshot/
https://www.wired.com/2014/05/should-spider-man-swing-or-run/
https://www.wired.com/2017/03/yes-spider-man-can-jump-6-meters-onto-moving-ferry-physics-says/

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