#doormat ethic

[aheartofwood]

The Rules:

 Rule One: Post the rules. 

 Rule Two: Answer the 11 questions the tagger asked you, then make 11 new ones. 

 Rule Three: Tag 11 people and link them to this post. 

Rule Four: Let them know you’ve tagged them.

Tagged by: doormat-ethic

 (I put the questions/answers and stuff under the cut because it’s long and obnoxious.)

Pen. I will always love pen because you can just write and draw and not have to erase anything and it's so beautiful ahhh i did all my best art last year without drawing it out in pencil first with just pen and it's so permanent but also you can draw on yourself and make nice things and there are so many nice pen kinds and ink and mmm yes

What’s the scientific/historical/cultural/etc inconsistency or inaccuracy in a movie/television show that bothers you the most?

i know there IS something, considering how much i love history and am a stickler for detail in shows. i can't think of anything right now, but a general example that is kind of unrelated---i don't like when things rhyme in one language but clearly do not in another. like, famous poems and books? those rhymes aren't ACCIDENTAL so clearly the translator took some liberties

  How much would someone half to pay you to (a) eat a spider? (b) eat a live spider? (c) drink from an unlabeled bottle of clear liquid from a scientific laboratory cabinet (given that it’s non-fatal)? (d) start vigorously picking your nose in front of the person you admire most?

diD YOU WRITE THIS JUST FOR ME

a. 1,305,284,390,294,023.03

b. uhhh...same...amount?

c. ehhhh depends i'd probably do it no matter what ALWAYS UP FOR A DARE WOT WOT

d. i mean, money things don't really matter to me, as you know from my illustrious job...plus i probably have done this

What was your last dream about?

i've been dreaming about my job like every night, and the other night i dreamt the kitchen exanded into the one in ratatouille sort of and a bunch of people worked there like all the cashiers and michele's little sister ordered some fancy sandwich that i had to run across a giant, dewy, realistic version of hyrule field at 9:00

Shetland ponies or staple guns? Please defend your answer.

well they both have merits

-shetland ponies: ADORABLE awwww they remind me of cats and hobbits

-staple guns: one of my favourite tools to use in props and sets, also kind of the first tool i ever really used for design on the set of les mis, stapling fabric and flowers and things to the barricades. i like them because they are simple and you don't have to be really good at things or accurate to use them. also, i bet they would be nice in an apocalypse

If you had a cool animal familiar, what animal would it be?

fox bc cat has been done too many times. i would just like a fox please. i mean come on that would be really awesome let's tell it like it is

also, i'm p. sure a fox would be my patronus or something, not to rustle anyone's jimmies. they're orange, standoffish, elusive, often appear in folk tales, and equal parts intelligent and derpy. does any of that not sound like me i think not

If you had to be a video game character, which would you be?

hmm...hMMM. well, i'm just gonna go with midna because she is a humongous bamf. come on admit it u all have a ladycrush on midna. but also chell and wheatley have merits

What creeps you out the most?

the song i'm listening to is REALLY creepy...then again, this is my 'creepy song' playlist. but to be honest, spiders really creep me out, of course. i also used to have really bad nightmares, like the time i dreamt about those worms with lights on their eyestalks that crawled under my toenails in the basement when i was five, but i also used to (and still do) have bad nightmares about imposing forces such as the supernatural, sentient technology, being mugged, and being entirely alone. also, sometimes i have like night terrors where i feel like the voice of the devil and/or god is beckoning me and i'm literally like plEASE let me remain mediocre. but yeah, the general feeling of aloneness creeps me out. like, are we the only people in the universe or are there other beings out there? either way is WEIRD AS FUCK.

What’s your favorite word?

i love a lot of words, but i really like 'mix' and 'maelstrom' because they're a good representation, almost, of an asmr feeling? but with a single word? like they're just very tangible and tasty 

What’s the answer to this question?

42.

Thanks and goodbye!

[aheartofwood]

my sister got into caltech!

here is your online congratulations 

[aheartofwood]

my sister is a fucking gem

last night i tried to download paint.net and instead got more than 20 viruses

so i called her at 10:45 and by midnight she had walked me through getting rid of all of them (WITHOUT anti-spyware because i'm a cheap-ass college student), through safe mode, and back into normal-computer-land. and this was from a computer that wouldn't even open the internet or let me do anything because of all the popups coming up

plus she had two essays to write

bless u

[maths-help]

Let's draw a picture. (Right, if anyone hasn't realized that this is a running theme with me...this is a running theme. Pictures are good! Pictures can be helpful! Pictures are pretty!)

When we say "tension" in a cable, all we're really saying is "find the force delivered by the cable". See, look: the disk isn't falling to the ground. But gravity exists! So it's pulling the disk downward, and the only reason the disk isn't falling is because the cables are pulling upward with enough force to stop it.

Let each of the cables be pulling on the disk with force F. (Since the situation is symmetric, every cable must be pulling with the same force.) Now, if the cables were hanging straight from the ceiling, F would be entirely upward. But looking at the picture (See? Important.) the cables aren't straight but slanted. Since F points in the same direction as the cable (where else could it possibly point?!) some of their force is going to be sideways, so the upward force is going to be less than F.

So how do we find just the force upward from a cable?

The official, physics-y answer is, you take the dot product of F with z-hat (that is, the unit vector pointing straight up).

See, the dot product is, informally, a way of picking out how much of each direction your vector is going. So dotting F with z-hat should give you the "upward component" of F.

The equivalent but more geometric answer is, you take F*sin a, where a is the angle marked on the diagram. Because you can think of F as the hypotenuse of a right triangle, which has as one of its legs lying along the radius of the disk, and that means the proportion of F pointing upward can just be obtained by basic trig.

Okay, so F*sin a is the tension in the cable. And now we note that

(where g is the gravitational constant ~10 m/s^2), since the LHS is the total force pulling the disk up, the RHS is gravity pulling it down, and those two forces must be equal for the disk to not fall (or rise up through the ceiling!).

(Quick note: You might want to convert the 24 lb into kg so the units work out nicely here.)

But no, wait, you say. That's not a function of L.

Ah. Right. That's true. Are we doomed, then?

No! We notice that the right triangle with the radius of the disk as one leg and the cable as hypotenuse also has the angle a in it. And sin a there happens to be

where the numerator is obtained via the Pythagorean theorem. Therefore we finally have

Okay, quick sanity check. Does this answer make sense?

What happens when L gets really large? In that case, the cables are pointing almost entirely straight up. And sqrt(L^2 - 18^2) approaches L (since if L is large, it's going to overpower the 18^2), so the answer's just 24*g/3 = (8 lb)g. And that's a third of the gravitational force, which is good, since there are three cables.

When L gets nearer and nearer to 18, the cables get nearly horizontal, so the force upward must become huge. And indeed, as L approaches 18 the bottom gets nearer to 0, making F quite large.

And now we're finally done.

- H2

P.S. I've been a bit loose with notation in this post; namely, I've been using the quantity F (the numerical value of the tension in the cable) interchangeably with the vector F (the thing that's pointing along the cable). Er. Don't do that. That's not good practice.