So I've read many answers on the internet and have not yet come to understand the origin of the normal force. What I've to come to understand about the normal force, is that it is the electromagnetic repulsion between the electrons of the two surfaces which come into contact with one another(is this right?) Secondly, I've read about asperities and the formation of cold welds between the asperities I understand the cold welds are due to bonds formed between the atoms in contact at the surface.  So here there are two forces, one is the repulsion and the other is the attraction forming bonds between surfaces. Which one of them is the normal force? How exactly do any of these forces cause friction?  f1 is the force trying to move the body, but f2 is the force trying to restore the body In the picture above, suppose I am trying to move one surface over another. Bonds have already been formed between the two surfaces, so when I try to move the objects relative to one another, the bonds oppose the motion, and try to restore it back to the original position. Do I think of friction this way? Please bear in mind I'm a student still in high school so kindly explain it as if you were explaining it at a fairly non advanced level.
It is a general concept that horizontal forces can only influence physical quantities along horizontal direction; similarly vertical force can produce acceleration etc. only along vertical direction. This is the same concept that helps us study projectile motion as a combination of two independent motions. If this relation is universally true, how come, then friction depend on a force which normal to it?
Selecting text in profile activity comments causes unexpected clipping I need to prove that $K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function  in $K$ is bounded.  One direction is obvious because of Weierstrass theorem. How can i prove the other direction? I tried to assume the opposite but it didn't work for me.  Thanks a lot. $4$ letter words taken from the letters of CONCENTRATIONS How many words with or without meaning can be made from the letters of the word CONCENTRATIONS by taking $4$ letters at a time?  There are  $14$ letters total present in the word. $4$ letters can be picked in $14\choose 4$ ways. $4$ letters can be arranged in $4!$ ways. So ideally answer has to be ${14\choose 4} * 4!$. But I know this answer is wrong because some letters are repeating. How do I solve this then? I appreciate any help. How do I pass the forest stage on Candy Box 2? I cannot pass the forest stage on Candy Box 2. The dogs and forest mosquitos kill me fast.  My stats and equipment are:   220 health Polished silver sword (7 damage, also have the trolls bludgeon; 12-16 damage) Leather boots and gloves (no stat bonus) Basic and advanced spells from the witch across the bridge   On another save I also increased my health to 1000 and still could not pass the forest stage, any advice?  Thanks. If a drive doesn't know about partitions and files systems why moving a file from one partition to another takes relatively long time, unlike the instantaneous move on the same partition? Is that file system inefficiency? In this case, NTFS. It seems like the file is being copied and then original is erased, instead of removing the entry about that file in one partition and making it in another? How To Create A 'Two-Sided' Unique Index On Two Fields? How can I efficiently create a unique index on two fields in a table like this: create table t (a integer, b integer);  where any unique combination of two different numbers cannot appear more than once on the same row in the table.  In order words if a row exists such that a=1 and b=2, another row cannot exist where a=2 and b=1 or a=1 and b=2.  In other words two numbers cannot appear together more than once in any order.  I have no idea what such a constraint is called, hence the 'two-sided unique index' name in the title.  Update: If I have a composite key on columns (a,b), and a row (1,2) exists in the database, it is possible to insert another row (2,1) without an error.  What I'm looking for is a way to prevent the same pair of numbers from being used more than once in any order... Samsung netbook NP300E5A dimming on battery My Samsung netbook NP300E5A screen is continually dimming.  The screen is forty percent dim on battery, but if I plug in the charger, the screen will be normal. I have tried all I know and I could not fix it. What should I do? what am trying to explain  is that the system is dimming like flooricent light  the screen resolution systems are all ok. When I pluging my charge the dimming we stop but when is on battery it look like flashing someone  light when driving Limit of a function with powers (L'Hopital doesnt work) I have a little problem with limit of this function:  $\lim_{x \to \infty} x^2(2017^{\frac{1}{x}} - 2017^{\frac{1}{x+1}})$  I have tried de L'Hopital rule twice, but it doesn't work. Now I have no idea how to do it. Yesterday I upgraded my Ubuntu 18.10 to Ubuntu 19.04, and after the restart, the trash icon and my Desktop files have disappeared from the UI. If I go to the Desktop folder from my personal folder, I can see the files, but my Desktop is empty.  How can I show my files in the Desktop again? I've just finished running my first session with only one player, and it felt pretty different from running a session for a group.  Could someone with more experience in this talk about what one should do differently in that situation?  I'm not referring to mechanics like encounter-building, but just how to handle the change to the social dynamics. For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$? $$x^n-a$$  So $n$ is any integer greater than 1, and $a$ is any integer.  $a$ being any integer is where I am running into trouble.  I have already shown and worked out a proof for this being irreducible when a is prime.  Now I am just working through examples, trying to figure out a pattern.  The exercise is asking for application of Eisenstein's Criterion only, so I am assuming that the value of n should have no effect on the irreducibility. Given $S \hookrightarrow T$ construct $U ≈ T$ disjoint from $S$ in Z set theory? Can I use the Adwaita theme in Unity without installing GNOME shell? I recently installed Ubuntu 11.10 (new install). I would like to use the Adwaita theme with Unity, but it seems that it is not available in the theme selection dialog. I know I get it there after installing gnome-shell, but is there a way to use Adwaita theme for Unity without installing gnome-shell? Why am I getting shopping trolley notifications about local store savings? I am getting "Shopping Trolley" notifications appearing regularly. The notification looks like this:   The notification is about "Store savings" at a local supermarket and that is it!   Is this notification from Google Maps or another application like Google Assistant? I'm struggling to find the specific setting to disable the notification.  I am also interested to know if this notification could in any way be targeted advertising generated by the store. My marketing preferences with the store are opt-out and this strikes me as very dumb advertising. Surely Google isn't doing this? Is there a means that a store can generate notifications like this? Could it be targeted if they have my email address?  These are pain and I want to understand why they are spamming me and disable them without disabling everything else.  I can see various options under Google Maps, settings, notifications. Which setting would apply? Could it be "New on maps, Get occasional updates about new features in your area"? I can't see what setting to suppress!  Thanks for all help. Undefined variable problem with PHP function I am looking to set up Ubuntu Server as a headless NAS for my home. I would like to have file storage there, as well as a central hub for my MP3s and pictures.  What are the best packages out there to handle this? Can someone post a link to a good tutorial or post some tips?  One constraint I have is that it has to be Windows 7 friendly. By that I mean the shares and streaming should work for a Windows machine. Support anchor names in posts I admit this feature request is probably somewhat limited in useful scope, but I'm throwing it out there anyway. Inspired by , and because I want to use it on , I'm requesting that name be supported on a tags in posts.  On very long answers, such as the closing/migration guidance answer, this would allow direct linking to the specific closure reason. This would then allow us, when someone , to link directly to the appropriate reason and description thereof.  I recognize the limited scope of this, however, I have seen other long answers that could stand to have that kind of "deep" linking ability as well.  (The original incarnation of this post had either name or id, but preferenced name. Per Koper's answer, which I agree with, I took out the idea of supporting id, because Koper's right -- too dangerous.) What is the role of NS records at the apex of a DNS domain? $ORIGIN example.com. ; not necessary, using this to self-document  $TTL 3600 @        IN     SOA   ns1.example.com. admin.example.com. (                       1970010100 7200 1800 1209600 300)  @        IN     NS   ns1.example.com. @        IN     NS   ns2.example.com.  @        IN     A    198.51.100.1 ns1      IN     A    198.51.100.2 ns2      IN     A    198.51.100.3  sub1     IN     NS   ns1.example.edu.  sub2     IN     NS   ns1.sub2 ns1.sub2 IN     A    203.0.113.1 ; inline glue record   The role of a NS record beneath the apex of a domain is well-understood; they exist to delegate authority for a subdomain to another nameserver. Examples of this above would include the NS records for sub1 and sub2. These allow the nameserver to hand out referrals for portions of the domain that it does not consider itself authoritative for.  The purpose of the NS records at the apex of a domain, ns1 and ns2 in this case, seem to be less understood by the internet at large. My understanding (which may not be holistic) is as follows:   They are not used by caching DNS servers in order to determine the authoritative servers for the domain. This is handled by , which is defined at the registrar level. The registrar never uses this information to generate the glue records. They  used to delegate authority for the entire domain to other nameservers. Trying to do so with software such as ISC BIND will not result in the "expected" referral behavior at all, as the nameserver will continue to consider itself authoritative for the zone. They are not used by the nameserver to determine whether it should return authoritative responses (AA flag set) or not; that behavior is defined by whether the software is told to be a master or a slave for the zone. Most nameserver software will quite happily serve apex NS records that disagree with the information contained by the upstream glue records, which will in turn cause well-known DNS validation websites to generate warnings for the domain.   With this being the case, what are we left with? Why are we defining this information if it doesn't appear to be consumed by caching DNS servers on the internet at large? How do I start a process from C#? How do I start a process, such as launching a URL when the user clicks a button? Sweave.sty causing error in verbatim environment?