Two-Body Problem: Assignment 2

Nov 9th, 2015
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  1. Two-Body Problem
  2. By IceMan
  4. Assignment 2: Two-Body Problem with Rotational Momentum
  6. Chapter Theme: https://www.youtube.com/watch?v=VXRSsge__n8
  8. >You finish scribbling down a string of letters, both Greek and Roman, and a few numbers.
  9. >Another problem set complete.
  10. >Your efficiency has greatly increased since you started doing them with a partner.
  11. >Having a friend to bounce ideas and solutions off of has made them significantly easier.
  12. >And the post-problem set cuddling was always a plus as well.
  13. “If I can say one thing about this class, it is this,” you say as you drop your pencil on the table with a thwack. “I am really goddamn tired of masses on springs.”
  14. >“When your professor specializes in classical mechanics, it’s kinda hard to avoid those situations,” Twilight says.
  15. “Well, he could at least try to mix it up a little bit. There have to be other situations that you can model as a damped harmonic oscillator. What about LRC circuits? What about damped quantum harmonic oscillators? It’s just ridiculous. I mean, on one hand, I’m happy to just get the same problem 15 times in a row, ‘cause it makes the problem sets easier, but on the other hand, I’d appreciate a little more of a challenge.”
  16. >“Yeah.... Wait, what day is today?” Twilight asks.
  17. “Uh, Tuesday?”
  18. >“You wouldn’t mind helping me do some laundry, would you?”
  19. “Not at all. What are friends for?”
  20. >“Great. Hang on a sec.”
  21. >Twilight gets up from the table and pads off towards her room in her socked feet.
  22. >She comes back with a large, rectangular plastic basket loaded with a pile of slightly wrinkled clothes.
  23. “Your parents make you do your own laundry?” you ask.
  24. >“Yeah? Yours don’t?” Twilight replies.
  25. “No. I’ve never had to do my own laundry”
  26. >You follow her to the laundry room, a small room with some cabinets, a sink, and the pair of black square boxes with round doors and LCD screens of a modern washer and dryer.
  27. >“Well, I guess I could give you a lesson then.”
  28. “Sure. Why not? Can’t be that hard.”
  29. >“It really isn’t. Okay, first, get the detergent from that cabinet over there.”
  30. >Twilight points to a cabinet on the right, setting the basket of laundry on top of the washing machine and opening the hatch to it.
  31. >You open up the cabinet and quickly find the oddly-shaped bottle of detergent.
  32. >“You’ll need maybe half a capful of that,” Twilight says.
  33. >Unscrewing the cap, you fill it halfway to the top with the slightly viscous, sweet-smelling, blue liquid.
  34. “Alright,” you say, indicating you’ve finished the task to Twilight, who is focussed on tossing various articles of clothing into the washing machine.
  35. >She looks up for a second and says, “Okay, now put it in the detergent slot,” then points to a square, closed receptacle on the top of the washing machine.
  36. “Is that the technical term for it?” you say as you open up the slot.
  37. >“I don’t know, just pour it in there.”
  38. >You open the receptacle and pour the detergent into the slot neatly marked “detergent.”
  39. >Twilight puts the last handful of clothes into the machine.
  40. >“Now just turn the knob to ‘delicates’ and press the start button.”
  41. >You do as she says.
  42. >The washing machine hums to life, the inner cylinder turning, the LCD screen displaying “Determining load amount...” as well as a timer counting down from 60 minutes.
  43. >After a few rotations, water begins to flood the inner cylinder.
  44. “Well, now what?” you ask.
  45. >“We wait for the wash cycle to be finished.”
  46. >You dust off your hands.
  47. “You were right, then. That was easy.”
  48. >“Well, we’ve still got to put all the washed clothes in the dryer. And then fold everything and put it away.”
  49. “But that’s not for another hour. So what do we do until then?”
  50. >“I don’t know.”
  51. “Uh... is your research going well?”
  52. >“I guess. I got another spike just this last Saturday....”
  53. “What? Really? Any clue as to what it was?”
  54. >“Hang on, let me get my computer, and I’ll show you.”
  55. >You head back into the kitchen and sit down at the table as Twilight heads to her room to get her laptop.
  56. >She comes back a minute later and unfolds the black rectangle to reveal a galaxy map background behind a neatly organized desktop.
  57. >You scooch your chair over next to her to get a better view.
  58. >Twilight pulls up a data mapping program, and opens the file named “CHS EM Spectrum Research.”
  59. >There’s a huge, sudden spike, a giant upwards dent in the otherwise relatively flat line, on the graph around 9:30 PM last Saturday.
  60. >“So, yeah, that’s it. Just this huge sudden burst of energy coming from....”
  61. >Twilight pulls up an EM heatmap of your local county overtime.
  62. >“Looks like the old stadium. But why there? The last time it came from the school.”
  63. “Wasn’t CHS having some kind of Battle of the Bands thing last Saturday? I heard a few people who have friends there mention it....”
  64. >“I don’t think speakers, microphones, and poorly-played rock covers could produce this much energy.”
  65. “Then what the hell would? Does CHS have some kind of nuclear Boy Scout or something? Did he use a homebrew nuclear plant to power his band’s instruments or something? I mean, Jesus, you picked up photons in the giga-electron volt range. What the hell were they doing there to produce that much of an anomaly? And, how is, I don’t know, the FBI, or whatever, not investigating this? It’s seriously like they set off some kind of radiation bomb or something. That’s the only thing that could produce photons of that much energy. How is the whole city not irradiated by now?”
  66. >“I don’t know. Maybe it’s some form of new type of energy or something, that just reads as electromagnetic radiation. Whatever it is, I decided yesterday to head over there and put some sensors around, just to take some readings at the two sites of the anomalies.”
  67. “Well, that was smart. Just hope nobody finds those things. People are seriously getting way too paranoid about these Friendship Games coming up. I’d imagine it wouldn’t bode well if CHS thought we weren’t playing fair. Not with me, I mean. I couldn’t care less.”
  68. >“Same here. Still it would be better if - wait, hold on, something’s happening.”
  69. “What is it?”
  70. >“One of the sensors has picked up another EM spike.”
  71. “What? Right now? Holy -”
  72. >“Okay, sensor 3... readings of photon energy levels up to 30 GeV.... It’s not as big of spike as last time, but still.”
  73. >You watch as Twilight takes down the data.
  74. >Two minutes later, the pulse ends.
  75. “Okay... now what?”
  76. >“I don’t know! Ugh, why does this have to be so infuriating? Why do these things always happen when I’m not there to directly observe them?”
  77. “Based on these readings, I don’t think you’d wanna be anywhere near what’s going on there. Getting a bunch of 30 GeV gammas to the face wouldn’t be very good for your chance of living a cancer-free life in the near future.”
  78. >“But that’s just it! If it were gammas that we were seeing, then the radiation monitors would be going off like crazy. But no, they’re silent! And the school isn’t irradiated, though I’m willing to bet there’s not a single Geiger counter near that place other than the ones I’ve put there.”
  79. “Then where is also this electromagnetic energy coming from? And what is it?”
  80. >You think for a second.
  81. “I guess that’s the million dollar question.”
  82. >Twilight sags back in her chair, and then against your shoulder.
  83. >“Maybe it’s what I said... some new form of energy that just reads as EM waves, but is actually something else?”
  84. “But what is that ‘something else?’ Twilight, you know as well as I do that it’s best to first seek explanations that fit within our models of reality, rather than looking for some new thing that we don’t understand and can’t model. If there’s not some scientific explanation for this, then we’d be better off calling it ‘magic’ or something.”
  85. >Twilight sighs.
  86. “Hey, buck up. At least you don’t have to fill out twenty more forms to get your satellite put on a rocket to space. And you might have discovered a new type of energy at 18. That’s pretty good, if I don’t say so myself. I mean, Newton was 22 when he literally started physics.”
  87. >“It won’t matter if I’ve discovered some new type of energy if I can’t explain what it is. It’s like you said. I might as well call it ‘magic’ or some other silly thing. I’d be no better than those people who go around looking for ghosts or UFOs or bigfoot or something.”
  88. “That’s not true. You’re better than them. We’re better than them. We know what it means to come to a rational conclusion about something. You always look for an explanation that fits within our current understanding of the universe first. So, what are you going to -”
  89. >Twilight shoots up, ramrod straight.
  90. >“Another pulse!”
  91. >You jump up out of your seat, startled.
  92. “What? This soon?”
  93. >More data streams in from the sensor.
  94. >“That’s strange. It’s all coming from sensor 3. I put that one near the science lab.”
  95. “Okay, someone is definitely messing around with something big there then. I’m putting a point for that nuclear Boy Scout hypothesis. Maybe we should call the FBI or something, or tell the school to have someone check their basement radiation monitors. I think this area has a bit of a radon problem, right?”
  96. >“And what if I’m right, and it is some new type of energy, something that can’t be explained with our current understanding of physics? Do you really want the police getting involved in that?”
  97. “No. I don’t. Urgh, now I’m getting frustrated.”
  98. >You pace back and forth a bit.
  99. >“We have to head over there. We have to figure out what this is.”
  100. “But what about the laundry? It’s at least an hour busride out of the city. We can’t just leave it in the washing machine, right?”
  101. >“Argh, you’re right! Dammit, why do I have to be so obsessed with keeping to my laundry schedule? I could’ve just done it tomorrow.”
  102. >You stroke your chin and frown.
  103. >“Wait,” Twilight says. “If these spikes are occurring more frequently, and they’re occurring near the science lab, that may mean someone is experimenting with this energy. That means, maybe, we’ll see more of them more frequently.”
  104. “Yes! And -”
  105. >“Oh my God, here’s another one!”
  106. “Three in a row. What are they doing?”
  107. >“I need... what I need is some way to capture this energy, some way to contain it so I can study it when I need it. Like a trap or something. I could set it near the sensors, and then if they try to experiment with whatever this energy is.”
  108. “Well, we know that electromagnetic sensors respond to it. So maybe a high-strength magnet could capture it....”
  109. >“Like the cosmic ray capturing device on your satellite?”
  110. “Yes! Exactly! And it’s small, you could fit in a little sensor or something. I could give you the design. I’d just need to -”
  111. >Twilight jumps up rips you into a tight embrace.
  112. >“Thank you thank you thank you thank you thank you -”
  113. “Whoa, hey now, I get it, this all very exciting but -”
  114. >She kisses you, full on the mouth.
  115. >You blink and adjust your collar.
  116. >Both of your faces turning completely scarlet.
  117. >“I’m sorry, that was inappropriate, I should’ve -”
  118. “I- I... wow.”
  119. >You take a deep breath, feebly attempting to regain your composure.
  120. “Twilight, sometimes a bit of spontaneity is good in a relationship,” you say.
  121. >Thank you, internet dating advice tips website.
  122. >“No, I’m really sorry, I didn’t know how you’d react, or if we were at that level yet, or -”
  123. “You need to stop worrying about these things. I... Twilight, I love you. Truly. With all my heart.”
  124. >The washing machine gives a short jingle, indicating it has complete the cycle.
  125. “Looks like the washing machine’s done.”
  126. >“Do you think you can handle moving all that to the dryer? I really need to check and see if another pulse comes through.”
  127. “Alright. Any instructions for the dryer?”
  128. >Twilight is already completely absorbed by the data on the computer screen.
  129. >“Just set it to ‘delicates’ and press start once you’ve loaded it. Should be good from there.”
  130. >As you begin loading the dryer, a woop of excitement comes from the kitchen.
  131. >The mysteries of the universe grow ever larger day by day, from what it means to love another person, to how the universe works, to how to do a simple load of laundry.
  132. >You slam the door of the dryer shut, set it to run, and go back to solving the other two of those mysteries.
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