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DrD

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Everything posted by DrD

  1. Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #46 Comments on A Calculus Challenge I would like to thank all those who took part in the Challenge. My solutions and comments are attached. 46 CalcChallengeComments.pdf
  2. DrD

    A Calculus Challenge

    Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #45 (c) DrD, 2018 It has been quite a while since I last posted anything here, but an interesting problem has come to mind that I wanted to share with you. If you really know calculus, this should be straight forward; if you don't know calculus, don't even try! MEForumChallenge.pdf *********************************************************************************************************** THE CHALLENGE IS NOW ENDED. I WILL NOT RESPOND TO FURTHER ANSWERS. i EXPECT TO POST A SOLUTION AND A FEW COMMENTS IN THE NEXT FEW DAYS. ***********************************************************************************************************
  3. DrD

    A Calculus Challenge

    I'll get to you William. Please be patient. I have a few other things going on right now. DrD
  4. DrD

    A Calculus Challenge

    Dear Mucugia, The challenge is now closed, and I will not be reviewing additional work any longer. Thanks for the effort. DrD
  5. DrD

    A Calculus Challenge

    Dear Mucugia, Two problems: (1) It looks like you may have left out a page. You sent Page 1 and Page 3, but what about Page 2? (2) Neither of the pages that you sent are complete. The PDF does not show the final result on either page. You might do better to copy these pages over , writing a bit smaller so t hat the scan will capture the whole page. DrD
  6. DrD

    A Calculus Challenge

    Dear Amin, Well, I have both the 2nd and 5th editions of Roark, so I am unable to tell whether the book is correct (or if you read the book correctly). That's the problem with using a reference source (although Roark is widely recognized). I'm amused that you said, "When they ask "how do you gget formula?" the answer will be "here is the formula in the book." Does that really convince you? Are you more convinced by something in a book, or be a carefully worked out derivation that you can follow for yourself? I'll take the derivation every time!! It is certainly true that handbooks have their uses. The problem is, they also have their limitations. If there are assumptions made in the derivation, looking the formula up in a book may not tell you about those assumptions. I'm sorry that you evidently find the area moment of inertia expressions just too tedious to be worth your time. For those who want to find out if they really can use calculus, this remains a very useful exercise. DrD Dear HKS, You promised results after the New Year. Just which New Year did you have in mind? DrD
  7. DrD

    A Calculus Challenge

    Thanks for the information, Jarek. I do not like MS Word, and would never use it given any choice in the matter. But, I know many others like it, so this is useful. DrD
  8. DrD

    A Calculus Challenge

    Dear Jarek, Thanks for the comment on Mathtype. I have heard of it, but know little about it. I use LaTeX for all of my work, but I like the way your work looks very much. DrD
  9. DrD

    A Calculus Challenge

    Dear Jarek, Just as a matter of curiosity, how do you write the equations in your work? They are clearly type written, but I'm curious what software you use for this. Is it MS Word, some other word processor, or what? It looks good, but I'm interested to know more. DrD
  10. DrD

    A Calculus Challenge

    Dear Jarek, I cannot quite agree with your result. I think you may have an algebraic error in the calculation of y2-bar. I'd look there first. Interesting approach, I must say. DrD
  11. DrD

    A Calculus Challenge

    Dear Wasulia, Congratulations, you got the correct answer, almost. Two comments come to mind: (1) You made an error in factoring out R^2 in the last line; (2) You should learn that, when doing calculus, angles are always expressed in radians, so your factors 360, 180, etc are really errors. Learn to think in radians; it will help you a lot. You took the long way around, but you almost got here. Good effort. ----------------------------------------- Dear Jarek, You are correct in saying x-bar is zero. I'm amazed that no one else has seen that yet! Without saying yes or no to your result for y-bar, I have two comments for you: (1) I urge you to provide a sketch showing how you formed the integrals you offer as a route to the answer. (2) You already have an expression for the area, so I would urge you to substitute it and seek to simplify the result. DrD
  12. DrD

    A Calculus Challenge

    Dear Amin, There are a few problems with your answer. 1) If you are going to cite Roark, you should surely say which edition. There are many, and they are not all the same. I have two of them myself, but quite likely not the one you use. 2) You don't give your final result for the area. You simply cite Roark, but there is nothing here that I can check. Roark has been known to be wrong. 3) You give an answer for something you call "static moment," but you do not locate the centroid. 4) You say, "The same for moment of inertia." The same what? You have given any answer before (unless you meant your area result), so this is no answer at all. 5) You seem to think actually answering the question is beneath you because you know how to look in a book. What do you do if the book is not at hand? 6) You said, "When I had to deal with these kind of problems, I used to go to handbooks." Do you think handbooks have all the answers? Do you no longer do engineering? Overall, I'd say this is a fairly poor effort by someone who really is not very interested. DrD
  13. DrD

    A Calculus Challenge

    Well, as of now (4 Jan 2019), over 1000 people have looked at this problem, one person has worked one part of the problem statement, and another says he know how to do this without integration (and thus far, without results). You folks are real balls of fire!! DrD
  14. DrD

    A Calculus Challenge

    Dear Jarek, Your figures help a lot to explain your logic. Thank you. I'd say you definitely have the answer for the first part. Now, can you extend this to obtain the other answers ? DrD
  15. DrD

    A Calculus Challenge

    Dear Jarek, Your final result for the enclosed area is correct (if we ignore some notational inconsistency, r in place of R). Congratulations!! That said, I cannot follow your development. Would you explain your reasoning with some words, perhaps? In particular, you show the sum of two integrals equal to a third integral. How is that equality established? I cannot follow it. Also, you write in the integrand in one place xtgalpha; what is this? Is "tg" the tangent function? If so, it would help if you would enclose the argument in parentheses. Now, to all others, I hope you see that the problem is not impossible. Why are you so unwilling to try it yourself? DrD
  16. DrD

    A Calculus Challenge

    My word! An answer ... I'm simply stunned! If you are sure it can be solved without integration, go ahead. This will serve as a check on the results obtained by integration. If you use formulas from a book, please be sure to give their derivation as well. DrD
  17. DrD

    A Calculus Challenge

    Today, 29 December, there have been over 300 people look at this problem, and yet not a single comment! What is it with all of you? What are you thinking? Is the problem unrealistic, so that it would not be useful to know how to do it? I can cite cases where this geometry really appears. Is the problem too hard? You are supposed to be engineers, able to confront new situations and find ways to deal with them. Why is this any different? Is the problem too easy, and therefore beneath your dignity? If so, please humor an old man, and indulge him by answering the questions. Whatever the situation, somebody please say something!! DrD
  18. Sorry, JAG. It does not happen on my Win7 machine. I'm just old and past my "use by" date! DrD
  19. Wow!! Great article!! Just what language was that in, anyway?
  20. DrD

    A Calculus Challenge

    As I check this on 26 December, there have been over 200 people look at this problem. Thus far, not a single one has ventured even the first bit of an attempt. What do you folks do when confronted by a problem that is not in the textbook? DrD
  21. It is possible that I may be able to help you, but again, I may not. Please answer a few questions for me. 1) What college level math courses have you taken? 2) What college level mechanics courses have you taken (statics, dynamics, vibrations, theory of machines, etc)? 3) Where are you located? 4) Are you able to pay for tutoring? DrD
  22. As an older engineer, I am rather dismayed by what I see as the results of engineering education today. I have seen most young engineers come out of their college degree programs with a modest familiarity with come CAD program and a related Finite Element program, and an almost complete lack of capability to analyze machine components without the use of FEA. Thus they are unfamilliar with basic design calculations relating shear stress in a shaft to the power being transmitted, the shaft sped and the shaft diameter. Instead, they want to create an FEA model and run the numbers that way which is simply not the way you make any progress in designing a machine. It is certainly true that FEA allows for a good detailed stress analysis of complex geometries, something that was not possible in general by the older methods. But the results obtained are highly dependent on the skill of the user in applying the correct boundary conditions, something that is a bit of an art in itself. I have observed a tendency to even want to use FEA to do kinematics, rather than using simple, rigid body kinematic relations. This seems like pure foolishness in almost all cases. Are we not developing a tendency to lean too heavily on the computer, rather than to learn to think as engineers? I would be happy to hear some comments and discussion from others on these matters.
  23. A brake is a brake is a brake. Any brake has the potential to stop any rotating object. Whether it is a good idea or not is another matter, but certainly an automotive caliper brake has the potential to stop a winch drum. You really need to learn the difference between "brake" and "break." They are entirely different words, even though they sound alike in English.
  24. Wow! That was one boring video! I could not stay interested enough to watch it to the bitter end. The whole idea seems ludicrous. If you want to generate energy by human effort, why not apply it directly? Perhaps simply ride a bicycle, rather than try to generate electric power by pushing things. Talk about grasping at straws ...
  25. I rather doubt that you will ever get to the point where you fully understand the problem. Most of us find that there is always something more we can learn. At the same time, it seems foolhardy to commit to designing something about which you know so little. There is nothing about which I know everything, yet I would undertake to design some things but not others. I would design those things about which I already know enough to make a good start. I would avoid attempting to design something about which I now know nothing. Do you see the difference? DrD
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