[BÀI DỰ THI LE SPECTRE #23: SUPERPOWER?]

Tác giả: Từ Ngọc Huy
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Lớp MT17KH1 – Trường Đại Học Bách Khoa TP.HCM

Superpower? It’s still a long long way to save the world
Superheroes vs Villains movies are the blockbusters that dominate when it comes out so it wouldn’t be a surprise if some of us have ever wished that we possessed some kind of ability to fight against the bad guys or just simply to give us a boost in our daily life. But superpower always comes with a price that the writers don’t really want you to know or even explain how it is possible. In this essay, I will walk you through some scientific rule that lied behind some kinds of power before you are set to save the world.

Chapter 1 : Flash, the hero who commutes from one place to another in a blink of an eye. Before set to save the world, you may need to learn plenty of physical activities associated with your new-found speed. One important fact is that air is not empty but instead, it is like a box of air molecules, when your velocity is fast enough, air molecules and dust particles could become tiny missiles that burn your skin. Another thing to consider is the density of air, in normal room condition, the space between each pair of air molecules are 10 times larger than the air molecule itself [1] (nitrogen, oxygen), each move with the speed of 343m/s (sound speed when traveling through the air [2]). When running with the velocity faster than sound, the molecules pile up into a barrier in front of the human body and could blow up anything ahead without even touching.

Vice versa, the air behind you would become so low in density (in comparison with its surrounding) that it would turn itself into a vacuum (air molecules fill the empty space according to Fick’s laws of diffusion [3]) and suck anything into your trail behind.

The Doppler effect [4] represented by f= f0 * (c+v)/c (c is sound speed in its environment, v is the speed you come toward that sound, f0 is the original sound’s frequency) shifts the static source’s pitch of sound coming toward the receiver much higher than normal, hence distorting your ability to hear the original message.
How much food he must eat to produce such tremendous power to fuel the running process also matters. We calculate kinetic energy using KE = (1/2) m.v^2 (m is the mass, v is speed, KE is kinetic energy) Speed body weight is 88 kg [5] and we assume he normally runs at the speed of sound at 343 m/s. Then KE = ½. (88kg) * (343 m/s)^2 = 5176556 (kg-m^2/s^2) = 1237226 (calories), which is equivalent to 3300 average hamburgers [6] per second to generate such energy.

Into a spider verse, have you ever considered swinging from building to building with fragile spider silk in New York city possible? Since being spiderman does not give your body the capability to produce the spider silk yourself, you have to figure out a way to make it work with a little bit of science. There are a few forces that affect the object that is in motion: the external gravity from his body mass calculated by P = mg (where m is mass of the object, g is gravity acceleration), centripetal force that keeps him from falling to the ground and diverts him when swinging in circular motion calculated by Fc = m*v*v/R. [7] (where Fc is the centripetal force, v is speed, R is the radius of the orbit). Breaking these force up into two vectors can help you infer the following result :

Tmax = mg(3- 2cos(α0)) (where Tmax is the tension, α0 is the angle formed by the line through the equilibrium point and the central point of rotation). When α0 is 90 ° (starting point is at the same height as the pivot), the string will have to bear the maximum strength of 3 spiders’ mass at the lowest point of the circle.
But can you save your girlfriend from free-falling?

When her girlfriend Gwen Stacy has already been free-falling from the George Washington Bridge (which is 65 meters in height [8]). We calculate her speed using this formula: v*v = 2*g*h (where h is the length of the path a person falls through, h = 65). The velocity would be around 128 kilometers per hour. And using Newton’s second law: F = m*a. To stop her from hitting the ground (which reduce that in less than second, we assume it’s 0.25 sec, her weight is 55kg [9]) She has to put up with the lethal force of 7852N. Her fate is decided by the rapid change in speed, even if she hits any surface or not. This is why the car’s airbag came into existence, even your car stops, your body is still moving with the same speed, the airbag is there to safely reduce your velocity [10]. So next time, come up with a better idea to save people than just catching them directly when they are free falling.
Moving on, the tiny ant-man [picture 7], shrinking to the size of a bean using an unknown trick is not quite possible even with that scale but here we are going to look over that. Instead, we want to consider some limits to the communication ant-man has to experience compared with his human form. Let us take another look at the harmonic motion of the pendulum [11].
f = 1/T = 1/(2π)*√(g/l). (where f is the frequency of sound, T is the wavelength of the sound, l is the length of the pendulum) To put it simply, frequency^2 is inversely proportional to the length of the pendulum. How the vocal cord operates can be simplified to that of the pendulum in terms of harmonic motion [picture 8]. When human shrinks to the size of an ant [8] (6ft to 1cm) [picture 9], he would shrink 183 times, or the vocal pitch would be 13 times higher than its original point. A typical voice speech of a man range from 85 to 180 Hz [12], and that of the ant-man would be 1105hz to 2340hz, which is still hearable, but as we consider the loudness of that tiny speaker, communication will eventually experience some technical problems.
Another problem is his vision power, many insects as you can see, have a significantly different lens from ours. Take dragonflies [picture 10] as examples, their panoramic compound eyes consist thousands of lens [13] and each retina is formed by thousands of photoreceptors that are especially receptible to light [picture 11]. In the case of human, visible light (400 nm to 650nm in the wavelength spectrum) has to travel through the pupils in the shape of a cone and its reflection must be on the back of the eye (retina). When your pupil is shrunken but the light wave is still constant, your eye will lose focus and the image will be blurry, that’s why we may also have the eye of an insect to actually be ant-man (and do not forget the fact that ant does not have ear and their eyes are not for navigating, they feel the vibration through their feet and locate objects with smell).
Phew, that was quite a journey, you may find that having your own supernatural power does not necessarily make your life easier. To understand why landing in the sea in aviation accident doesn’t necessarily save your life, and why our body is not designed to grow bigger or smaller are to accept our human nature. In today’s worlds, heroes are all the scientists out there that go beyond those limitations to invent supersonic aircraft, super braid wire, or surgical microscope happen and make every one of us a superhero in our everyday life.

References :
[1] https://en.wikipedia.org/wiki/Mean_inter-particle_distance
[2] https://en.wikipedia.org/wiki/Speed_of_sound
[3] https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion
[4] https://en.wikipedia.org/wiki/Doppler_effect
[5] https://dc.fandom.com/wiki/Flash_(Barry_Allen)
[6] https://www.livestrong.com/article/306441-how-many-calories-does-a-hamburger-have/
[7] https://www.wikihow.com/Calculate-Tension-in-Physics
[8] https://en.wikipedia.org/wiki/George_Washington_Bridge
[9] https://spiderman.fandom.com/wiki/Gwendolyne_Stacy_(Earth-616)
[10] https://en.wikipedia.org/wiki/Airbag
[11] https://en.wikipedia.org/wiki/Simple_harmonic_motion
[12] https://en.wikipedia.org/wiki/Voice_frequency
[13] https://www.newscientist.com/article/dn27015-dragonfly-eyes-see-the-world-in-ultra-multicolour/
[14] https://en.wikipedia.org/wiki/Visible_spectrum

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