#Calculus in Physics

[innovativejunction]

Quantum Footprints in the Cosmos: The Calculus of Space Exploration

Quantum Footprints in the Cosmos: The Calculus of Space Exploration Quantum mechanics governs the behaviour of particles at microscopic scales. But space, with its vacuum, high radiation, and zero-gravity conditions, reveals phenomena that only quantum physics can explain. From precision in navigation systems to understanding black holes, quantum mechanics enables us to interpret and engineer…

[er-cryptid]

Physics and Integration [Ex. 1]

Patreon

[midnightfairy1]

Do Borrowers Actually Take Fall Damage? (calculus/physics answer)

hey guys! sorry I haven’t been active lately, but im about to finish up my finals so give me one more week before I start posting religiously. I just wanted to share with you some calculations I discovered during my studying for the Physics C AP Exam, with which I am expecting to interest borrower fanatics.

I am very proud of figuring this out and hope you guys find this as entertaining as I did! (By the way, I suggest scrolling to the bottom for the answer if you don’t want to read through all my math, although the math can also be interesting if you want it to be! 😁)

First, I found myself wondering something: If ants are so light that their is no height they could fall from in which they could injure themselves, and humans gain fairly serious injuries after a 16 ft (5 meter) drop, where do borrowers fall on the scale?

I took to my physics notebook and calculated the result.

I won’t share with you the trivial calculations it took to reach my first conclusion. To break normal human leg bones, an impact force a little over 2,000 newtons is needed. For more serious injuries (more serious than a fracture), once the impact force reaches above 3000 newtons the fall becomes very dangerous. By 4000 newtons, the fall will usually become fatal (this happens around a 15 meter or 50 foot drop). But within the 2000 newton to 4000 newton range, a fall with a weird landing can have serious effects. If it interests you or helps put it into perspective, the impact force (in newtons) is equal to (mass(kg)x(velocity(m/s))^2)/(2(distance leg compresses (m))).

Next, I tried looking into the air resistance factor of a borrower. Depending on how high the air resistance is, the terminal velocity will decide the borrower’s impact force. Terminal velocity is defined as the highest velocity one might reach while falling, because air resistance counteracts your gravitational force once you reach a certain speed.

A 5’8” person who’s weighs 150 lbs scaled down to a height of 4” weighs .0136 kg (equivalent to the weight of a few coins). If you’re wondering if the fact that their bones are weaker will affect the outcome, don’t fret. Even though borrower’s bones are literally weaker, their bones are stronger relative to body mass. This is because bone strength is directly proportional to cross sectional area (length squared), and mass is directly proportional to volume (length cubed). this means that mass diminishes at a faster rate than bone strength. In a falling scenario, bone strength relative to body mass is the only thing that matters.

Now back to air resistance and terminal velocity. After plugging the borrower’s dimensions as well as other constants to the air resistance (drag force) and terminal velocity equations, I now know that the terminal velocity is equal to 11.4 m/s. This means that, no matter how high the fall is, the borrower will reach a max speed of 11.4 m/s because the drag force at that point will reach a quantity that is able to equally counteract the gravitational force (mass (kg) x gravity (9.81 m/s^2)) acting on the borrower.

Plugging the terminal velocity back into our impact force equation will give us the maximum impact force acting on the borrower. I’m going to do this for all of us, and reveal that the maximum impact force would be roughly 88 newtons. Taking into account a greater drag force (the borrower would most likely be flailing around and wearing clothing while falling), we can assume the maximum impact force would be even lower than this.

We are almost done. The last thing I need to do now is calculate a lethal impact force for a borrower, because it is not the same as a human’s. Impact force corresponds to energy transfer. For the previously mentioned fatal fall of 15 meters for a human, roughly 10000 joules of energy is transferred to the human, cause brain damage or death. any more than this would also lead the fatality (most likely). Scaling this down to borrower size using the same proportions as before, a transfer of roughly 1.94 joules would be fatal to a borrower. This corresponds to an impact force of around 194 newtons, well above the injury threshold calculated earlier. However, it’s good to assume that a fall from a weird angle or onto a hard surface still has the possibility to greatly injure the borrower, even if it is unlikely to be fatal.

One last calculation if you were wondering: the fall height it would take for a borrower to reach their terminal velocity is a height of 6.6 meters (or 21.7 feet) however, this fall would generate a force less than half that of a fatal force.

In conclusion, it is highly unlikely for a borrower to pass away due to fall impact from any height because their maximum impact force is well below the minimum impact force it would take to kill them. However, they can still get injured (and possibly fracture) in unlucky scenarios. This post is in NO WAY encouraging the artists or writers out there reading it to start composing scientifically accurate media, because I love the trope where the human has to chauffeur the borrower around everywhere and keep the borrower safe from high heights 🥰. If there is anything in my math I may have overlooked, please let me know because I would love to learn more! I really appreciate anyone who took the time to read this long, mathy message!

Borrower Speed, Strength, and Durability

[ravings-of-a-mad-scientist]

Math

Geologist: I do more math than you might think

Chemist: I mean, chemical equations are basically mathematical equations. If you think about it (I also do math math)

Physicist: Oh, yeah, it’s all math but we just handwave it

Mathematician: YOU DO WHAT!?

Quantum Physicist: *regularly does math that is literally beyond human comprehension* *now resides in a higher plane of existence*

Engineer: If I don’t do this math correctly PEOPLE WILL DIE

Military Scientist: If I don’t do this math correctly PEOPLE WILL SURVIVE

Topologist: If I don’t do this math correctly PEOPLE WILL BE MOSTLY UNAFFECTED

Philosopher: But what even IS math, really? No seriously, what is it?

Organic Chemist: I kinda forgot how to do math, to be honest

Biologist: I literally only chose this field so I wouldn’t have to do as much math. I love stamp collecting

Biostatistician: wtf

[phospadparadscha]

A little late but here's my gift for the @palestaticexchange for @delphionix of their prompt, Harry interacting with the Pale / the Skills! It was hard to decide what to do for this piece but I think i'm very proud of how it turned out in the end. The wonderful @presentablemichael helped me with making this piece happen finally. Happy gift exchange!

[gojoikawa]

HE LOOKS SO SMOL pleaseeee i can't take any more

[kohakhearts]

forget about fatal flaws or mental illness or whatever. how does your blorbo feel about math

[kymuryacademia]

─── ･ ｡ﾟ☆: *.☽ .* :☆ﾟ. ────── ･ ｡ﾟ☆: *.☽ .* :☆ﾟ. ────── ･ ｡ﾟ☆

August 22𝕥𝕙, 𝟚𝟘𝟚𝟜

─── ･ ｡ﾟ☆: *.☽ .* :☆ﾟ. ────── ･ ｡ﾟ☆: *.☽ .* :☆ﾟ. ────── ･ ｡ﾟ☆

I've developed a new study method. I am trying to study the content of the classes before the class itself. And I'm trying to practice calculus every day, even if it is just a little.

I hope I can achieve good results this semester. Anyway, today I took the day to study, review the content I learned this week and prepare for other classes.

[wojenka]

i need more mutuals who are into coding and engineering!! more info under the cut!!

I planned to become an electrical engineer like my stepdad but then I decided to change my path to programming. I'm currently studying at technikum (<- wikipedia link so I don't have to explain the whole polish learning system), programmer major.

this year I have exams from web development (10th Jan - theory, 16th Jan - practical exams) and next year I have exams from App development (both mobile and desktop).

I know C family languages, Java, Python and those ones I am currently using. I also know a bit of Kotlin and I think I will continue learning it.

For web dev I know HTML and CSS ofc but also PHP and JS.

Planning on learning more languages I can use for App and operating system development as well as just to know them cause I want to after this year's exams!

my learning list:

Lua (I heard it's easy but I can't really get myself to read anything about this atm idk why)

Ruby

Assembly

Rust

As for electrical engineering I don't know much tbh but I would like to learn! I just used CAD programs for technical drawings (dad taught me some basic things when I was still thinking about going his path) helped my dad fix things on his Solar farm, houses of our neighbors and I made a few very simple circuits for fun a few years ago. Now I'm mostly focused on programming but since I learned most of the things I need for exams I have more time to do whatever I want now!

I'd like to get to know more people so I can share and mostly learn new things since even though I'm coding for years I consider myself a beginner and I am a total beginner when it comes to electrical engineering.

I'm willing to be friends or at least mutuals with anyone who codes or makes websites or is in STEM! no matter what your specialty/interest is exactly and no matter if you are a total beginner or a professional ^__^

I'd also like to have some mutuals who are into old web development and retro computing!!!!!!!!

edit: I forgot but I'm also interested in physics and quantum physics

[spacejax]

Resources that have helped me in my classes!

(will add to this list as I find/remember more)

Classes I've used these in so far:

Honors Mechanics

Honors Thermodynamics & Optics

Relativity & Quantum Mechanics

Theoretical Mechanics

Calculus I, II, III

Differential Equations

Mathematical Techniques in Physics

Introduction to Astronomy

Fundamentals of Astronomy

Astronomy & Astrophysics

- - - - Youtube Channels - - - -

Physics

Michel van Biezen - oh my god I love him. I think he uses Sears and Zemansky's University Physics for example problems. His channel has 10k videos (!!!) and is very well-organized. He also lectures on math (from 5th grade to linear algebra), chem & organic chemistry, and astronomy.

Calculus

The Organic Chemistry Tutor - I mostly watch his videos on Calculus I-III and Differential Equations, but he also covers physics and chemistry.

Nancypi - Precalculus, Calculus I, and some of Calculus II. I barely showed up to calc lectures my first semester so she was a great help. also i have a crush on her

Michel van Biezen - I usually don't watch his math videos because his notation and techniques are different from what my prof makes us use

Astronomy

Urknall, Weltall, und das Leben - my literal dream channel. perfect levels of dryness, and videos are usually at least 45 minutes long. It's entirely in German though lmao

Michel van Biezen - covers important topics in introductory astronomy, and also does example problems (although I think they're all algebra-based)

- - - - Textbooks - - - -

Introduction to Cosmology - Barbara Ryden

Foundations of Astrophysics - Ryden & Peterson

University Physics - Sears and Zemansky

Calculus - James Stewart

Modern Physics - Kenneth Krane

Classical Mechanics - John Taylor

- - - - Workbooks - - - -

Essential Modern Physics - Chris McMullen, Ph.d. ----- LIFE CHANGING. BUY THIS FOR INTRO TO QUANTUM.

[astro-studying]

- Sunday, Sept 24, 2023 -

busy, busy, busy.

This weekend has been chock full of catching up on work I got behind on (shout out ADHD, you suck ❤️)

My first physics exam is coming up, and shortly after is my first calc II exam. It's seriously time to get on top of my time management so I can perform my best!!

[dailypokemoncrochet]

Hello. I've been following your blog for a short while now, and I really love all your work. And dedication. Your crocheted Pokémon look all very nice.

Now, I know you said not to ask you for patterns, but I do enjoy crocheting myself a lot, and while I will not be asking you for a pattern, I thought I could try asking you for advice on creating my own patterns. I'd really appreciate it if you could provide some tips and tricks as you inspired me to wanting to create my own patterns as well.

Again, I highly love your work here, even if you can't help me! I hope you have a great day!

Hi! Thanks! :D

I've posted some stuff in the past under the tag #crochet tips.

But off the top of my head some more stuff that I don't know if I've said before... Really understand how crocheting in the round works. This still comes down to personal preference, but generally you don't chain and join between rounds because it makes a visible line running down the piece. Also note that continuous rows are not laid on top of each other evenly parallel like lego rows; they spiral like if you peeled a potato really nicely in one go, which affects stuff like where your starting stitch will be and how everything will look kind of slanted. Look at the piece as a whole after every row or few so you can make sure stuff still looks reasonably straight and not skewed, or if you need to adjust something.

Math is important. A lot of stable increases throughout rounds will be in multiples of 6 or 8. A good chunk of mine start off 6 12 18 (regular size ball shape). I like to start with 6 because it makes for some nice number sequences like 6 12 16 20 (more ovoid) or 6 9 12 15 (kind of pinhead).

Keeping track of how many sc are in each round is especially helpful for me determining the size of the following rounds. For example, most of my crochets have a max stitch count of 30 in a row because I want the whole thing to end up around 5" tall (palm of my hand sized) and over time that's just what I've learned is the limit for the way I crochet (gauge, yarn size, hook size, etc). If the biggest width is going to be midway around the body, and I'm only halfway through making a head, and the row stitch count is already 30, then I know the piece is going to end up way bigger than expected because I should've been building up to 30 more slowly. Like, in general if I look at stitch counts for rows I can guess the shape if the increases were happening evenly throughout. For a regular ball, the count is going to be something like steady increases for a few rows, smaller increases to the max width, max width rows for length, then reverse. 6 12 18 24 26 28 30 30 28 26 24 18 12 6.

Hope that helps! Don't forget to check the #crochet tips tag for more tips!

[hypercubecats]

Page 4: Kinematic Formulas Part 2, Calculus Edition! Krita brush pack by @abluskittle

◁ ¦﹉ PREVIOUS PAGE ﹉ ¦ ¦ ﹉ NEXT PAGE ﹉¦ ▷

[that-bluesybitch]

[ladysatoru]

It's hilarious how naruto has chemistry with almost every character in that show except hinata