Physics books that solve real world problems

[farleyknight]

Physics books that solve "real world" problems

Ever since I dropped physics last semester, I've been slowly accumulating books to try and find ones that speak to me. I'm a huge skeptic, always have been, and so far, many of them don't make a convincing case. Only one seems to speak to me (Landau's Mechanics) and my lack of education keeps me from reading it further.

Just this afternoon, I began reading the applied section in my diff eq book. I started to get that bad taste in my mouth again, where physics just doesn't make sense. But I kept reading and the author introduced 1) the force of gravity, 2) (okay fine, it's everywhere, big whoop) the force of an object on a spring hanging from a ceiling (okay.. what kind of spring? what kind of object? where on the Earth...? how do I know... baahh!). And then 3) the damping force of the medium. This last one had me pause a bit.

For some reason, I felt less aggravated when he introduced this third force that would account for the resistance of the spring by the surrounding air. I felt as though he wasn't lying to me (as much), and was genuinely trying to model a "real life" scenario. Rarely have I found this to be the case in the books that I've read. Air resistance was mentioned briefly in my original textbook, but we didn't cover it. Otherwise, the books I've seen neglect everything and strip it down to such simple terms that I just don't believe in what they're telling me.

So that combined with another post on the forum has got me thinking: Well, if physics can't prove their laws from first principles, at least do a better job at modeling the environment so it's believable. All this stuff about working in frictionless vacuums makes me doubt physics books.

It would be nice if books could ask questions that stated questions where you were told what materials are being used or what kinds of forces were being applied, or other gorey details that you would have to solve if you were say, MacGauver. I'm sure a guy like that would need physics and would know a good bit about everyday objects to make the problems actually worth while to solving.

Would this make home work sets more complicated? Well, of course.. But wouldn't that make it more "realistic"? I think so. The scenarios I read are half-real, half-abstract, in such a way that my math side rejects it for being too concrete and my real life side rejects it for being too abstract. It's unnerving and hard to focus on the particular parts of the problem.

tl;dr Are their any physics books that describe problems in complete detail? Or do they all try to make it abstract in some way?

 

[Cvan]

I don't think typical "physics"(mechanics is probably more accurate for the kind of book you're looking for) books are at all 'abstract'. You have to understand the theory behind the operating principles of forces, frames, analysis of differential elements, etc; before you go and start making simplifying assumptions or real world considerations. To be honest; a lot of what's done in industry is TRYING to model those real world scenarios more accurately since it's nigh impossible to completely account for everything that happens in a system.

Understanding the basic relationships between motions, forces, energy conservation, etc is absolutely fundamental to the process of designing simulations or coming up with predictions for physical systems. In the end though, all the things you can't model (because the theory is either too messy or doesn't exist at all--think turbulent flow for example) is typically dealt with using simulations sometimes based on theory (with a lot of assumptions), empirical data fits, that sort of thing. It's useful to know for instance that the drag force goes as the square of the velocity, but are you going to trust that notion exactly when you're designing something?

Understanding the theory is pivotal (at least in engineering) to knowing a few things: 1) What you should expect for results in general. 2) Where you should expect your results to be off from theory (or researching why/how). 3) Most importantly: What assumptions are justified in your analysis? Without knowing the accepted models on the macroscopic scale for how the laws of physics behave, there is no basis for knowing where to even begin modelling a system, let alone how to simplify your analysis without going out and experimentally verifying EVERYTHING with no preconceived notion of the results (absurd and costly)

tl;dr. Don't think any physics books attempt to model every little effect. Theory is important; but the difference between theory and reality often comes from a mix of empirical data and simplified theoretical considerations (which a course in experimentation/instrumentation, dimensional analysis/model building, or something of the like can remedy, since in general this is not typically a difficult thing to do compared with modelling impossibly complicated systems).

 

[farleyknight]

Understanding the theory is pivotal (at least in engineering) to knowing a few things: 1) What you should expect for results in general. 2) Where you should expect your results to be off from theory (or researching why/how). 3) Most importantly: What assumptions are justified in your analysis?

My main beef is that those taking intro physics courses have little if any of these three things. This lack of experience creates gaps in the learners knowledge and when a curve ball is thrown on an advanced test, screw it.. You know won't about those corner cases unless you have the experience you're speaking of right now.

You can say something silly like "well, we wouldn't expect students to take into account air friction". But there is always some Russian or Chinese teacher who doesn't give a f*ck what you did or didn't learn from your last teacher and expects you to know it like he does.

Sorry.. got a little carried away. Back to the "real world" argument topic.

You have to admit that intro physics is not a hire-able skill, but yet we force many science majors to take it because it's supposed to help enrich their understanding of the world. It's enough not to be fooled in some rare circumstances, but for the most part, it doesn't teach you about the real world, just some half-abstract, half-real version of it. If there was a book that spoke as if the problems actually happened in the real world, or went the other direction and became more abstract, then it would settle some of my nerves. Just wondering if there were books that spoke with that tone.

 

[Yanick]

The real world is complicated. You can't just take a kid who has never heard of Newton's Law's and drop real world examples on him which take into account every single thing possible (as already mentioned, that might not truly be possible anyway, regardless of level of education). The whole point of an intro course is to give you a foundation which is built upon as you learn more and more within that area. Crawl before you walk and walk before you run etc.

For example in my intro course we started with basic kinematics (definitions, relationships, equations) in one dimension. Then we learned about motion in 2D which is really the same thing with an added dimension of difficulty (no pun intended). Fast forward a couple of weeks and everything that we were taught in the beginning is still there but the level of difficulty is a lot greater because we are slowly but surely getting closer and closer to 'real world.' You start getting into hills, normal forces, gravity, friction, pulleys etc. Can I take my knowledge and build a bridge? Hell no, I'm in a freshman level physics class. But if I were to go on to get an engineering degree or something, in a couple of years time I would have learned enough to model 'real world' examples, and all of my advanced knowledge would be built upon the foundation which I am learning now.

Its good that you have that desire to learn and apply your knowledge but don't forget that you have to 'pay your dues.' Same as anything else in this world.

PS Physics absolutely teaches you about the real world. Its just that an Intro Physics course proves things that we intuitively already know (Physics just gives you a much deeper understanding of why its harder to push a heavy box up a slope for instance).

And no, you don't learn any useful/marketable skills in an intro to physics class. But that's true for any intro class. If you can learn a couple of hundred to a thousand years of science in one semester with enough detail to actually be able to apply it in the real world, why the hell would we have med schools or grad schools? There would just be a medicine class and them bam your a doctor. Or take 1 biochem class and all of a sudden be able to obtain, read and interpret EPR data?

 

[Gokul43201]

Ever since I dropped physics last semester, I've been slowly accumulating books to try and find ones that speak to me. I'm a huge skeptic, always have been, and so far, many of them don't make a convincing case.

Skeptic about what exactly?

Just this afternoon, I began reading the applied section in my diff eq book. I started to get that bad taste in my mouth again, where physics just doesn't make sense. But I kept reading and the author introduced 1) the force of gravity, 2) (okay fine, it's everywhere, big whoop) the force of an object on a spring hanging from a ceiling (okay.. what kind of spring? what kind of object? where on the Earth...? how do I know... baahh!). And then 3) the damping force of the medium. This last one had me pause a bit.

For some reason, I felt less aggravated when he introduced this third force that would account for the resistance of the spring by the surrounding air. I felt as though he wasn't lying to me (as much), and was genuinely trying to model a "real life" scenario.

If this is what was included (damping from air resistance), I would have felt the almost the opposite to your feeling. Air resistance is rarely the dominant source of damping in most everyday springs.

Rarely have I found this to be the case in the books that I've read. Air resistance was mentioned briefly in my original textbook, but we didn't cover it. Otherwise, the books I've seen neglect everything and strip it down to such simple terms that I just don't believe in what they're telling me.

What they're telling you is that the following approach (which neglects blah1, blah2, etc) gives you an approximate solution to the problem, and just as importantly, introduces you to the physics that dominates the problem.

There's a rather famous quote (can't recall the source or the exact words) that I'll paraphrase here, as it's very relevant to this discussion: Physics, inasmuch as it is an accurate representation of reality is rarely simple, and when it is simple, is rarely accurate.

There's almost always a trade-off between mathematical complexity (and therefore computation time and pedagogic value) and accuracy of a model. If there's a problem that you can solve to 95% accuracy by doing a simple calculation in your head in a matter of seconds, but requires several hours or days of computational time to get a 99% accurate number, what are you going to choose? Well, depending on the situation, one or the other approach may be optimal.

When it comes to textbooks, it is incumbent upon the author to explain what simplifying assumptions are being made in any case, and the circumstances under which they are justified.

In this context, I would recommend (albeit at the undergraduate level) an excellent book - it gives you real world problems, asks you to make whatever assumptions you believe are necessary, and use appropriate values for relevant data in your solution. The book is "Thinking Like a Physicist - Physics Problems for Undergraduates", edited by N Thompson.

Here's a link to the title at Amazon: https://www.amazon.com/dp/0852745133/?tag=pfamazon01-20

I like the review of the book found at the link above. Quoting the relevant part: "I am in NO WAY denigrating these [formulaic] kinds of problems or these kinds of exams! They are and were an essential part of training in physics.

But Thompson's book is different. It's about messy, squishy, ugly real life problems. Things like interstellar gunk condensing into a planet or star, surface tension and viscosity in real fluids, i.e. more realistic models of the physical world. For that reason, this book is a gem, not to be missed. It is very much in the spirit of Pippard's "Cavendish Problems in Physics," another gem. But unlike Pippard, Thompson gives detailed solutions. "

 

[farleyknight]

The real world is complicated. You can't just take a kid who has never heard of Newton's Law's and drop real world examples on him which take into account every single thing possible (as already mentioned, that might not truly be possible anyway, regardless of level of education). The whole point of an intro course is to give you a foundation which is built upon as you learn more and more within that area. Crawl before you walk and walk before you run etc.

My best response to this is that you could in fact structure an intro physics to be applied very readily to real world problems. But only trivial ones, most likely. On the other hand, educational conventions has led us to doing otherwise. Put this in contrast to a completely different science, Computer Science. You can learn enough CS in the first couple chapters of a beginners programming book to know how to write programs. Quality aside, you could potentially solve some trivial real problems with this knowledge. An office monkey could make quick work of his daily tasks if he knows a bit of Visual Basic. However, I wouldn't have a clue how to apply Newton's laws to my daily life. Feel free to enlighten me on that last one.

For example in my intro course we started with basic kinematics (definitions, relationships, equations) in one dimension. Then we learned about motion in 2D which is really the same thing with an added dimension of difficulty (no pun intended). Fast forward a couple of weeks and everything that we were taught in the beginning is still there but the level of difficulty is a lot greater because we are slowly but surely getting closer and closer to 'real world.' You start getting into hills, normal forces, gravity, friction, pulleys etc. Can I take my knowledge and build a bridge? Hell no, I'm in a freshman level physics class. But if I were to go on to get an engineering degree or something, in a couple of years time I would have learned enough to model 'real world' examples, and all of my advanced knowledge would be built upon the foundation which I am learning now.

Its good that you have that desire to learn and apply your knowledge but don't forget that you have to 'pay your dues.' Same as anything else in this world.

PS Physics absolutely teaches you about the real world. Its just that an Intro Physics course proves things that we intuitively already know (Physics just gives you a much deeper understanding of why its harder to push a heavy box up a slope for instance).

There's a lot of physics that's not intuitive. At least for me it wasn't. Perhaps it's because I'm more of a formalist than an intuitionist. Something as "real" as https://www.physicsforums.com/archive/index.php/t-342077.html" was not clear to me the first time around. Only after a teased out a better definition was I able to understand it.

Another example: The definition for potential energy in my physics book (Halliday & Resnick) was

"Technically potential energy is energy that can be associated with the configuration of a system of objects that exert forces on one another. This is a pretty formal definition of something that is actually familiar to you."
​

This annoyed me so much when I read it that I wrote the works "F*ck you" in the margin. You could never get away with a definition like that in a math book. There's no substance to it. It's just words on a page without any meaning like "colorless green". That was bad but what takes the cake for me is Feynman's definition of a field. In Lectures on Physics he says:

"A more adequate representation of the situation is to say that the existence of the positive charge, in some sense, distorts or creates a "condition" in space, so that when we put the negative charge in, it feels a force."​

Yeah, like a "condition" 'n' stuff, you know.. dude.. WTF is wrong with this guy, I don't even know. Maybe he's written better stuff, I'm not sure. I stopped reading after that section. But knowing how highly you physics guys view him, I thought he'd be a brilliant expositor..

And no, you don't learn any useful/marketable skills in an intro to physics class. But that's true for any intro class. If you can learn a couple of hundred to a thousand years of science in one semester with enough detail to actually be able to apply it in the real world, why the hell would we have med schools or grad schools? There would just be a medicine class and them bam your a doctor. Or take 1 biochem class and all of a sudden be able to obtain, read and interpret EPR data?

Of course not. That would be ridiculous.

My main point was this: If it's going to be a theory course, go all the way and be pure theory. Don't talk about the real world. Cut out the word force and use (fixed) vector instead. Prove various corollaries of Newton's laws, if they are in fact so fundamental.

If it's not a theory course and you want to talk about the real world then go all the way and solve (trivial) real world problems. What exactly? I dunno.. Maybe have 3 labs a week instead of 1. Build or improve something that uses the laws instead of measuring stuff. It annoys me that lab was somehow supposed to be a re-enactment of history (something that only true physics majors would enjoy) instead of making practical use of said knowledge (where non-physics majors might potentially learn from).

 

[Gokul43201]

Another example: The definition for potential energy in my physics book (Halliday & Resnick) was

"Technically potential energy is energy that can be associated with the configuration of a system of objects that exert forces on one another. This is a pretty formal definition of something that is actually familiar to you."
​

This annoyed me so much when I read it that I wrote the works "F*ck you" in the margin. You could never get away with a definition like that in a math book. There's no substance to it. It's just words on a page without any meaning like "colorless green".

That looks like a perfectly rigorous (and meaningful) definition. Do you have a better one?

 

[farleyknight]

Skeptic about what exactly?

Damn near everything. I have huge problems with authority. I've been an anarchist in some form or another as far back as I can remember. Getting drunk and chatting existential philosophy is perhaps my favorite form of socializing.

In regards to physics, I'm skeptical about the "fundamental laws" themselves. How do we know they are true? How do we know that some alternate theory isn't possible? I understand that they have been heavily tested over hundreds of years by people much smarter than me. But there's this creeping thought in the back of my head that there are edge cases where the laws just don't add up and a different set of theories would have to be created to account for them. How do I account for that when I do physics problems? I can't ignore it because my problem could be dealing with these cases in some way. I point out a specific case this a little later.

If this is what was included (damping from air resistance), I would have felt the almost the opposite to your feeling. Air resistance is rarely the dominant source of damping in most everyday springs.

What they're telling you is that the following approach (which neglects blah1, blah2, etc) gives you an approximate solution to the problem, and just as importantly, introduces you to the physics that dominates the problem.

There's a rather famous quote (can't recall the source or the exact words) that I'll paraphrase here, as it's very relevant to this discussion: Physics, inasmuch as it is an accurate representation of reality is rarely simple, and when it is simple, is rarely accurate.

There's almost always a trade-off between mathematical complexity (and therefore computation time and pedagogic value) and accuracy of a model. If there's a problem that you can solve to 95% accuracy by doing a simple calculation in your head in a matter of seconds, but requires several hours or days of computational time to get a 99% accurate number, what are you going to choose? Well, depending on the situation, one or the other approach may be optimal.

When it comes to textbooks, it is incumbent upon the author to explain what simplifying assumptions are being made in any case, and the circumstances under which they are justified.

This is probably one of my bigger gripes with the way physics was taught to me. https://www.physicsforums.com/showthread.php?t=373388&page=2" I mention it in more detail. You'll have to read posts #28-32 to get the complete story.

But if it's tl;dr, my main point was that in some cases that small degree of accuracy is necessary to predict which way events will turn. Not being able to rigorously prove that I'm correct gives me an itch I can't scratch.

In this context, I would recommend (albeit at the undergraduate level) an excellent book - it gives you real world problems, asks you to make whatever assumptions you believe are necessary, and use appropriate values for relevant data in your solution. The book is "Thinking Like a Physicist - Physics Problems for Undergraduates", edited by N Thompson.

Here's a link to the title at Amazon: https://www.amazon.com/dp/0852745133/?tag=pfamazon01-20

I like the review of the book found at the link above. Quoting the relevant part: "I am in NO WAY denigrating these [formulaic] kinds of problems or these kinds of exams! They are and were an essential part of training in physics.

But Thompson's book is different. It's about messy, squishy, ugly real life problems. Things like interstellar gunk condensing into a planet or star, surface tension and viscosity in real fluids, i.e. more realistic models of the physical world. For that reason, this book is a gem, not to be missed. It is very much in the spirit of Pippard's "Cavendish Problems in Physics," another gem. But unlike Pippard, Thompson gives detailed solutions. "

I'll add this to my wishlist... My wishlist is pretty big, but it's less than $10 so I might order it sooner rather than later.

 

[farleyknight]

That looks like a perfectly rigorous (and meaningful) definition. Do you have a better one?

I understand what it means now. Kind of. But I remember writing that when I first read it being completely confused. I still don't "completely" understand that definition. I don't think I would know how to apply this idea to other forces that I'm not familiar with, but for gravitational potential energy, a decent attempt at a mathematical version would be something like:

Def: Given two objects O_1, O_2, with corresponding masses M_1 > M_2, we may define the gravitational potential energy of O_1 as the gravitational force F exerted on O_2 by O_1. This is, of course, before the objects reach one another.

Rmk: Informally, it is sometimes said that the force F is "stored" in O_2, when it is clear from the context that O_1 is the object causing the gravitational force.

Ex: (Show abstract 3D diagram with two spheres labeled O_1 much bigger than O_2, and a large arrow being drawn from O_2 to O_1)

Prob: Consider the significant figures system R_4 (all reals truncated to 4 decimal places). Show that for any such objects O_1, O_2, O_3, .. O_n that if M_1 is "such and such" larger than all M_2 up to M_n than the gravitational potential energy exerted by O_2, O_3, ... O_n on O_1 will never have an effect on any interaction between O_2 to O_n.​

Now that would be a proof I'd love to write. As you can probably guess, unless I made a mistake, it's basically saying the mass of the Earth would never have an effect on objects of our size, if we truncate all numbers to 4 places. (Is 4 enough?) If there were more problems like that I would have more intuition into physics. Instead of the mindless number crunching that I'm expected to do where you don't learn much of anything besides how fast trains and cars go.

UPDATE: Ugh, you know what, I think I see one of the errors I could have made.. It should be the magnitude of said force, not the force itself. My prof would use the two concepts interchangeably. Blame him for that mistake.

 

[Yanick]

My best response to this is that you could in fact structure an intro physics to be applied very readily to real world problems. But only trivial ones, most likely. On the other hand, educational conventions has led us to doing otherwise. Put this in contrast to a completely different science, Computer Science. You can learn enough CS in the first couple chapters of a beginners programming book to know how to write programs. Quality aside, you could potentially solve some trivial real problems with this knowledge. An office monkey could make quick work of his daily tasks if he knows a bit of Visual Basic. However, I wouldn't have a clue how to apply Newton's laws to my daily life. Feel free to enlighten me on that last one.

You cannot possibly compare the study of nature and the study of man made things. Computer science and their languages are created by humans, which inherently means we know every single thing there is to know about the language. There is not one letter or piece of data that we don't know about (because we created it). If you open a computer you can be sure that you can know exactly what each piece of wire/plastic does, why its there, what problems it may cause if it breaks. Its the same reason why you can learn to fix refrigerators and or cars in a weekend or two (not be an expert mind you, but you'd definitely learn a lot more practical stuff). My brother taught himself how to switch an automatic transmission to a manual transmission and did it in 1 week his first time around. Second time took him 2 days.

Compare that to studying nature. Let's take a simple example like gravity. Yeah we know it exists and there is some kind of force that attracts to particles which have mass. We've known that for hundreds of years. But even today the smartest people in the world debate how it occurs, whether it occurs the way we think it does etc. We can pop open a person's head and look at there brain and we truly don't have any idea how a conglomeration of firing neurons, fatty tissue, blood vessels etc can combine to give us this 'picture' that we call awareness. We have theories and we can explain a lot of things but in the hundreds and thousands of years that science has been trying to make sense of the world, we are still scratching the surface.

You cannot compare learning visual basic to learning physics.

Simple fact of the matter is that nature is infinitely complex and scientists and scientific studies/experiments rarely give answers. All they really do is provide better questions to be answered.

The other point I want to re-iterate is that taking every single factor into account to make a calculation that is 99.999% accurate is almost impossible when dealing with the real world. That kind of precision occurs in pure mathematical problems, which to me are very abstract.

Take the example of scientists trying to model proteins and their 3D conformations. In theory we can look at a sequence of DNA, figure out what amino acids it codes for and from that information we should be able to tell you exactly how the molecule will fold in space because we know exactly what atoms are on what amino acid, which interactions will occur etc. Well guess what, it is pretty much impossible to do that. The interactions are just too great in number to be able to model and calculate with any real certainty how a brand new protein will fold in space solely based on its amino acid sequence. Instead scientists rely on homology of similar proteins and perform experiments, with a good amount of rounding off, and neglecting before a somewhat clear picture emerges from the infinitely complex system.

 

[farleyknight]

You cannot possibly compare the study of nature and the study of man made things. Computer science and their languages are created by humans, which inherently means we know every single thing there is to know about the language. There is not one letter or piece of data that we don't know about (because we created it). If you open a computer you can be sure that you can know exactly what each piece of wire/plastic does, why its there, what problems it may cause if it breaks. Its the same reason why you can learn to fix refrigerators and or cars in a weekend or two (not be an expert mind you, but you'd definitely learn a lot more practical stuff). My brother taught himself how to switch an automatic transmission to a manual transmission and did it in 1 week his first time around. Second time took him 2 days.

Computer science can get hairy too. Image recognition is a fairly difficult problem. As is the natural language processing & info retrieval stuff that Google does. Lots of data. All generated by humans. Not easy to decipher.

Compare that to studying nature. Let's take a simple example like gravity. Yeah we know it exists and there is some kind of force that attracts to particles which have mass. We've known that for hundreds of years. But even today the smartest people in the world debate how it occurs, whether it occurs the way we think it does etc. We can pop open a person's head and look at there brain and we truly don't have any idea how a conglomeration of firing neurons, fatty tissue, blood vessels etc can combine to give us this 'picture' that we call awareness. We have theories and we can explain a lot of things but in the hundreds and thousands of years that science has been trying to make sense of the world, we are still scratching the surface.

You cannot compare learning visual basic to learning physics.

Simple fact of the matter is that nature is infinitely complex and scientists and scientific studies/experiments rarely give answers. All they really do is provide better questions to be answered.

I think the main reason for your anger is that the word physics has taken on multiple meanings in this dialogue. In some cases I used the word to mean just one particular aspect of physics, enough to make it relevant to something in day-to-day life, perhaps related to making money. In that definition you could say that an automotive technician uses physics since he works with the combustion engines of cars. Of course, he doesn't have to know much theory behind it, but he is aware of it on an implicit level and could gain a better understanding through the theory. However, the type of theory they would need or want to use would be much different than a physics major would.

You could argue that that is not physics, and as far as I care, you can be correct. But that was what I meant in my examples.

If you want to use the terms in this way, and say that science is only theory and direct application of it, then Visual Basic is not computer science, since it involves the technical aspects of computers but doesn't really study computation in any fundamental way. But even if they don't know it, when they work with conditional expressions and database queries they are using boolean algebras that are theories that belong to CS.

In fact, with that definition, much of the courses a CS major has to take are just technical courses. It's for that reason I switched to Mathematics instead, since at least I brush up against enough theory to make life worth living.

The other point I want to re-iterate is that taking every single factor into account to make a calculation that is 99.999% accurate is almost impossible when dealing with the real world. That kind of precision occurs in pure mathematical problems, which to me are very abstract.

Take the example of scientists trying to model proteins and their 3D conformations. In theory we can look at a sequence of DNA, figure out what amino acids it codes for and from that information we should be able to tell you exactly how the molecule will fold in space because we know exactly what atoms are on what amino acid, which interactions will occur etc. Well guess what, it is pretty much impossible to do that. The interactions are just too great in number to be able to model and calculate with any real certainty how a brand new protein will fold in space solely based on its amino acid sequence. Instead scientists rely on homology of similar proteins and perform experiments, with a good amount of rounding off, and neglecting before a somewhat clear picture emerges from the infinitely complex system.

Maybe you have a better ability to withstand internal skepticism. But I doubt everything.

Personally, I would enjoy it if an author would admit and say what you just said. If the writers of my physics textbook were to play along with my idea and actually give every single detailed layout out over 5 or 6 pages for some silly little friction problem.. Well, I would probably be very confused. At the end, they would state their solution and say why this won't be repeated, giving a similar paragraph to yours.

They'd probably end that section saying the rest of the book will just show abstract versions, to make calculations simple. So you can forgive the author for their glaring omissions. But they have to show all the details at least once, to give the big picture. Otherwise, the book is just a big fat dictionary of laws that aren't correlated in any real way.

 

[Gokul43201]

I understand what it means now. Kind of. But I remember writing that when I first read it being completely confused. I still don't "completely" understand that definition. I don't think I would know how to apply this idea to other forces that I'm not familiar with, but for gravitational potential energy, a decent attempt at a mathematical version would be something like:

Def: Given two objects O_1, O_2, with corresponding masses M_1 > M_2, we may define the gravitational potential energy of O_1 as the gravitational force F exerted on O_2 by O_1. This is, of course, before the objects reach one another.
​

This definition is wrong on many levels, but I do not have the time for a full-fledged correction, so if no one else wants to take it up, I'll get to it when I find more time.

 

[dx]

You seem to always assume that when you don't understand something it's the problem of the textbook or the author (even when the author is Feynman... wow). Unfortunately, as you've demostrated with your 'decent attempt at mathematical definition' of gravitational potential energy (which is a high school level idea), the problem is simply that you haven't understood. If you can be a bit more humble and honest about your level of understanding, you'll be more receptive to the many excellent explanations that can be found in textbooks, and maybe you'll learn something.

 

[Yanick]

Computer science can get hairy too. Image recognition is a fairly difficult problem. As is the natural language processing & info retrieval stuff that Google does. Lots of data. All generated by humans. Not easy to decipher.

And I doubt that an intro to CS class is going to have students create facial recognition software. Which brings us back to my first point. You need a proper foundation of the 'easy stuff which doesn't really teach you anything useful' before you can get into the nitty gritty real world/advanced applications. I remember hanging out with my brother when he was taking that C++ stuff and his projects were things like making programs that take averages and standard deviations and such. I think by the end he made a 'video game' which had a little stick figure jump over a hole. This was an intro or beginner's class, and I doubt that he knows how to create facial recognition software.

I think the main reason for your anger is that the word physics has taken on multiple meanings in this dialogue. In some cases I used the word to mean just one particular aspect of physics, enough to make it relevant to something in day-to-day life, perhaps related to making money. In that definition you could say that an automotive technician uses physics since he works with the combustion engines of cars. Of course, he doesn't have to know much theory behind it, but he is aware of it on an implicit level and could gain a better understanding through the theory. However, the type of theory they would need or want to use would be much different than a physics major would.

You could argue that that is not physics, and as far as I care, you can be correct. But that was what I meant in my examples.

If you want to use the terms in this way, and say that science is only theory and direct application of it, then Visual Basic is not computer science, since it involves the technical aspects of computers but doesn't really study computation in any fundamental way. But even if they don't know it, when they work with conditional expressions and database queries they are using boolean algebras that are theories that belong to CS.

In fact, with that definition, much of the courses a CS major has to take are just technical courses. It's for that reason I switched to Mathematics instead, since at least I brush up against enough theory to make life worth living.

I don't really understand your point here. My personal view of physics is that it studies the world around us and proposes mathematical theories to explain the phenomenon. Its just that in the beginning it seems like hogwash because its intuitive that an object will move in the same direction as the net force applied (if I push you you're not going to fall on top of me). But these seemingly simple and abstract theories are the basis for all of the more advanced study. Once again we come back to the crawl before you can walk point.

Also because the 'official' definition of Physics is just, the study of matter and energy, anything anyone does can be grouped into this definition. But its just not true. Mechanics do not study physics. They acquire a task oriented skill (busted nut or bolt, replace, test, your on your way), I doubt they would sit down and tell you how much torque would be required to rip the bolt off the wheel, for instance. He probably intuitively uses physics to his advantage (watch them try to take off a stuck-on bolt, they use thermodynamics, levers, friction etc) but that is not science.

The use of principles that science has elucidated is not really being a scientist. We use these principles every single day without one thought about how and why they work the way they do. Why is walking down stairs easier than up? There is an inherent amount of potential energy stored when you ascended the stairs at some point which is going to do some work on you and allow for 'easier' descent. Is an obese person who takes elevators up but walks down considered a physicist because he's using a physics theorem to his advantage? I don't think so.

Maybe you have a better ability to withstand internal skepticism. But I doubt everything.

No I just don't get worked up over how applicable my introductory physics textbook is to the real world. Its painfully obvious to me how complex and chaotic the real world is, and I understand that to gain enough knowledge to really understand and model such a world is well beyond the scope of an intro class. Also I'm a Nurse and Chemistry major and will only be doing 1 year of physics so its really not on my list of priorities to nit pick every detail of my physics textbook. I am always arguing with the guys in the lab where I volunteer about chemistry stuff though, I tend to never just take a person's word for why something is that way. I drive them pretty crazy but at the same time I keep them on their toes and usually we both learn something.

Personally, I would enjoy it if an author would admit and say what you just said. If the writers of my physics textbook were to play along with my idea and actually give every single detailed layout out over 5 or 6 pages for some silly little friction problem.. Well, I would probably be very confused. At the end, they would state their solution and say why this won't be repeated, giving a similar paragraph to yours.

They'd probably end that section saying the rest of the book will just show abstract versions, to make calculations simple. So you can forgive the author for their glaring omissions. But they have to show all the details at least once, to give the big picture. Otherwise, the book is just a big fat dictionary of laws that aren't correlated in any real way.

I can understand that to a degree. But just to play devil's advocate for a bit. What would you really gain from an author who took a simple box on a slope problem and elucidated on aerodynamics of the box, possible wind conditions or whatever else you can think of. Considering you are in an intro class, which probably means you don't know anything, what benefit does that really give you? It doesn't help at all, all you've done is read a bunch of big words and equations that means nothing to you because you still have no idea what friction really is and how it is defined mathematically etc. If you want a disclaimer in the front of every book saying that you need to get to an advanced physics class before you can really model the effect of a head wind on a Boeing 747 traveling blah blah blah, I guess you have a point but it just seems a bit nitpicky to me.

 

[farleyknight]

You seem to always assume that when you don't understand something it's the problem of the textbook or the author (even when the author is Feynman... wow). Unfortunately, as you've demostrated with your 'decent attempt at mathematical definition' of gravitational potential energy (which is a high school level idea), the problem is simply that you haven't understood.

You're absolutely right. I don't understand a lot of it. I think that was one of the main issues behind this entire thread, right? I mean, if you read through a couple of posts, I said myself that I was confused when I read it.

On the one hand, the book gives a bad (IMO) definition of something, one of the central principles of the entire chapter from which I must thoroughly understand to actually solve the problems.

Then after giving this definition, they assume that "Informally, you already know what this is". So they re-leave themselves of giving better definition or going into further details about it. They give some informal examples but as you can tell, that doesn't help my understand much.

After reading this I, as I said before, write an expletive to show how much I'm annoyed by their vague use of the English language. At this point whether it's the books or my own fault for not understanding we can debate forever.

Regardless, I manage to make due and after reading I start on the assigned homework. The entire HW set is computerized so I know when I'm correct.. I managed to finish it although I'm mostly blundering my way through the problems, trying whatever works, never sure if my formulas are correct because I can't write formal proofs or anything. From this I assume that I understand it well enough to take a test on it.

Test time comes around and the prof throws a curve ball on exactly this topic. Suffice to say I put down something or another but it was nonsense. After falling into depression I drop the course, annoyed with the chain of events and determined to make sure it doesn't happen that way again. Thus I'm on this forum trying to get some better advice.

So for those who tl;dr I've been meditating on my own ignorance for some time and I thought I had made that clear before. I'm simply trying to find out how to correct these issues without coming back here again and again asking for help on every single problem.

Now.. as for an actual solution, you can go the self-superior route and say that I'm stupid for not understanding it. That's what many of my instructors do and for that I f*cking hate them. But whatever.

The standard thing to do is just correct me and give me a better definition. That would be nice and I would thank you for that.

But there are thousands more informal definitions that I will probably come across in other texts. Unless the members on this forum want me to post every single definition, that would be a waste of time.

What I want are the tools for understanding physics in the way that physics is taught.

I would love to find a text that taught physics as if it were mathematics, but I haven't come across that yet and I'm not going to hold my breath.

I would equally enjoy a text that showed me how to solve physics problems for people who think they don't need physics, kind of a "working mans" guide to physics that cuts across many fields. If I had practical applications of it in my life then I would be more welcoming and maybe I could start to "see" what you guys do.

Barring those two things, if I had a way to turn vague definitions into formal ones and ways of self-correcting my own problem solving, then that would probably guarantee my next shot at physics will get me an A. But for now I'm basically screwed.

 

[farleyknight]

I can understand that to a degree. But just to play devil's advocate for a bit. What would you really gain from an author who took a simple box on a slope problem and elucidated on aerodynamics of the box, possible wind conditions or whatever else you can think of. Considering you are in an intro class, which probably means you don't know anything, what benefit does that really give you? It doesn't help at all, all you've done is read a bunch of big words and equations that means nothing to you because you still have no idea what friction really is and how it is defined mathematically etc. If you want a disclaimer in the front of every book saying that you need to get to an advanced physics class before you can really model the effect of a head wind on a Boeing 747 traveling blah blah blah, I guess you have a point but it just seems a bit nitpicky to me.

Two things:

First, if the authors put in all of the details for one or two examples, and then later just neglected things, then I have the big picture for those examples and when I have to find out how fast an actual box will be going down an actual ramp I can say, with certainty, the actual forces that will be needed to measure. Trivial? Of course. Useful? Probably not. Empowering? In a small way, yes.

Second, Mathematics books mention more advanced books all of the time. Proofs are often omitted from undergrad books and left for graduate level books, and the authors will state that said proof can be found in another volume listed in the bibliography. If you aren't a math major than you might scratch you head about that.. But if you're a skeptic and demand proofs for everything, at least you can hunt them down.

 

[dx]

Well, if you're really serious, you should stop blaming the textbooks for not solving 'real world' problems. Face it, if you wanted to read about complicated real world problems, you can easily find advanced books that do exactly that. Pick up a book on design of particle accelerators, and you'll see exactly how complicated that can be.

The concepts that are used in these advanced applications are the same ones that you learn about in your elementary physics courses; what is different is the complexity of the problem. One of the important purposes of introductory courses is to understand and familiarize yourself with the basic concepts themselves, and considering idealized situations is a very good way to do this.

Also, it is not true that no real world problems are considered in elementary textbooks/courses. For example, you can calculate the shape of planetary orbits, Kepler's laws, the motion of heavy projectiles near the surface of the planet, the frequency of oscillation of a pundulum or a spring, the pressure in a fluid such as the atmosphere and how it depends on height, the relationship between pressure, voume and temperature for a rarefied gas, etc. I can go on on with this list. All of these are very real world situations, and they can all be understood using relatively simple arguments starting from Newton's laws. Once you understand these things, you can go on to more complicated situations.

Also, you are right. Many elementary textbooks are badly written. But there are enough well written books that anyone who is serious can easily find these books. Books such as Feynman's lectures, Landau's course etc. are masterpieces of exposition. That doesn't mean you can read them like novels; you will still have to work hard at them, but you will be rewarded.

 

[kjohnson]

What I would suggest doing is taking away what you can from introductory courses and books, you will always need the basic physics to solve advanced problems. What I try to do is as I'm learning something new try to figure out how it relates to all the other material i currently know. By doing this I gain a deeper understanding of all the material, often even learning much more about something I thought I already knew well. In addition if I am skeptical about something, I will propose a problem and work through it on my own until I am convinced everything is correct and fits into the big picture. Proposing your own real world problems is not that hard, look all around you..its unlocking the correct physics/math that is the challenge. It's kind of like a game, in nature you can see the end result, but you need to determine the rules and how it got that way in a manner that is repeatable.

 

[zorro]

I.E Irodov-Problems in Physics is a good book. You can solve it to develop deeper concepts.

 

[farleyknight]

This thread is mostly dead. I can't be bothered to re-read what I said. But let me at least respond to the general sentiment:

When I said solve "real world problems", I may have used some bad examples, but what I was trying to point out was that the profuse use of "neglecting quantities" that introductory texts use prevents anyone with intuition of the "real world" to be able to solve the problem.

Take for example, the projectile problem. Intuitively, you know that the are forces like gravity, air resistance, the spin of the projectile, etc all act on the projectile while in motion. For a truly accurate and precise measurement, down to the width of a human hair, of where that projectile will land, you must have these, along with a lot more.

It is in this sense that I mean "real world", as any sufficiently advanced method for computing the trajectory of an object should at least include these. If I was asking too much then it is due to my naivety about what problems in physics are reasonable and which are not. As far as I knew at the time, physicists were supermen that can be accurate to 200 decimal places if they wanted. ****, they have to do that for spacecraft . Why not for us?

Continuing with my projectile example, most textbooks will tell you to "neglect air resistance". Why? Well, if you're at the introductory level, you won't be told why. But you're expected to accept this anyways. This acceptance may sit well with you or maybe it doesn't.

I know some people might be "okay" with being "approximately right". Call me a silly existentialist, but I would prefer to be exactly correct. If I can't, then either the problem is ill-posed or I am somehow flawed.

As someone with a heavy computer science background, I prefer the discrete topology {true, false}, not the open interval (0, 1) when I most provide answers to important questions.

You find out later on that introducing air resistance makes the differential equation (why didn't they use *those* instead of the silly algebraic equations? they are much more elegant) unsolvable by elementary methods and that it is usually solved by numerical methods.

I hope you can see that I'm approaching this from a completely different angle than the average student and therefore I do not understand how average people can accept what is said in these textbooks.

I really feel like I won't "understand" physics until I understand it's limitations. I doubt anyone can make a complete list of them, either. It will just boil down to me accepting what is in front of me like some Sunday school boy being told God created Man and any questions about who created God is silly.

 

[kjohnson]

This is out of my realm, so someone correct me if I'm wrong..but i believe what farleyknight is talking about is pretty much chaos theory. The idea that there are so many variables to a "real world" problem that it is impossible to include all of them. This is why one can't predict the weather for all time (or even for short times haha). For instance if you change the initial conditions to some complex differential equation the solution may be very different.

 

[farleyknight]

This is out of my realm, so someone correct me if I'm wrong..but i believe what farleyknight is talking about is pretty much chaos theory. The idea that there are so many variables to a "real world" problem that it is impossible to include all of them. This is why one can't predict the weather for all time (or even for short times haha). For instance if you change the initial conditions to some complex differential equation the solution may be very different.

I've been attracted to chaos theory well before I enrolled in college. Whether my doubts about the validity of mathematical models was put into question before then, I'm not sure.

But I'm rather happy that, even though I'm taking Diff Eq again after transferring to a 4 year school, it's more focused towards Dynamical Systems, so all the better.