Why does friction does not depend upon area of contact? Why does friction does not depend upon area of contact ? Now we know that friction=(coefficient of friction)*Normal.So also is, why does friction arise.Is it because of the irregularities of a surface or because of the electrostatic forces in between the surfaces?
Dependence of Friction on Area Is  really independent of area? The friction force, $f_s = \mu_s N$. The equation says that friction only depends on the normal force, which is $ N = W = mg$, and nature of sliding surface, due to $\mu_S$.   Now, less inflated tires experiences more friction compared to well inflated tire. Can someone give clear explanation, why friction does not depend on area, as the textbooks says?
Is there a way to make an Oracle query behave like it contains a MySQL limit clause? In MySQL, I can do this: select *  from sometable order by name limit 20,10  to get the 21st to the 30th rows (skip the first 20, give the next 10). The rows are selected after the order by, so it really starts on the 20th name alphabetically. In Oracle, the only thing people mention is the rownum pseudo-column, but it is evaluated before order by, which means this: select *  from sometable where rownum &lt;= 10 order by name  will return a random set of ten rows ordered by name, which is not usually what I want. It also doesn't allow for specifying an offset. What are these auxiliary file descriptors? While poking around /proc/self folder for my mksh shell,  I found a peculiar thing: in /proc/self/fd/* there are all the standard file descriptors (0 for stdin, 1 for stdout, and 2 stderr) some file descriptors, but also some extra ones - 24, 25, 3. And I technically can list them with a glob in the shell:  $ for fd in /proc/self/fd/* ; do echo $fd ; done                                                       /proc/self/fd/0 /proc/self/fd/1 /proc/self/fd/2 /proc/self/fd/24 /proc/self/fd/25 /proc/self/fd/3   But when I try to stat them or use find on them, they are reported as non-existent.  $ find  /proc/self/fd/*                                                                                /proc/self/fd/0 /proc/self/fd/1 /proc/self/fd/2 find: ‘/proc/self/fd/24’: No such file or directory find: ‘/proc/self/fd/25’: No such file or directory /proc/self/fd/3   Same occurs in bash , but just with just one auxiliary file descriptor.  $ for fd in /proc/self/fd/* ; do echo $fd; done /proc/self/fd/0 /proc/self/fd/1 /proc/self/fd/2 /proc/self/fd/255 /proc/self/fd/3  $ find /proc/self/fd/* /proc/self/fd/0 /proc/self/fd/1 /proc/self/fd/2 find: ‘/proc/self/fd/255’: No such file or directory /proc/self/fd/3   Question is: what are those additional file descriptors? What is their purpose? When you energise a taut string, the following resonant modes of vibration occur:    Plotting on the frequency domain, you can see their corresponding frequencies:    But what is the underlying physical principle? Why does this happen?  Is there any way of explaining it that could be understood by a smart 15 year old?  EDIT: I'm going to give my best attempt so far. Here goes:   We can start with sympathetic resonance. Sounding a particular frequency, a pure sinewave.  And noticing the string resonates sympathetically at the frequency of each harmonic. Say this is explained and understood. Now imagine that plucking a string is equivalent to a burst of white noise, which contains frequencies all the way through the spectrum. This could be approached backwards, by starting with random frequencies and noticing that resultant wave produced looks like white noise.   If the above is scientifically correct, then it restricts the domain of the question.  I would really like to be able to understand it scientifically and also be able to explain it intuitively.  PS Images from Quantum mechanics and everyday nature Is there a phenomenon visible to the naked eye that requires quantum mechanics to be satisfactorily explained? I am looking for a sort of quantic Newtonian apple. Suppose Alice chooses a random Prime $p$ and a random private Key $a \in \mathbb{Z}^*_p$. By accident, she also chooses a random number $g \in \mathbb{Z}^*_p$, which is not a generator of $\mathbb{Z}^*_p$ and therefore  $$\langle g\rangle \subset \mathbb{Z}^*_p$$  as opposed to $\langle g\rangle = \mathbb{Z}^*_p$, which would yield a valid key. Alice then computes $A \equiv g^a \pmod{p} $ and publishes the Tuple $(p,g,A)$ as her public key.  Bob now encrypts a message $M$ using Alices public key by computing  $$C_1 = g^b \pmod{p}$$ $$C_2 = M \cdot A^b \pmod{p}$$  Is it possible for an attacker (Eve) to distinguish a “real” ciphertext $(C_1,C_2)$ from a random ciphertext $(Z_1,Z_2) \stackrel{$}{\longleftarrow} \mathbb{Z}^*_p$ with significant advantage (say $Adv \geq \frac12$)?    Edit: I guess it should be enough to show, that the ciphertext cannot be random, if  $$\langle g \rangle \neq \langle C_1 \rangle \quad(\text{or $Z_1$, respectively})$$  But how can Eve check for this property efficiently? Can someone point me in the right direction here?    Edit: A real-world situation where this flaw occurred Another Question in Hatcher Making 3 points stick on a plane / flag with wind I have a flag I want to waft in the wind. I imported the shape as an SVG from Adobe Illustrator.  I converted the mesh to a curve.  It wouldn't let me make some subdivisons but it still seems to work with the cloth property.    When I press play, you can see the structure of the flag stops.  How can I make those last 3 points intact? Also the fill colour seems to have disappeared, do you know why and how I can bring it back?    Thanks  Steve  File here: Using a Sprite image with input When umpire change the cricket ball, was the old ball thrown as waste or keep for reuse? How to insert a figure between two texts? I'd like to create something similar to what is give below: text on either side of a vertically centred image: why are the best questions the ones which have been closed? I frequently come across a really useful answer on StackOverflow which has been closed because it doesn't match the Q&amp;A format.  Examples include  ,  ,   ,  and there are others.  Where should this information be exchanged if it's not on stackoverflow?  It seems the moderators are often somewhat overzealous...  ---edit  When I say best, I mean they are informative and useful for someone who's looking for an answer to them.  Even if they do become a bit of a discussion, I value other people's opinions on the relative merits of the different JPA frameworks.  I come here looking to choose one and the answer helps me.  So what if it's not a definitive answer?  ---edit  I don't care how popular a question is, nor how interesting it is.  Users are interested in stuff that's useful to them.  Plenty of those were useful (as judged by the upvotes on the answers: 'This answer is useful'), but closed because they didn't have a definitive answer, as far as I can tell.  ---edit  Seems I'm not the first person to think this: there are various similar questions to mine like this one:   In it the user lists lots of other useful questions which have been closed:                    So isn't there a place on stackoverflow for these questions?  A discussion section, maybe? Are $_SESSION variables stored on the client or the server? I'd like to assign a frequently used string to a shortcut key, so when I press it, it types it in whatever application I'm in. So for example, when I type Shift-F12, it types "This is wonderful!" in whatever Gnome app I'm in at that time. Which is better: Employer-sponsored HSA or opening an HSA individually? So I know that:   Employer-sponsored HSA's allow you to deduct contributions directly from your paycheck, pre-tax With individual HSAs, you must contribute using post-tax dollars, then deduct those contributions from your taxable income when you do your taxes   Given those facts, I guess it's marginally better to use an employer-sponsored HSA because it means the government doesn't temporarily hold on to your taxed income, only to return it later after you do your taxes; you could theoretically put that money to work in an investment vehicle instead of having the government hold it hostage for a while.  But are there any other benefits (either way) that I'm not aware of? The  kind of threw me with the following statement:     The main advantage of making pre-tax contributions is the Federal Insurance Contributions Act tax (FICA) and Medicare Tax deduction, which amounts to a savings of 7.65% each to the employer and employee (subject to limits of the Social Security Wage Base).   But I'm not really sure what that's telling me.  My employer is offering an HSA, but is not offering to contribute to the HSA or match my contributions. So if it's all pretty much the same, I'd rather use the bank of my choosing and manage it privately.  Thanks. I added addresses of python 2.7, and Anaconda 4.1.1(Python 3.5) to PATH variable in Windows 10, whenever I run "python" from cmd, program which was added earlier is executed.How can I access both of them depending on my choice without altering name of either my 4 week old daughter will not stop crying. We've tried everything from sucking, both on pacifiers and fingers to breastfeeding, white noise, movement, diaper is clean she doesn't seem to have a fever.   We've tried everything we can read about and think of.  We are both a little bit ill, the common cold and the baby may have gotten it and be upset but we are just at the end of our nerves when nothing helps our poor little one!   Does anyone know anything we can do to help? How to deal with hierarchical / nested data in machine learning Restore main APFS container to full disk What is the Python equivalent of static variables inside a function? What is the idiomatic Python equivalent of this C/C++ code?  void foo() {     static int counter = 0;     counter++;     printf("counter is %d\n", counter); }   specifically, how does one implement the static member at the function level, as opposed to the class level? And does placing the function into a class change anything? What happens if you are refused entry between two countries? Last month, I was travelling on a backpacking trip across Russia and the Baltic states (Schengen zone). I'm an Indian by nationality. So I had to get the respective single entry visa for Russia and Schengen Europe.  At the border crossing into Estonia by road (at Ivangorod-Narva), I exited the Russian border with an exit stamp (so now I can't go back to Russia since I had a single entry visa). When I was at the immigration checkpoint of Estonia, I was heavily questioned on the intent of my travel to Europe while entering Estonia by road.   Though I finally got into Europe, It got me wondering - what happens if a foreign national is denied entry into a country not at the airport but by land between 2 countries he cannot go into ?  Generally, if you are denied entry at the airport the airline has the obligation to fly you back to your country. But what happens when you are stuck between two countries and you cant get into either ? What happens to you then ?