DrD

Is it really necessary to ask such a question? Consider what would happen if the heat were not dissipated, and you'll quickly come to the answer.+

Can this question really be answered in general, that is, without specifying the machine element? For some, strength is a major consideration, while for others corrosion resistance it the main determinant. The list goes on and on. This question has no answer.

Whatever in the world is an "economical joint"? In American slang, a "joint" is sometimes a bar or restaurant, so an "economical joint" might be one where the prices are modest. In other American slang usage, a "joint" refers to a marijuana cigarette, so presumably an "economical joint" might be inexpensive marijuana. Just what in the world did the Administrator have in mind for an "economical joint"?+

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

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

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

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

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

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

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

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

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

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

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

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