Merch link here: store.dftba.com/products/coffee-and-the-problem-notebook-sticker-sheet?variant=41112780243019 Comes as a sticker only or sticker + notebook.
Hi Angela , any possibility you could cover the double split experiment with particular reference to the observer effect because I don’t get it and there does not seem to be any reasonable explanation so it is brushed over , I think you are clever and brave enough to tackle it. Thanks in anticipation Ian
Regarding the first problem, we do not need to find theta if the velocity x (east) and y (north) components are taken as the description of the direction after the collision. And we can do it without using a calculator as follows: The momentum toward north is 1500*25 . The momentum toward east is 2500*20 which is 2000*25. Now, the ratio of the momentums is 1500/2000 = 3/4 which signifies the 3-4-5 right triangle with a scale factor. This means the total momentum is 5*500*25 = 62500 (remember the components are 3*500*25 and 4*500*25). The speed after the collusion is then 62500/(1500 + 2500) =15.625 = 5 * 3.125. Therefore, the north velocity component is 4 * 3.125 =12.5 and the east component is 3 * 3.125 = 9.375. Check: 12.5^2 + 9.375^2 = 244.141 = 15.625. Side note: I remember from the nationwide high school competitions in my country Turkey, we knew (approximately) that the right triangle with 37-53-90 degrees is equivalent the 3-4-5 triangle with some scale factor, i.e, similar. Per learning physicsI was not watching your videos until recently, so I missed the book recommendation. But I have my own schedule. I am studying the following books in parallel as much as I can (other than my full-time job of being a computer scientist): Quantum field theory volume 1 by Robert Klauber, general relativity by Hubson et. al., and the latest edition of Schultz's a first course in general relativity among others. Also I have Young and Friedmann. Though I read Kleppner's introduction to mechanics and David Morin's introduction to classical mechanics.
Regarding the first problem, we do not need to find theta if the velocity x (east) and y (north) components are taken as the description of the direction after the collision. And we can do it without using a calculator as follows: The momentum toward north is 1500*25 . The momentum toward east is 2500*20 which is 2000*25. Now, the ratio of the momentums is 1500/2000 = 3/4 which signifies the 3-4-5 right triangle with a scale factor. This means the total momentum is 5*500*25 = 62500 (remember the components are 3*500*25 and 4*500*25). The speed after the collusion is then 62500/(1500 + 2500) =15.625 = 5 * 3.125. Therefore, the north velocity component is 4 * 3.125 =12.5 and the east component is 3 * 3.125 = 9.375. Check: 12.5^2 + 9.375^2 = 244.141 = 15.625. Side note: I remember from the nationwide high school competitions in my country Turkey, we knew (approximately) that the right triangle with 37-53-90 degrees is equivalent the 3-4-5 triangle with some scale factor, i.e, similar. Per learning physics: I was not watching your videos until recently, so I missed the book recommendation. But I have my own schedule. I am studying the following books in parallel as much as I can (other than my full-time job of being a computer scientist): Quantum field theory volume 1 by Robert Klauber, general relativity by Hobson et. al., and the latest edition of Schultz's a first course in general relativity among others. Also I have Young and Freedman. Though I read Kleppner' s introduction to mechanics and David Morin's introduction to classical mechanics.
Regarding the first problem, we do not need to find theta if the velocity x (east) and y (north) components are taken as the description of the direction after the collision. And we can do it without using a calculator as follows: The momentum toward north is 1500*25 . The momentum toward east is 2500*20 which is 2000*25. Now, the ratio of the momentums is 1500/2000 = 3/4 which signifies the 3-4-5 right triangle with a scale factor. This means the total momentum is 5*500*25 = 62500 (remember the components are 3*500*25 and 4*500*25). The speed after the collusion is then 62500/(1500 + 2500) =15.625 = 5 * 3.125. Therefore, the north velocity component is 4 * 3.125 =12.5 and the east component is 3 * 3.125 = 9.375. Check: 12.5^2 + 9.375^2 = 244.141 = 15.625. Side note: I remember from the nationwide high school competitions in my country Turkey, we knew (approximately) that the right triangle with 37-53-90 degrees is equivalent the 3-4-5 triangle with some scale factor, i.e, similar. Per learning physics: I was not watching your videos until recently, so I missed the book recommendation. But I have my own schedule. I am studying the following books in parallel as much as I can (other than my full-time job of being a computer scientist): Quantum field theory volume 1 by Robert Klauber, general relativity by Hobson et. al., and the latest edition of Schultz's a first course in general relativity among others. Also I have Young and Freedman. Though I read Kleppner' s introduction to mechanics and David Morin's introduction to classical mechanics.
Your comment in the "How to Teach Yourself Physics" video about an in-person class being the best way to, y'know, actually learn physics, convinced me to take Physics 1 as an elective earlier this year. I've been following your channel for a while before that, and usually the math parts fly right over my head. But today, I finally completely understood a question for the first time! (The two cars crashing one) Feeling pretty darn proud of myself!!
I strongly, STRONGLY urge people to solve problems symbolically before plugging in the numbers. Only plug in the numbers as the very last step. By not plugging in the numbers right away, you can get a general solution for any similar problem. If you plug in right away, and then get a similar problem with only the numbers different, then you have to start all over again. Plugging in last also lets you look at your answer and see the physics of the problem. You can see how the answer depends on m_1 or v_2. Once, when I was a TA, a gave the students a quiz with no numbers in it, but I still got some numerical answers. You should never do that.
I was doing another problem in Serway and Jewett where they gave numerical values. I instinctively did as you suggest here. Lo and behold, the very next problem asked us to solve the general case. I wasn't entirely surprised that they even used exactly the same notation for the variables that I had chosen. So I just wrote, "See above." 😀
my gen physics prof had us do this, students would regularly ask him to plug numbers in when we were doing example problems but he would just tell them no, it's easier without the numbers. i never understood why there was such a vocal crowd of people taking that class that got genuinely angry that he wouldn't do the problems with numbers. it just takes longer and introduces much more room for error (especially for a prof who is trying to speed through as many examples as possible to give us good frameworks for our notes). yeah it feels weird at first if you've never done problems that way before but it's necessary if you want to actually learn anything.
I always did this when I was studying physics. It allows you to more easily follow the logic of what you're doing. I was a TA for the upper division math methods class. When asked to prove something, students would keep plugging some numbers that they pulled out of their butt, show that it worked for those numbers, and call it proved. Yeesh.
You are so right about having the learner do the problem (whether physics or whatever). At work, I try to teach folks how to use a tool or thing, and they go "ooh, you use that tool nice, man" but what I really want them to do is explore with the tool, try stuff, and then show me something cool I never learned. Some folks do that, other folks don't. You've inspired me to really emphasize the "play along" aspect, not just observe. Thanks!
Over the last few years, I have been learning to not hate math. I had to deal with some really awful math teachers in college and it soured me on the discipline. This video has helped me in my progress. Thank you.
28:52 - eh, not great. But my day is brightened a bit by thinking about how we'll always have people out there wanting to teach, no matter what happens with the governmental agencies tasked with such things. If I was in a space where I was wanting to learn more physics, and/or had kids that were, or whatever, I love the idea that folks like you will be around to share your enthusiasm, knowledge, etc. Thank you for being you, and for doing what you do.
I recently retired, and one of my main goals has been to relearn the physics I took in college and, from there, try to build a proper understanding of quantum mechanics. But I also moved to my wife's hometown, İstanbul, so I am prioritizing learning Turkish over other projects. But then I did watch that video, though only a few months ago, and was very inspired. So I looked for and found the Turkish edition of Serway and Jewett. Now my education in physics supplements my Turkish courses. Of course, this will be a slower journey, but my only deadline is the ultimate one: either my death or the heat death of the universe, whichever comes first.
Happened to me. We had a uni exam (Microcomputer Architecture 1989) where you were allowed to bring your textbooks. In my overconfident youth, I didn't attend lectures and barely looked at the book until the exam. When I sat down, I realized I hadn't brought the books with me. Still a B-. Happy days.
@@AbuMohandes-p2c I guess microcomputers must not have been that complicated back in 1989. Was there much to talk about other than Von Neumann and Harvard architectures?
@@portobellomushroom5764 Don't knock it, the rich kids had mathematical coprocessors back then :-) And separate interrupt controller chips, timers, etc, etc. Today's chipsets in other words.
@@portobellomushroom5764 The Wintel imperium was only starting, so VAX, DEC, SEL, Motorola were all still on the menu. Did you know SEL had a 32-bit CPU in 1975, about 10 years before Intel got around to it? It was the size of a minivan and cost a measly $150k.
Even for someone not in physics or currently trying to learn it, these are good for helping me unlearn my physics trauma from fully-online AP physics a few years ago
I only listened to the "how to teach yourself physics" about a couple weeks ago. I am doing the challenge! I hopefully will be able to finish my time machine by the end of it. And come back and edit this comment to say I did it!
Never mind the time machine, a year is not so long, come back then ok? Like next Halloween 2025? I just got the book too and shared a problem with my old uni mates , they made a better fist of it than me without even reading the book ... I'm so challenged and up for it now lol!
I'll be honest, at the beginning when you invited viewers to try and solve the problem, my thought was "I'll make a coffee but I don't know about solving the problem." And I guess I just imagined it'd be like some of your other videos it sorta gets into some intimidating math (which is fine! Keep doing that). But then I saw the problem and I was like, ok, it's been a while since I did this in High School, but I'll give it a shot! Update: Got to problem 2. Uh oh.
The past week has been stressful as hell (being a queer woman in the USA right now is not fun), but it turns out solving a high school physics problem is better stress relief than I expected, thank you
I'm not queer, not a woman, not in the USA, and I find it stressful. So best wishes. Any advice would be patronizing, so I'm sending more best wishes instead.
Sending best wishes to both of you. There are many things about this life I can be unhappy about, but there are also some awesome things, like this new video, and cats :)
I am a discouraged math student that failed miserably at physics, so I never watched that Teach Yourself Physics video, but now I know the name of that textbook and I can give it another shot over winter break or something. Appreciate it :)
Don't give up! The perspective gained from even a basic highschool physics education opens up a hugely rewarding realm of understanding the universe around you. Always happy to hear about someone giving learning a 2nd chance, I sincerely hope the book gives you some eurekas.
18:22 @nathanschmidt1843 Yup, I also loves me some "it's fine", man (LOL!😂)! So, one sweet classic Dr. Collier "It's Fine!" slipped in here at 18:22. Whew, & yay! Now, Dr. Angela @acollierastro, about that "Quantum quantum quantum!"...😜
@nathanschmidt1843 Correction: Sorry, my bad. Actually, she gave us a bonus double-ItsFine, there. Also, watching further, another "It's Fine" at 19:35. So, I'm good (fine!) for today. Thanks, Dr. Angela! @acollierastro BTW, Dr C, I was watching another channel and, in a discussion about the styles and effectiveness of Science Communicators, was pleased to hear you cited, in a positive light and in good company.👍
I didn't read the Serway&Jett book but your channel is part of the reason that I grew to really love physics during the last two years of high school. I'm doing an undergrad in theoretical physics now
Focus pumping is a known issue on some cameras. It's easy to fix. You need to use manual focus. You can let the camera focus automatically and then switch to manual focus before you start recording. Alternatively, you can just focus manually. In both cases a second person would be helpful: one to sit in front of the camera and another to focus the camera on the eyes of the first person. If you need assistance or have questions about your camera, lighting or sound, please let me know, I'll be glad to help. People like your videos, please keep them coming. Best.
I've studied theater and teach drama and performing arts and I have less than basic understanding about physics. But for some reason I enjoy your videos and always watch/listen to them. Maybe I've even learnt something along the way 😄 maybe it's the passion that you have for your field that reaches over boundaries (and the shared passion for star trek) 😂
As someone who is studying mechanics at the moment this could not come at a better time. It was really great to have a validation that I'm taking the correct basic approach. I am absolutely convinced that the only way to get good at this stuff is to actually do the problems. This is exactly like when a musician practices scales. You need the repetition to build "muscle memory" in skills otherwise they won't be available to you when you need them for a real application.
Thanks Angela. I really enjoy your videos, whether they're book reviews, Coffee and the problem, or general physics topics. The rigor of your method really shines on the second problem. I studied undergrad Physics and spent my career in IT with 20 years of University lecturing. When teaching, we often have to deal with simplified cases, like your first problem. As you're speaking I'm using my hands to visualise the situation, going "conservation of momentum and vector arithmetic", and getting to the point of "so I need X where tan(X) = .75, and do some Pythagoras". But by using your method you are teaching the method that works for any problem. Good job. And I especially like your reality check at the end :-)
Having got an answer using methods that were pretty obvious and self evident for me, and despite getting a little worried when Angela used a very different route it was really fun and insightful to see another way to approach the problem! Was a relief that my method had got me the right numbers (although the angle took a few goes because it's been several years since I last converted radians to degrees)
That "how to teach yourself physics" video was how I found your channel, and although I watched it late and been going through the Serway/Jewett book too slowly (only at chapter 6...) to apply to the challenge you mentioned, it's been really helpful in my learning of Physics, so thanks Angela :) (Also like your other videos, they're casual in a way that's very easy to listen to)
So, I just picked up the Serway/Jewett 7th ed with Modern Physics last week and intend to work through it through 2025. I'll touch base after a year to remind you that you can make a difference 😊
I love your enthusiasm. Unbelievably you chose the problem from Jackson that I have circled in my decades old copy of Jackson (red cover). That must mean my book isn't out of date yet even if it is older than you.
Haven't really done physics in like 8 years, so I'm happy I was able to solve the first problem relatively easily. Had some doubts after reviewing my result, but I figured it's fine & I was right. For the second question, I got stuck for a few reasons: 1) Most of the variables weren't defined, 2) I have never seen Poisson's equation, 3) I have never done a Laplacian, 4) I have never dealt with Dirac delta functions, 5) I barely remember what "potential" is. ... Well, at least I tried. I got to draw a hydrogen atom & it was pretty close to yours.
I’m about halfway through the year, it has helped me a bit with my personal issues. Also remembering a lot of things i was supposed to master in engineering school.
You are responsible for my attempt at teaching myself physics which involved getting 2 chapters into a physics textbook realising I'm not as good at math as I thought and proceeding to read half a linear algebra textbook
also thank you angela for inadvertently convincing me to major in physics. im studying mechanics with serway and jewitt rn. i love the subject and hopefully with more practical problem solving it loves me back :p
Learning about the Dirac Delta function is such a wonderful memory. Infinite height. Zero width. Area of one. I was laughing with joy and how amazing that is. A horn of Gabriel moment.
I still have Physics Parts I & II combine 3rd edition by Halliday and Resnick from my first year of my EE degree in 1985. It's a 1978 edition. I recall finding it lacking - although there's surprising number of commercial cartoons in it, that us hip college engineering students in Milwaukee were hep to, like Peanuts. Groovy. I made notes in it, which are so fun to examine now. I re-drew a circuit diagram - a single loop RCL circuit. The dozen supplemental topics in the back remind me of Angela Collier videos. Since, we didn't have the Internet, the back appendixes of textbooks had mountains of supplemental information, log tables, the periodic tables, the weights of the planets, conversion factors,hundreds of mathematical formulas, and a list of physics Nobel prize winners ending in 1977!
When Donald Knuth was an undergraduate with a scholarship to study physics at the Case Institute of Technology (now CWRU), it was rumored that he worked all the problems in the math textbooks, not just the assigned problems. He ended up switching his major to math and at graduation, in addition to receiving his B.S. in Mathematics, the faculty awarded him a bonus Masters degree. So, it sometimes pays dividends to work those extra problems!
Glad my highschool physics was still enough to solve the first problem! I don't think I have done a physics problem in over a decade. (I calculated the x and y direction components of the final velocity separately but put them together to get the same answer.)
Recently I had one of my oddest experiences with physics. In a span of a few years I had went from studying graduate level electromagnetics and statistical mechanics, to all of a sudden teaching a first year physics course in college (in Canada, college is more akin to "community college", but it's a polytechnic college, so they can upgrade to a degree with a 4th year if they want to). That introductory physics course, which I will be teaching again soon, honestly lit a fire in me for solving problems. Kinematics, and forces, and newton's laws, basic thermodynamics, allowed me to step back and think about problem solving in such a broad way. Things like non-conservative forces had such a concrete meaning and are so elegant in simple Newtonian physics. After teaching this course I was motivated to go back and look at Griffith's QM, for instance, and just start working on some of the problems at the end of the chapters. Some of them have really deep answers that get you to think about the physics quite a bit. Moreso than the preceding chapters had by presenting equations and writing paragraphs about them. Solving problems is my favorite way to engage with physics. Not attending a lecture, not reading a textbook, but actually doing the problems. Thanks for sharing your walkthrough of these problems!
2:12 - 4,000kg 'mass' travelling at 15.625 m/s at 36.870deg CW from North. 11:06 - Aside from sig figs and that I adjusted to use North as datum (which is arguably the wrong thing to do I know) we agree, cool, glad to see my brain hasn't completely vegetated.
pffft, who needs the DOE when you have dr collier? physics? science. physics computations? math. science history? history. science communication? communication arts!
Yeah, but the real question is: without the DOE, do you get Dr. Colliers? Idk if her workplace is funded by government grants, but I know a lot of other physicists' workplaces are.
@@GSBarlev Indeed. There were no physicists before 1979 when the DOE was created. The only people who could read before that were clergy, and only in Latin.
You confused potential and field at 16:55. Field is force on a test charge. Potential is work done to move a charge to that location. (Per unit charge in both cases.) Didn't affect your solution afterwards. I hadn't thought about the Laplacian in a long time, so I appreciated that.
I haven't really done any physics since graduating high school 8 years ago, as my focus since has been languages (notwithstanding the occasional autism-fueled endeavour to produce a calculator for the tension of guitar strings at a given pitch and sounding length - which worked, because it broadly relates to school-level physics - or to figure out how many stacks of gold you'd need to put in a Minecraft chest to create a black hole - which may or may not have worked since it relates to physics way above my pay grade and I have no way of double checking), so it was really encouraging to see the first problem and go "Oh! I can do this!" and get the answer right!
The Physics module of the Open University in the UK gave this advice: 1.Draw a diagram first, if possible 2.Always complete manipulation of the formulae before entering any values 3.State the relevant formulae using standard abbreviations 4.Identify vectors. Use curly underline to write vectors (or print in bold) 5.State the direction by giving the unit vectors (unless explicitly instructed to use another coordinate system) 6.For numerical quantities: 1.Convert all values to SI equivalent 2.Express all figures in scientific notation 3.State the appropriate level of precision (significant figures) 4.Give the units of SI measurement 7.Check the result
I will say that reading through his treatment of the gyroscopic top finally gave me a physical intuition of why you needed a vector cross product to explain the top's response to being pushed perpendicular to its axis of rotation.
Use both! Modem science stands on the shoulders of those who came before. Having what we knew then with what we know now, you can see how much more has been learned!
Really took me back to my first physics course at UVa in 1968. Thanks for that! I spent the summer of 1963 reading a book my dad used in college: Essentials of Modern Physics, 1922. The author ironically was Charles E. DULL. If you want to know why a company of soldiers was advised to break step when crossing a wooden bridge, this will book provides the answer.
I noticed two things about problem 1: first I would take the angle from N (the y axis) not E, since that will give you the compass direction. That doesn't really matter at all of course. But I think the second thing is not quite so trivial, and it has to do with jumping into the calculation too quickly. To solve the problem I drew a picture of the momentum vectors, and it didn't take me long to notice that we're looking at a 3-4-5 triangle. So (no spoilers) you can get a result for the magnitude of the velocity vector without pulling in any rounding errors that you might get from multiplying by the arc tan. If that makes sense. I think drawing pictures is great, and I also think students can benefit from not taking their calculators out too soon.
1: Yes, but convention. Cartesian coords, sin, cos as circular functions, cos 0 = 1, sin 0 = 0, theta is counterclockwise from our x-axis. Maybe the rotation is easy for you in your head, but it's mental gymnastics for some pupils. 2: Yes, but we're not multiplying anything by theta. However we choose to round theta, that's our *answer* for the direction. It's not used at all for the magnitude. Since you're at it, may as well mention only one step left. Convert the resultant momentum to velocity, ie, divide by combined mass. In a similar spirit, noticing 3-4-5 only saves two one-liners, theta = arctan p2/p1, no sweat; and p3 = sqrt(p1^2 + p2^2), big deal. Then v3=p3/m3, m3=m1+m2. There are two things you noticed that didn't have to be, but the problem builds them in. One, the vectors are at right angles, so we're looking at a right triangle. Because of that, the resultant pops out by Pythagoras. Two, as you note, we can skip even that step as the momenta are cooked to make a very familiar shape. Not every pupil will jump straight to momentum vectors. The problem is more confusing if they draw a picture of velocity vectors. Arguably, punishing them for that mistake is a key lesson of this exercise.
Separately, I'll use this opportunity to mention a different teaching point. I do like it when Dr. Collier throws in an extra little tip, like solving vectors one component at a time, that's a good habit. At the same time, I learned from Don Knuth, it's also in his Art of Computer Programming book series, if you want pupils not to take a particular shortcut, you pick a problem where the shortcut punishes them. That is, they're forced to use the technique you're trying to teach them. In this case, the problem is completely solved by momentum vectors alone. I have a little story about a slight variation that punishes you for making that same mistake. Almost half a century ago, I took my first midterm. I scored top of class. That was by pure luck. The class was 4 units, 2 hours each Tue/Thu AM. The midterm used up one of those 2hr sessions. I'd stayed up too late cramming, overslept. Showed up with only 20min left. The very first problem, of 6, was kind of a trick. We could solve it by brute force, literally, but working the force vectors got complicated. I rushed in, saw my math start to get tangled, no time for that. I skipped it, moved along. Got full credit on a couple problems, partial on a couple more, time called. Everyone else wasted almost the full 2hrs trying to grind it out. I got 29/60, next highest score was 14. This problem was cribbed from an MIT PhD qual exam. We were frosh. Here it is. Preliminaries: classical mechanics, no friction, collisions perfectly elastic, ignore Dr. Collier's question of Do we need more physics? The table's gigantic, heavy as heck, the whole experiment's in a huge vacuum chamber, the gravitational field is perfectly uniform, little g is a constant, every surface is flat and polished. We are not gonna get any points taken off for neglecting all that stuff. So on the table is a triangular ramp, like a tire block, it slides on the table. At the top of the ramp is a brick, we let it go, it slides down the ramp. Eventually it hits the table, the brick & the ramp glide away from each other, & the system is in a steady state. If you're thinking, "Collision? What collision?" that's OK. It won't cost you points. Write the equations of motion for the brick & the ramp. Your answer will be in two pieces. The acceleration curves for the brick sliding down the ramp & the ramp sliding across the table. And their final velocities. I got back to the dorm, went to lunch, & thought back to that problem. I solved it in only fifteen minutes, thanks to no time pressure. I knew my first approach was good enough, but a serious pain in the neck in practice. I realized what Dr. Collier talked about for the similar but simpler problem of a car crash, energy is clearly not conserved. But we were given all prerequisites to use energy conservation. There had to be a reason for that. Write down the kinetic energies, relate the two things we know to each other. Ie, solve one, plug into the other. Gee, the answer tumbles out like a nut out of a nutcracker. Such a sweet little problem. And a nasty lesson for many of us. :)
Just bought the physics for scientists and engineers 2 days ago. I decided it's finally time. I'm a material scientist and I know enough physics that whenever I encountered someone talking about physics I knew just enough that I could fool myself into thinking that "yeah, this is easy, I understand/I could solve this too". But deep down I always knew that was bullshit, so I finally decided to do something about it. I'm excited for it to get here. I plan on spending six months to a year on it and then I'll teach myself quantum physics and astrophysics! That's the plan anyway.
I was into the idea of getting back into learning physics in what passes for my spare time. I did physics and mathematics in high school 30 years ago and got "A"s. Since then I did CompSci at Uni, and then coding professionally... web stuff, but with some matrices, quaternions, trig, and so on. So, I thought I'd brush up on some mathematics on Khan Academy in preparation for doing some undergraduate level physics. Um... NO. I keep having to restart further and further back, and got all the way to simple factorization before I felt properly comfortable. Trig identities I swear I never learned in the first place, and stuff with Limits that I have no memory of. Frankly, I'm not _that_ far ahead of my 12 year old kid, and she'll probably catch up before too long. :/
I finally bought the Jewett-Serway book in September and it'll take 2-3 years for me to process it. When I finish it I won't be as young as I used to be. In one hand, I always believed spontaneous activity is superior to structuring time artificially, the older I get the dumber the latter seems and physics is not spontaneous enough to me to read faster. In the other hand, I never really bought into the idea that stockpiling books is shameful. I'm also following a 70 yo mom on TH-cam who has a couple degrees in anthropology and literature and her desk is always covered with large piles of interesting, rare books. If that evokes an emotion from me, I rather envy her optimism.
Watching this, I realised just how much I know compared to the average person, and how much I don't know compared to someone with practice in physics. The gulf on either side is large.
Growing up, we had two sets of encyclopedias at home, a newer set and an older set. The newer set was Collier's. The older set, maybe World Book or Brittanica, was published before WWII, and it's entry for WWI was called The Great War.
I "did" the challenge with a different book (Resnick Halliday I believe), that a family friend (who happens to have a PhD in physics) lent me! Still definitely by your inspiration :)
I'd just like to say I want to support Dr. Collier, but I'm also sure she's going to be as OK as any of us. We need above all to stick together. As Americans those of us who are that. As humans for all of us. We're a good group of folks gathering around this nice fire by a good person. It's undiminished by our political union being less than perfect. Physics rules!
Last steps of solving a problem are asking yourself if the answer you reached is reasonable, is it good enough, and do you need more physics. Makes perfect sense, you always need to do some basic sanity checks on a calculated solution to make sure you didn't miss something significant. Second/last sample problem, reaching the end of the calculation, getting a result... Is the answer reasonable? No. is it good enough? No. Do we need more physics? Yes. Done, problem solved. Moving On.😀🤣 I'm not sure if this was supposed to be very blunt humor, or subtle humor, but it did achieve a *literal* physical LOL, which is rare. ( Reminds me of the less funny versions, in my high-school physics class, when we were learning kinematics. The teacher gave questions where the velocity of trains/cars/superman were occasionally much higher than c, and didn't realize why I was complaining since I obviously could solve the equations and reach the "correct" solution... )
We're in such a weird state when "how to solve a physics problem" is how we're coping as a society. I mean, not for me because I went to college for this but I'm not used to others joining in
How'm I doing? Not great, TBH. "Recent events" do not agree with me. And I have to admit that watching this video gave me flashbacks to my physics classes from 40 (argh! yes!) years ago. My career didn't use much physics, and I've lost it all. I could follow the first problem, mostly, but the second washed over me in a way that I am not proud of. But I still enjoyed the video, and the merch looks cool. Thanks!
This is generally the right advice and the right process, but maybe don't use an example problem with a gimmie shortcut you're supposed to use to speed up your rote homework/test answering. It's a 3:4:5 right triangle, and if you memorized it for the SAT/GRE/GMAT what have you, you'd know the Theta is 53.13 or 0.91 Radians. Start with simplifying by dividing speeds by 5, masses by 300, and you get 5*4 up and 3*5 right, IE 20 by 15, or 3 over 4 up, so distance is 5. So 53.13 for the combined 4 tonnes mass. Assuming point-mass collisions combining as stated. It's similar but different for the velocity: the Velocity-Mass is the same after collision in each north and east directions but the mass changes by combination and affects the imparted velocity; Lets rescale masses down by 500, keep the velocities scaled down by 5, so one orthogonal is (3kg*5m/s)/8kg=1.875m/s and the other orthogonal is (5kg*4m/s)/8kg=2.5m/s. They're like lengths to the sides of the hypotenuse, so sum of squares wise: 2.5*2.5=6.25 and 1.875*1.875=3.515625, added are 9.76525 square rooted for the hypotenuse being ~3.125, scaled back up by 5 is 15.625m/s. It's mildly more exact than going the arctan route. The next problem doesn't have the same kind of gimmie, so, pretty interesting for both. Thanks!
Yeah, well I guess that's about right. Only, I lost you about the arctan thing being subject to inaccuracy. Theta isn't even involved in the magnitude calculation. You already made the right call since we're using conservation of momentum, the relevant vectors are the momenta, ie, P3 = P1 + P2. Magnitudes in lower case. You noted the ratio p2/p1 = 4/3, it's a right angle, so resultant = hypotenuse = 5 or p3 = 5/3 * p1 = 5/3 * 37500 = 62500. And p3 = m3 v3 so v3=p3/m3=62500/4000. I don't know if your simplifications meant you could carry it all in your head, but to me it just seems like extra steps for no reason. As for 53.13, the exact answer is theta = arctan p2/p1 = arctan 4/3 = 53.1301024, rounding error is wherever you choose. And theta is the answer to the direction, its usefulness is otherwise over.
It is funny because it's true. One of the most useful things I learned at school was in mechanics. Say the problem, d draw the problem, solve the simplest version of the drawing. Check the result isn't daft. Check if the solution is good enough. If not, draw a better diagram and go again.
A triangle symbol with its base at the bottom is called the Laplacian. The triangle symbol with its base at the top is called the nabla or del operator. The square of the nabla equals the Laplacian.
I remember, my electrodynamics professor based his lectures on the Jackson and that problem was one of the problems he gave us to solve in his course :D
I literally just started the Conservation of Momentum chapter with collisions in my physics class this week. Am I doing the homework? No. Am I doing physics with Angela? Yes 😅
That first physics problem about the car wreck is impossible to answer because we dont' have nearly enough information. 1: What's the road surface like? (Asphalt? Gravel? Dirt Road?) 2: What is the length of each vehicle? 3: Is the ground completely flat, or is it on any slope at all? 4: Is the weight equally distributed in each vehicle? (For instance it could be front heavy b/c engine) 5: Have the wheels been lifted on either vehicle to raise the center of gravity? 6: Is the collision dead center, or glancing blow is it hitting the front or rear of the vehicle? 7: Did either driver hit the brakes or accelerator at all before, during, or after the collision? 8: What is the conditions of the tires on each vehicle, and how much traction do they have? 9: Are there any other circumstances such as chains on the tires? 10: Did either driver turn the wheel at all before or after the collision? 11: Does the weight of the car include the weight of the driver, and passengers, and luggage? 12: Did this collision happen in a vacuum? If not what direction is the wind blowing and what speed? 13: Was either vehicle lifted into the air from the collision at all? 14: What's the horsepower of each vehicle? 15:What is the exact angle of the collision?
@@suttoncoldfield9318 The problem is an over simplification. I didn't even mention the energy lost when the metal is deformed, and the noise made and all that.
Ah yes, camera angled with a great gap between top of the head and top of the frame. A classic cinematographic indicator of "the vibes being bad" as it were.
Very excited about merch, but once I slap one of these stickers on my laptop there's a risk that it might make people think that I am Smart and Know Things About Science, and that's not going to end well for anyone involved.
I was not watching your videos until recently, so I missed the book recommendation. But I have my own schedule. I am studying the following books in parallel as much as I can (other than my fulltime job of being a computer scientist): Quantum field theory volume 1 by Robert Klauber, general relativity by Hobsun et. al., and the latest edition of Schutz's a first course in general relativity among others.
I did pause the video and answer it myself, for fun. Then I was dismayed when I saw how you were solving it, I thought I must have done it completely wrong because your way seemed more complex! (I also got worried when I did a sense-check because I forgot Kinetic energy isn't conserved in inelastic collisions 😂) But we got the same answer (phew! I haven't forgotten everything!), I just did it a bit more visually by constructing a right-angle triangle with the legs equalling the two initial momenta and got the vector sum that way. Oh and I dock you a point (no criticism here, just embodying the professor vibe) for the first problem for the way you gave the answer for the angle. It's somewhat ambiguous (without referring to your diagram) and I'd be expecting an answer in the same basis as the problem, which used compass directions. For example as a bearing - 36.9 degrees.
She isn't a pupil. You don't dock the teacher. The techniques she uses are more than as needed on this problem, sure. But they're helpful as tips. If you as a pupil didn't have trouble equating her angle to your bearing, there's no serious conflict.
the modern physics class i'm taking rn uses the serway/moses/moyer modern physics textbook! i don't think it's the same one you recommended but i remembered thinking it sounded so familiar when i heard it and i ust realized it was from your video lol
Merch link here: store.dftba.com/products/coffee-and-the-problem-notebook-sticker-sheet?variant=41112780243019
Comes as a sticker only or sticker + notebook.
Hi Angela , any possibility you could cover the double split experiment with particular reference to the observer effect because I don’t get it and there does not seem to be any reasonable explanation so it is brushed over , I think you are clever and brave enough to tackle it.
Thanks in anticipation
Ian
The camera is awesome by the way! Happy to see your channel slowly refining over time.
Regarding the first problem, we do not need to find theta if the velocity x (east) and y (north) components are taken as the description of the direction after the collision. And we can do it without using a calculator as follows: The momentum toward north is 1500*25 . The momentum toward east is 2500*20 which is 2000*25. Now, the ratio of the momentums is 1500/2000 = 3/4 which signifies the 3-4-5 right triangle with a scale factor. This means the total momentum is 5*500*25 = 62500 (remember the components are 3*500*25 and 4*500*25). The speed after the collusion is then 62500/(1500 + 2500) =15.625 = 5 * 3.125. Therefore, the north velocity component is 4 * 3.125 =12.5 and the east component is 3 * 3.125 = 9.375. Check: 12.5^2 + 9.375^2 = 244.141 = 15.625. Side note: I remember from the nationwide high school competitions in my country Turkey, we knew (approximately) that the right triangle with 37-53-90 degrees is equivalent the 3-4-5 triangle with some scale factor, i.e, similar.
Per learning physicsI was not watching your videos until recently, so I missed the book recommendation. But I have my own schedule. I am studying the following books in parallel as much as I can (other than my full-time job of being a computer scientist): Quantum field theory volume 1 by Robert Klauber, general relativity by Hubson et. al., and the latest edition of Schultz's a first course in general relativity among others. Also I have Young and Friedmann. Though I read Kleppner's introduction to mechanics and David Morin's introduction to classical mechanics.
Regarding the first problem, we do not need to find theta if the velocity x (east) and y (north) components are taken as the description of the direction after the collision. And we can do it without using a calculator as follows: The momentum toward north is 1500*25 . The momentum toward east is 2500*20 which is 2000*25. Now, the ratio of the momentums is 1500/2000 = 3/4 which signifies the 3-4-5 right triangle with a scale factor. This means the total momentum is 5*500*25 = 62500 (remember the components are 3*500*25 and 4*500*25). The speed after the collusion is then 62500/(1500 + 2500) =15.625 = 5 * 3.125. Therefore, the north velocity component is 4 * 3.125 =12.5 and the east component is 3 * 3.125 = 9.375. Check: 12.5^2 + 9.375^2 = 244.141 = 15.625. Side note: I remember from the nationwide high school competitions in my country Turkey, we knew (approximately) that the right triangle with 37-53-90 degrees is equivalent the 3-4-5 triangle with some scale factor, i.e, similar.
Per learning physics: I was not watching your videos until recently, so I missed the book recommendation. But I have my own schedule. I am studying the following books in parallel as much as I can (other than my full-time job of being a computer scientist): Quantum field theory volume 1 by Robert Klauber, general relativity by Hobson et. al., and the latest edition of Schultz's a first course in general relativity among others. Also I have Young and Freedman. Though I read Kleppner' s introduction to mechanics and David Morin's introduction to classical mechanics.
Regarding the first problem, we do not need to find theta if the velocity x (east) and y (north) components are taken as the description of the direction after the collision. And we can do it without using a calculator as follows: The momentum toward north is 1500*25 . The momentum toward east is 2500*20 which is 2000*25. Now, the ratio of the momentums is 1500/2000 = 3/4 which signifies the 3-4-5 right triangle with a scale factor. This means the total momentum is 5*500*25 = 62500 (remember the components are 3*500*25 and 4*500*25). The speed after the collusion is then 62500/(1500 + 2500) =15.625 = 5 * 3.125. Therefore, the north velocity component is 4 * 3.125 =12.5 and the east component is 3 * 3.125 = 9.375. Check: 12.5^2 + 9.375^2 = 244.141 = 15.625. Side note: I remember from the nationwide high school competitions in my country Turkey, we knew (approximately) that the right triangle with 37-53-90 degrees is equivalent the 3-4-5 triangle with some scale factor, i.e, similar.
Per learning physics: I was not watching your videos until recently, so I missed the book recommendation. But I have my own schedule. I am studying the following books in parallel as much as I can (other than my full-time job of being a computer scientist): Quantum field theory volume 1 by Robert Klauber, general relativity by Hobson et. al., and the latest edition of Schultz's a first course in general relativity among others. Also I have Young and Freedman. Though I read Kleppner' s introduction to mechanics and David Morin's introduction to classical mechanics.
Your comment in the "How to Teach Yourself Physics" video about an in-person class being the best way to, y'know, actually learn physics, convinced me to take Physics 1 as an elective earlier this year. I've been following your channel for a while before that, and usually the math parts fly right over my head.
But today, I finally completely understood a question for the first time! (The two cars crashing one)
Feeling pretty darn proud of myself!!
I'm proud of you too!
Keep it up 👍
Congrats!
Aww yall's comments are so sweet. Can't wait to learn more and wish you guys luck on your journeys as well!
This is awesome. Good luck!
doing my actual homework regularly and on time : 🚫
solving problems with angela for fun : ✅
Go do your homework Phil...
Go do your homework Phil...
Phil... Do your homework, Phil...
Phil, I know how good it feels to do questions with Angela and blackpenredpen, but go do your homework, Phil...
Phil, the homework is calling.....
I strongly, STRONGLY urge people to solve problems symbolically before plugging in the numbers. Only plug in the numbers as the very last step. By not plugging in the numbers right away, you can get a general solution for any similar problem. If you plug in right away, and then get a similar problem with only the numbers different, then you have to start all over again. Plugging in last also lets you look at your answer and see the physics of the problem. You can see how the answer depends on m_1 or v_2. Once, when I was a TA, a gave the students a quiz with no numbers in it, but I still got some numerical answers. You should never do that.
I was doing another problem in Serway and Jewett where they gave numerical values. I instinctively did as you suggest here. Lo and behold, the very next problem asked us to solve the general case. I wasn't entirely surprised that they even used exactly the same notation for the variables that I had chosen. So I just wrote, "See above." 😀
it's especially important for programmers to do this.
Unless you know one of your numbers is zero, then it's very well possible that the whole problem gets a lot simpler
my gen physics prof had us do this, students would regularly ask him to plug numbers in when we were doing example problems but he would just tell them no, it's easier without the numbers. i never understood why there was such a vocal crowd of people taking that class that got genuinely angry that he wouldn't do the problems with numbers. it just takes longer and introduces much more room for error (especially for a prof who is trying to speed through as many examples as possible to give us good frameworks for our notes). yeah it feels weird at first if you've never done problems that way before but it's necessary if you want to actually learn anything.
I always did this when I was studying physics. It allows you to more easily follow the logic of what you're doing.
I was a TA for the upper division math methods class. When asked to prove something, students would keep plugging some numbers that they pulled out of their butt, show that it worked for those numbers, and call it proved. Yeesh.
You are so right about having the learner do the problem (whether physics or whatever). At work, I try to teach folks how to use a tool or thing, and they go "ooh, you use that tool nice, man" but what I really want them to do is explore with the tool, try stuff, and then show me something cool I never learned. Some folks do that, other folks don't. You've inspired me to really emphasize the "play along" aspect, not just observe. Thanks!
Over the last few years, I have been learning to not hate math. I had to deal with some really awful math teachers in college and it soured me on the discipline. This video has helped me in my progress. Thank you.
28:52 - eh, not great. But my day is brightened a bit by thinking about how we'll always have people out there wanting to teach, no matter what happens with the governmental agencies tasked with such things. If I was in a space where I was wanting to learn more physics, and/or had kids that were, or whatever, I love the idea that folks like you will be around to share your enthusiasm, knowledge, etc. Thank you for being you, and for doing what you do.
I recently retired, and one of my main goals has been to relearn the physics I took in college and, from there, try to build a proper understanding of quantum mechanics.
But I also moved to my wife's hometown, İstanbul, so I am prioritizing learning Turkish over other projects. But then I did watch that video, though only a few months ago, and was very inspired. So I looked for and found the Turkish edition of Serway and Jewett. Now my education in physics supplements my Turkish courses. Of course, this will be a slower journey, but my only deadline is the ultimate one: either my death or the heat death of the universe, whichever comes first.
imagine doing the challenge and hearing "wait this is the wrong book"
Happened to me. We had a uni exam (Microcomputer Architecture 1989) where you were allowed to bring your textbooks. In my overconfident youth, I didn't attend lectures and barely looked at the book until the exam. When I sat down, I realized I hadn't brought the books with me. Still a B-. Happy days.
@@AbuMohandes-p2c
I guess microcomputers must not have been that complicated back in 1989. Was there much to talk about other than Von Neumann and Harvard architectures?
@@portobellomushroom5764 Don't knock it, the rich kids had mathematical coprocessors back then :-) And separate interrupt controller chips, timers, etc, etc. Today's chipsets in other words.
@@portobellomushroom5764 The Wintel imperium was only starting, so VAX, DEC, SEL, Motorola were all still on the menu.
Did you know SEL had a 32-bit CPU in 1975, about 10 years before Intel got around to it? It was the size of a minivan and cost a measly $150k.
Even for someone not in physics or currently trying to learn it, these are good for helping me unlearn my physics trauma from fully-online AP physics a few years ago
i cant believe that i spent an entire year in a physics class when i couldve just watched angela collier videos???
I only listened to the "how to teach yourself physics" about a couple weeks ago. I am doing the challenge! I hopefully will be able to finish my time machine by the end of it. And come back and edit this comment to say I did it!
You must have failed.. or your time machine didn't work.. probably because you started it before finishing the book.
Never mind the time machine, a year is not so long, come back then ok? Like next Halloween 2025? I just got the book too and shared a problem with my old uni mates , they made a better fist of it than me without even reading the book ... I'm so challenged and up for it now lol!
@@BB-fff1 alright one year I'll be here
Just make sure you're using the right book.😂
I'll be honest, at the beginning when you invited viewers to try and solve the problem, my thought was "I'll make a coffee but I don't know about solving the problem." And I guess I just imagined it'd be like some of your other videos it sorta gets into some intimidating math (which is fine! Keep doing that).
But then I saw the problem and I was like, ok, it's been a while since I did this in High School, but I'll give it a shot!
Update: Got to problem 2. Uh oh.
The past week has been stressful as hell (being a queer woman in the USA right now is not fun), but it turns out solving a high school physics problem is better stress relief than I expected, thank you
I'm not queer, not a woman, not in the USA, and I find it stressful. So best wishes. Any advice would be patronizing, so I'm sending more best wishes instead.
Sending best wishes to both of you. There are many things about this life I can be unhappy about, but there are also some awesome things, like this new video, and cats :)
Uk, male, but I decided to take my mind off it by writing a chess program. Same energy, I think.
What high school is using Jackson? Those poor kids.😅 But seriously, right there with you on the stress.
@@mrpocock Oh, that's fun. Are you following the usual alpha-beta pruning path, or doing sth else?
I have Serway 10th edition. My daughter and I are starting the challenge today!
I am a discouraged math student that failed miserably at physics, so I never watched that Teach Yourself Physics video, but now I know the name of that textbook and I can give it another shot over winter break or something. Appreciate it :)
Don't give up! The perspective gained from even a basic highschool physics education opens up a hugely rewarding realm of understanding the universe around you. Always happy to hear about someone giving learning a 2nd chance, I sincerely hope the book gives you some eurekas.
That your camera decided to do a couple focus pulls right at "How you doin'?" at the end, I think spoke for all of us.
Needed an "it's fine" this week
This! It's fine
18:22 @nathanschmidt1843 Yup, I also loves me some
"it's fine", man (LOL!😂)!
So, one sweet classic Dr. Collier "It's Fine!" slipped in here at 18:22. Whew, & yay!
Now, Dr. Angela @acollierastro, about that
"Quantum quantum quantum!"...😜
@nathanschmidt1843 Correction: Sorry, my bad. Actually, she gave us a bonus double-ItsFine, there.
Also, watching further, another "It's Fine" at 19:35.
So, I'm good (fine!) for today.
Thanks, Dr. Angela! @acollierastro
BTW, Dr C, I was watching another channel and, in a discussion about the styles and effectiveness of Science Communicators, was pleased to hear you cited, in a positive light and in good company.👍
I didn't read the Serway&Jett book but your channel is part of the reason that I grew to really love physics during the last two years of high school. I'm doing an undergrad in theoretical physics now
Focus pumping is a known issue on some cameras. It's easy to fix. You need to use manual focus. You can let the camera focus automatically and then switch to manual focus before you start recording. Alternatively, you can just focus manually. In both cases a second person would be helpful: one to sit in front of the camera and another to focus the camera on the eyes of the first person. If you need assistance or have questions about your camera, lighting or sound, please let me know, I'll be glad to help. People like your videos, please keep them coming. Best.
Just got off my shift, needed this. It will probably go in one ear and out the other but I can at least tell myself I'm being productive.
I've studied theater and teach drama and performing arts and I have less than basic understanding about physics. But for some reason I enjoy your videos and always watch/listen to them. Maybe I've even learnt something along the way 😄 maybe it's the passion that you have for your field that reaches over boundaries (and the shared passion for star trek) 😂
As someone who is studying mechanics at the moment this could not come at a better time. It was really great to have a validation that I'm taking the correct basic approach. I am absolutely convinced that the only way to get good at this stuff is to actually do the problems. This is exactly like when a musician practices scales. You need the repetition to build "muscle memory" in skills otherwise they won't be available to you when you need them for a real application.
Thanks Angela. I really enjoy your videos, whether they're book reviews, Coffee and the problem, or general physics topics.
The rigor of your method really shines on the second problem. I studied undergrad Physics and spent my career in IT with 20 years of University lecturing. When teaching, we often have to deal with simplified cases, like your first problem. As you're speaking I'm using my hands to visualise the situation, going "conservation of momentum and vector arithmetic", and getting to the point of "so I need X where tan(X) = .75, and do some Pythagoras". But by using your method you are teaching the method that works for any problem. Good job.
And I especially like your reality check at the end :-)
Having got an answer using methods that were pretty obvious and self evident for me, and despite getting a little worried when Angela used a very different route it was really fun and insightful to see another way to approach the problem! Was a relief that my method had got me the right numbers (although the angle took a few goes because it's been several years since I last converted radians to degrees)
That "how to teach yourself physics" video was how I found your channel, and although I watched it late and been going through the Serway/Jewett book too slowly (only at chapter 6...) to apply to the challenge you mentioned, it's been really helpful in my learning of Physics, so thanks Angela :) (Also like your other videos, they're casual in a way that's very easy to listen to)
So, I just picked up the Serway/Jewett 7th ed with Modern Physics last week and intend to work through it through 2025. I'll touch base after a year to remind you that you can make a difference 😊
I did actually start reading the book because of your video! Life has kinda got in the way, but i’m making progress
That Feynman quote reminds me about the high school students who came up with the first trigonometric proof for the Pythagorean Theorem!
I love your enthusiasm. Unbelievably you chose the problem from Jackson that I have circled in my decades old copy of Jackson (red cover). That must mean my book isn't out of date yet even if it is older than you.
I know two things about physics, jack and $#!T, but I watch these because I love listening to you. Thanks for doing your thing.
I skipped the problems because I never even studied physics in high school, but great video! Feinmann really was inspirational for the most part.
I have a physics test tomorrow so this is perfect timing
Hey Angela, thanks for all the great videos. They are always interesting
Haven't really done physics in like 8 years, so I'm happy I was able to solve the first problem relatively easily. Had some doubts after reviewing my result, but I figured it's fine & I was right.
For the second question, I got stuck for a few reasons: 1) Most of the variables weren't defined, 2) I have never seen Poisson's equation, 3) I have never done a Laplacian, 4) I have never dealt with Dirac delta functions, 5) I barely remember what "potential" is.
... Well, at least I tried. I got to draw a hydrogen atom & it was pretty close to yours.
was just watching the space elevator video for a nice chill coffee and a problem when this was released
I’m about halfway through the year, it has helped me a bit with my personal issues.
Also remembering a lot of things i was supposed to master in engineering school.
You are responsible for my attempt at teaching myself physics which involved getting 2 chapters into a physics textbook realising I'm not as good at math as I thought and proceeding to read half a linear algebra textbook
summoning all my physics major friends to this video rn
also thank you angela for inadvertently convincing me to major in physics. im studying mechanics with serway and jewitt rn. i love the subject and hopefully with more practical problem solving it loves me back :p
Learning about the Dirac Delta function is such a wonderful memory. Infinite height. Zero width. Area of one. I was laughing with joy and how amazing that is. A horn of Gabriel moment.
Keeping TH-cam Smart one problem at a time - thanks Angela - cheers.
I still have Physics Parts I & II combine 3rd edition by Halliday and Resnick from my first year of my EE degree in 1985. It's a 1978 edition. I recall finding it lacking - although there's surprising number of commercial cartoons in it, that us hip college engineering students in Milwaukee were hep to, like Peanuts. Groovy. I made notes in it, which are so fun to examine now. I re-drew a circuit diagram - a single loop RCL circuit. The dozen supplemental topics in the back remind me of Angela Collier videos. Since, we didn't have the Internet, the back appendixes of textbooks had mountains of supplemental information, log tables, the periodic tables, the weights of the planets, conversion factors,hundreds of mathematical formulas, and a list of physics Nobel prize winners ending in 1977!
When Donald Knuth was an undergraduate with a scholarship to study physics at the Case Institute of Technology (now CWRU), it was rumored that he worked all the problems in the math textbooks, not just the assigned problems. He ended up switching his major to math and at graduation, in addition to receiving his B.S. in Mathematics, the faculty awarded him a bonus Masters degree. So, it sometimes pays dividends to work those extra problems!
Glad my highschool physics was still enough to solve the first problem! I don't think I have done a physics problem in over a decade. (I calculated the x and y direction components of the final velocity separately but put them together to get the same answer.)
things aren't great, but this was a good vid. Be well.
Recently I had one of my oddest experiences with physics. In a span of a few years I had went from studying graduate level electromagnetics and statistical mechanics, to all of a sudden teaching a first year physics course in college (in Canada, college is more akin to "community college", but it's a polytechnic college, so they can upgrade to a degree with a 4th year if they want to). That introductory physics course, which I will be teaching again soon, honestly lit a fire in me for solving problems. Kinematics, and forces, and newton's laws, basic thermodynamics, allowed me to step back and think about problem solving in such a broad way. Things like non-conservative forces had such a concrete meaning and are so elegant in simple Newtonian physics.
After teaching this course I was motivated to go back and look at Griffith's QM, for instance, and just start working on some of the problems at the end of the chapters. Some of them have really deep answers that get you to think about the physics quite a bit. Moreso than the preceding chapters had by presenting equations and writing paragraphs about them.
Solving problems is my favorite way to engage with physics. Not attending a lecture, not reading a textbook, but actually doing the problems.
Thanks for sharing your walkthrough of these problems!
2:12 - 4,000kg 'mass' travelling at 15.625 m/s at 36.870deg CW from North.
11:06 - Aside from sig figs and that I adjusted to use North as datum (which is arguably the wrong thing to do I know) we agree, cool, glad to see my brain hasn't completely vegetated.
pffft, who needs the DOE when you have dr collier? physics? science. physics computations? math. science history? history. science communication? communication arts!
Yeah, but the real question is: without the DOE, do you get Dr. Colliers? Idk if her workplace is funded by government grants, but I know a lot of other physicists' workplaces are.
@@GSBarlev Indeed. There were no physicists before 1979 when the DOE was created. The only people who could read before that were clergy, and only in Latin.
You confused potential and field at 16:55. Field is force on a test charge. Potential is work done to move a charge to that location. (Per unit charge in both cases.) Didn't affect your solution afterwards. I hadn't thought about the Laplacian in a long time, so I appreciated that.
I haven't really done any physics since graduating high school 8 years ago, as my focus since has been languages (notwithstanding the occasional autism-fueled endeavour to produce a calculator for the tension of guitar strings at a given pitch and sounding length - which worked, because it broadly relates to school-level physics - or to figure out how many stacks of gold you'd need to put in a Minecraft chest to create a black hole - which may or may not have worked since it relates to physics way above my pay grade and I have no way of double checking), so it was really encouraging to see the first problem and go "Oh! I can do this!" and get the answer right!
It's on 1080p, you did it. Congrats.
The Physics module of the Open University in the UK gave this advice:
1.Draw a diagram first, if possible
2.Always complete manipulation of the formulae before entering any values
3.State the relevant formulae using standard abbreviations
4.Identify vectors. Use curly underline to write vectors (or print in bold)
5.State the direction by giving the unit vectors (unless explicitly instructed to use another coordinate system)
6.For numerical quantities:
1.Convert all values to SI equivalent
2.Express all figures in scientific notation
3.State the appropriate level of precision (significant figures)
4.Give the units of SI measurement
7.Check the result
I taught myself physics in the 6 weeks before my exam after not listening in class for about 2 years. I got a grade 2 CSE. Not entirely bad.
Nice quote from Feynman! I miss solving physics problems from uni... more fun than argue with business people about ridiculous requests...
I had dreams of teaching myself physics using Feynman's Lectures on Physics once but it'd probably be a lot more productive to use a modern textbook
Yes. My thermal physics teacher was in that class, and he and his classmates found it very hard, almost too hard, even for Cal Tech freshmen.
I will say that reading through his treatment of the gyroscopic top finally gave me a physical intuition of why you needed a vector cross product to explain the top's response to being pushed perpendicular to its axis of rotation.
Use both! Modem science stands on the shoulders of those who came before. Having what we knew then with what we know now, you can see how much more has been learned!
Really took me back to my first physics course at UVa in 1968. Thanks for that! I spent the summer of 1963 reading a book my dad used in college: Essentials of Modern Physics, 1922. The author ironically was Charles E. DULL. If you want to know why a company of soldiers was advised to break step when crossing a wooden bridge, this will book provides the answer.
I noticed two things about problem 1: first I would take the angle from N (the y axis) not E, since that will give you the compass direction. That doesn't really matter at all of course. But I think the second thing is not quite so trivial, and it has to do with jumping into the calculation too quickly. To solve the problem I drew a picture of the momentum vectors, and it didn't take me long to notice that we're looking at a 3-4-5 triangle. So (no spoilers) you can get a result for the magnitude of the velocity vector without pulling in any rounding errors that you might get from multiplying by the arc tan. If that makes sense. I think drawing pictures is great, and I also think students can benefit from not taking their calculators out too soon.
1: Yes, but convention. Cartesian coords, sin, cos as circular functions, cos 0 = 1, sin 0 = 0, theta is counterclockwise from our x-axis. Maybe the rotation is easy for you in your head, but it's mental gymnastics for some pupils.
2: Yes, but we're not multiplying anything by theta. However we choose to round theta, that's our *answer* for the direction. It's not used at all for the magnitude.
Since you're at it, may as well mention only one step left. Convert the resultant momentum to velocity, ie, divide by combined mass.
In a similar spirit, noticing 3-4-5 only saves two one-liners, theta = arctan p2/p1, no sweat; and p3 = sqrt(p1^2 + p2^2), big deal. Then v3=p3/m3, m3=m1+m2.
There are two things you noticed that didn't have to be, but the problem builds them in. One, the vectors are at right angles, so we're looking at a right triangle. Because of that, the resultant pops out by Pythagoras. Two, as you note, we can skip even that step as the momenta are cooked to make a very familiar shape.
Not every pupil will jump straight to momentum vectors. The problem is more confusing if they draw a picture of velocity vectors. Arguably, punishing them for that mistake is a key lesson of this exercise.
Separately, I'll use this opportunity to mention a different teaching point. I do like it when Dr. Collier throws in an extra little tip, like solving vectors one component at a time, that's a good habit. At the same time, I learned from Don Knuth, it's also in his Art of Computer Programming book series, if you want pupils not to take a particular shortcut, you pick a problem where the shortcut punishes them. That is, they're forced to use the technique you're trying to teach them. In this case, the problem is completely solved by momentum vectors alone. I have a little story about a slight variation that punishes you for making that same mistake.
Almost half a century ago, I took my first midterm. I scored top of class. That was by pure luck. The class was 4 units, 2 hours each Tue/Thu AM. The midterm used up one of those 2hr sessions. I'd stayed up too late cramming, overslept. Showed up with only 20min left. The very first problem, of 6, was kind of a trick. We could solve it by brute force, literally, but working the force vectors got complicated. I rushed in, saw my math start to get tangled, no time for that. I skipped it, moved along. Got full credit on a couple problems, partial on a couple more, time called. Everyone else wasted almost the full 2hrs trying to grind it out. I got 29/60, next highest score was 14.
This problem was cribbed from an MIT PhD qual exam. We were frosh. Here it is. Preliminaries: classical mechanics, no friction, collisions perfectly elastic, ignore Dr. Collier's question of Do we need more physics? The table's gigantic, heavy as heck, the whole experiment's in a huge vacuum chamber, the gravitational field is perfectly uniform, little g is a constant, every surface is flat and polished. We are not gonna get any points taken off for neglecting all that stuff. So on the table is a triangular ramp, like a tire block, it slides on the table. At the top of the ramp is a brick, we let it go, it slides down the ramp. Eventually it hits the table, the brick & the ramp glide away from each other, & the system is in a steady state. If you're thinking, "Collision? What collision?" that's OK. It won't cost you points. Write the equations of motion for the brick & the ramp. Your answer will be in two pieces. The acceleration curves for the brick sliding down the ramp & the ramp sliding across the table. And their final velocities.
I got back to the dorm, went to lunch, & thought back to that problem. I solved it in only fifteen minutes, thanks to no time pressure. I knew my first approach was good enough, but a serious pain in the neck in practice. I realized what Dr. Collier talked about for the similar but simpler problem of a car crash, energy is clearly not conserved. But we were given all prerequisites to use energy conservation. There had to be a reason for that. Write down the kinetic energies, relate the two things we know to each other. Ie, solve one, plug into the other. Gee, the answer tumbles out like a nut out of a nutcracker. Such a sweet little problem. And a nasty lesson for many of us. :)
Just bought the physics for scientists and engineers 2 days ago. I decided it's finally time. I'm a material scientist and I know enough physics that whenever I encountered someone talking about physics I knew just enough that I could fool myself into thinking that "yeah, this is easy, I understand/I could solve this too". But deep down I always knew that was bullshit, so I finally decided to do something about it. I'm excited for it to get here. I plan on spending six months to a year on it and then I'll teach myself quantum physics and astrophysics! That's the plan anyway.
I was into the idea of getting back into learning physics in what passes for my spare time. I did physics and mathematics in high school 30 years ago and got "A"s. Since then I did CompSci at Uni, and then coding professionally... web stuff, but with some matrices, quaternions, trig, and so on. So, I thought I'd brush up on some mathematics on Khan Academy in preparation for doing some undergraduate level physics.
Um... NO.
I keep having to restart further and further back, and got all the way to simple factorization before I felt properly comfortable. Trig identities I swear I never learned in the first place, and stuff with Limits that I have no memory of. Frankly, I'm not _that_ far ahead of my 12 year old kid, and she'll probably catch up before too long.
:/
Hi Angela, I have the Jewett eighth edition with modern physics thanks to you!
I finally bought the Jewett-Serway book in September and it'll take 2-3 years for me to process it. When I finish it I won't be as young as I used to be. In one hand, I always believed spontaneous activity is superior to structuring time artificially, the older I get the dumber the latter seems and physics is not spontaneous enough to me to read faster. In the other hand, I never really bought into the idea that stockpiling books is shameful. I'm also following a 70 yo mom on TH-cam who has a couple degrees in anthropology and literature and her desk is always covered with large piles of interesting, rare books. If that evokes an emotion from me, I rather envy her optimism.
0:25 WOULDNT THAT BE CRAZY HUH! Amazing start 😆(cry laughing)
The project 2025 reference was depressing. Great vid.
I'll take your videos over the 300 & 400 level math teachers I had in undergrad.
Thank you very much Angela Collier !
Top Ten episode of Coffee and the Problem ever. Going down in history of Coffee and the Problem episodes, for sure.
Watching this, I realised just how much I know compared to the average person, and how much I don't know compared to someone with practice in physics. The gulf on either side is large.
It is kind of cool hearing how other people think lol. Thanks for the video Angela! I appreciate it :)
Ive been using the book from your recommendation for about a month!
i love coffee and i love problems, thank you Angela
Growing up, we had two sets of encyclopedias at home, a newer set and an older set. The newer set was Collier's. The older set, maybe World Book or Brittanica, was published before WWII, and it's entry for WWI was called The Great War.
I "did" the challenge with a different book (Resnick Halliday I believe), that a family friend (who happens to have a PhD in physics) lent me! Still definitely by your inspiration :)
I'd just like to say I want to support Dr. Collier, but I'm also sure she's going to be as OK as any of us. We need above all to stick together. As Americans those of us who are that. As humans for all of us. We're a good group of folks gathering around this nice fire by a good person. It's undiminished by our political union being less than perfect. Physics rules!
Last steps of solving a problem are asking yourself if the answer you reached is reasonable, is it good enough, and do you need more physics. Makes perfect sense, you always need to do some basic sanity checks on a calculated solution to make sure you didn't miss something significant.
Second/last sample problem, reaching the end of the calculation, getting a result... Is the answer reasonable? No. is it good enough? No. Do we need more physics? Yes.
Done, problem solved. Moving On.😀🤣
I'm not sure if this was supposed to be very blunt humor, or subtle humor, but it did achieve a *literal* physical LOL, which is rare.
( Reminds me of the less funny versions, in my high-school physics class, when we were learning kinematics. The teacher gave questions where the velocity of trains/cars/superman were occasionally much higher than c, and didn't realize why I was complaining since I obviously could solve the equations and reach the "correct" solution... )
We're in such a weird state when "how to solve a physics problem" is how we're coping as a society. I mean, not for me because I went to college for this but I'm not used to others joining in
How'm I doing? Not great, TBH. "Recent events" do not agree with me. And I have to admit that watching this video gave me flashbacks to my physics classes from 40 (argh! yes!) years ago. My career didn't use much physics, and I've lost it all. I could follow the first problem, mostly, but the second washed over me in a way that I am not proud of. But I still enjoyed the video, and the merch looks cool. Thanks!
This is generally the right advice and the right process, but maybe don't use an example problem with a gimmie shortcut you're supposed to use to speed up your rote homework/test answering. It's a 3:4:5 right triangle, and if you memorized it for the SAT/GRE/GMAT what have you, you'd know the Theta is 53.13 or 0.91 Radians. Start with simplifying by dividing speeds by 5, masses by 300, and you get 5*4 up and 3*5 right, IE 20 by 15, or 3 over 4 up, so distance is 5. So 53.13 for the combined 4 tonnes mass. Assuming point-mass collisions combining as stated.
It's similar but different for the velocity: the Velocity-Mass is the same after collision in each north and east directions but the mass changes by combination and affects the imparted velocity; Lets rescale masses down by 500, keep the velocities scaled down by 5, so one orthogonal is (3kg*5m/s)/8kg=1.875m/s and the other orthogonal is (5kg*4m/s)/8kg=2.5m/s. They're like lengths to the sides of the hypotenuse, so sum of squares wise: 2.5*2.5=6.25 and 1.875*1.875=3.515625, added are 9.76525 square rooted for the hypotenuse being ~3.125, scaled back up by 5 is 15.625m/s. It's mildly more exact than going the arctan route.
The next problem doesn't have the same kind of gimmie, so, pretty interesting for both. Thanks!
Yeah, well I guess that's about right. Only, I lost you about the arctan thing being subject to inaccuracy. Theta isn't even involved in the magnitude calculation. You already made the right call since we're using conservation of momentum, the relevant vectors are the momenta, ie, P3 = P1 + P2. Magnitudes in lower case. You noted the ratio p2/p1 = 4/3, it's a right angle, so resultant = hypotenuse = 5 or p3 = 5/3 * p1 = 5/3 * 37500 = 62500. And p3 = m3 v3 so v3=p3/m3=62500/4000.
I don't know if your simplifications meant you could carry it all in your head, but to me it just seems like extra steps for no reason. As for 53.13, the exact answer is theta = arctan p2/p1 = arctan 4/3 = 53.1301024, rounding error is wherever you choose. And theta is the answer to the direction, its usefulness is otherwise over.
It is funny because it's true. One of the most useful things I learned at school was in mechanics. Say the problem, d draw the problem, solve the simplest version of the drawing. Check the result isn't daft. Check if the solution is good enough. If not, draw a better diagram and go again.
4:56 Point 2 could be named "establish the invariants", at least whenever we're asked to solve a before/after type of problem.
A triangle symbol with its base at the bottom is called the Laplacian. The triangle symbol with its base at the top is called the nabla or del operator. The square of the nabla equals the Laplacian.
I remember, my electrodynamics professor based his lectures on the Jackson and that problem was one of the problems he gave us to solve in his course :D
outros are always good :3
_Hon hon hon_ 🥖
It's bizarre that the department of education is even at risk here... good luck to you Americans.
Thank you. We're going to need it. The US is about to get real dark and I'm not a happy boy being stuck living in this shithole country.
As a physics student I recommend having tissue while solving Physics problem.(TO CLEAR YOUR TEARS )
I love physics but not THAT much, buddy
As a physics master I can tell you a pen and a notebook will suffice (and occassionaly a processor)
@@ninadgadre3934 TO CLEAR YOUR TEARS WTF
oh shit I'm here so early, I thought the algorithm was just feeding me old Angela
I literally just started the Conservation of Momentum chapter with collisions in my physics class this week. Am I doing the homework? No. Am I doing physics with Angela? Yes 😅
Thankfully I was initiated into the cult of the Free Body Diagram early in my highschool science education.
That first physics problem about the car wreck is impossible to answer because we dont' have nearly enough information.
1: What's the road surface like? (Asphalt? Gravel? Dirt Road?)
2: What is the length of each vehicle?
3: Is the ground completely flat, or is it on any slope at all?
4: Is the weight equally distributed in each vehicle? (For instance it could be front heavy b/c engine)
5: Have the wheels been lifted on either vehicle to raise the center of gravity?
6: Is the collision dead center, or glancing blow is it hitting the front or rear of the vehicle?
7: Did either driver hit the brakes or accelerator at all before, during, or after the collision?
8: What is the conditions of the tires on each vehicle, and how much traction do they have?
9: Are there any other circumstances such as chains on the tires?
10: Did either driver turn the wheel at all before or after the collision?
11: Does the weight of the car include the weight of the driver, and passengers, and luggage?
12: Did this collision happen in a vacuum? If not what direction is the wind blowing and what speed?
13: Was either vehicle lifted into the air from the collision at all?
14: What's the horsepower of each vehicle?
15:What is the exact angle of the collision?
You're kinda overthinking things I feel.
@@suttoncoldfield9318 The problem is an over simplification. I didn't even mention the energy lost when the metal is deformed, and the noise made and all that.
Your humanity comes across in all your videos.
Ah yes, camera angled with a great gap between top of the head and top of the frame. A classic cinematographic indicator of "the vibes being bad" as it were.
Very excited about merch, but once I slap one of these stickers on my laptop there's a risk that it might make people think that I am Smart and Know Things About Science, and that's not going to end well for anyone involved.
I only just found you but will definitely look into that book
With the first problem it would have been interesting if you also calculated out the kinetic energies.
I was not watching your videos until recently, so I missed the book recommendation. But I have my own schedule. I am studying the following books in parallel as much as I can (other than my fulltime job of being a computer scientist): Quantum field theory volume 1 by Robert Klauber, general relativity by Hobsun et. al., and the latest edition of Schutz's a first course in general relativity among others.
Also I have Young and Friedmann. Though I read Kleppner' introduction to mechanics and David Morin's introduction to classical mechanics.
"it's fine, it's fine ... It's gonna be fine."
I have a test tomorrow. Please, Angela, save me from my hubris.
you should do more videos just like this.
If she does enough of them, I can just transcribe as needed and turn them in!
I did pause the video and answer it myself, for fun. Then I was dismayed when I saw how you were solving it, I thought I must have done it completely wrong because your way seemed more complex! (I also got worried when I did a sense-check because I forgot Kinetic energy isn't conserved in inelastic collisions 😂)
But we got the same answer (phew! I haven't forgotten everything!), I just did it a bit more visually by constructing a right-angle triangle with the legs equalling the two initial momenta and got the vector sum that way.
Oh and I dock you a point (no criticism here, just embodying the professor vibe) for the first problem for the way you gave the answer for the angle. It's somewhat ambiguous (without referring to your diagram) and I'd be expecting an answer in the same basis as the problem, which used compass directions. For example as a bearing - 36.9 degrees.
She isn't a pupil. You don't dock the teacher. The techniques she uses are more than as needed on this problem, sure. But they're helpful as tips. If you as a pupil didn't have trouble equating her angle to your bearing, there's no serious conflict.
Angela is all of us right now
the modern physics class i'm taking rn uses the serway/moses/moyer modern physics textbook! i don't think it's the same one you recommended but i remembered thinking it sounded so familiar when i heard it and i ust realized it was from your video lol
Missing: use of math as language to describe the picture. This is implicit but ppl struggling usually need it explicit.