I have a sphere moving forward with v (pre collision) = v1i  A second sphere colliding with the first one has its own pre collision velocity = v2i  The collision should be not totally inelastic (like, you know, the case of two human bodies colliding each other), but for my purpose I think I can consider the coefficient of restitution = 0  Using the formula   $$ I  = mv_f - mv_0$$   and replacing I with F * (delta)t I woul like to know how can I compute that F, since I don't know what will be v(post collision) because it is my final unknown to compute. And I think that force should be computed with the relative velocity of the two spheres, but I have no idea at the moment on how to proceed. Any suggestion will be strongly appreciated.  UPDATE  Thank you for your suggestion ja72.  So in that case can I write something like this?  $$  F *\Delta t = \frac{ (\epsilon+1) \left(v_2-v_1\right)}{\frac{1}{m_1}+\frac{1}{m_2}} $$   But in this case, how am I supposed to evaluate final velocity of the two spheres?
It has come to the point in my computing program now where I have 5 swinging pendulums that are all modified at once by slider values. These values are drawn onto the from and passed through the class pendulum. To change the values the update button is run, and their is a default option to use a setup that works. The values are also shown on screen through some simple labels. The zero button sets all values (except length) to zero.  The values for each pendulum drawn is:   String length angle Acceleration (angular) Angluar velocity Damping or friction Gravity   My calcuations for these values: (Bob = the weight at the end of the string, and there are X and Y Co-ordiantes for it.  bobX = originX + (Math.Sin(angle) * length);         bobY = originY +(Math.Cos(angle) * length);   Caclulate Acceleration:  Angular Acceleration = (-1 * gravity / length) * Math.Sin(angle);    Increment Velocity:          Angular Velocity += Angluar Acceleration;   Increment Angle          angle += AngularVelocity;   Friction action, pendulum eventually 0's          AngularVelocity*= damping;   Now my next task is to make the pendulums collide "realistically" and recreate a newtons cradle type effect. I've looked into elastic collision solutions on particle e.g. here is an excellent example:    I've also looked at the raw physics behind it  but my brain couldn't get to grips with the raw physics side of things.  So I'm wondering if anybody could help me figuring out the theory for the collisions.  My current idea is when the co-ordinates meet the velocity will simply change polarity e.g. +10 to -10 in the opposing pendulum. Am I correct here?  If you are into code I've posted the code on stack overflow
Count occurrences of each element in a List[List[T]] in Scala sorry fresh user. I installed about 9 days ago and had issues with Unity disappearing which took 5 days of headaches to fix. It never did fix, I reinstalled.   I set up Plex (media server) and while the server is running and can be accessed by external network devices, I can't add files. Plex says this is because of permissions. I have gone up and down the forums here and at Plex to get an answer. It seems everyone says   chmod -R 755 /media/My\ Book/Videos   will change permissions to allow the folder "Videos" on my external USB 2.0 NTFS 3TB Western Digital drive (which is mounted and accessible through the file manager) as well as every sub-directory and file contained therein to be accessible to user "Plex".  I have used file manager and as soon as you click to change permissions it changes right back. When I chmod with -c it tells me every file is changed (usually 600) to 755 as I commanded it to do. I did   ls -l   to verify and there is no change. (I also used ls -l to make sure I knew who the owner was and it is me (mvl1014). ls -al gives me the same info.)  I swear to god I tried to sudo it and after smashing my head against this keyboard for basically the entirety of my day, I tried it as root. I was scared shi-less but couldn't come up with anything else. sudo su to root and then chmod -R -c /media/My\ Book/Videos  Same result. -c told me every single file was changed and a check in Unity or in terminal confirmed not a darn thing changed.  Now it seems to me that even if that isn't the thing stopping Plex from working there is still a problem with this command not going through.  12.04LTS -- on gen 1 i7 (2.7 GHz I believe) with 6 GB ram   I've attempted to attach a screenshot but I'm told I need 10 reps to do so, which means I'm copy/pasting too.  Please excuse my obfuscation, but Lorem Ipsum seemed unnecessary. And I tried multiple ways to format this but it looks perfect every way and messed up each time in the preview below. (Ugh, I'm a mess.)  $ chmod -R -c 755 /media/My\ Book/Videos  .....  .....  .....  mode of `/media/My Book/Videos/xxxx/xxxx/xxxx.mkv' changed from 0600 (rw-------) to 0755 (rwxr-xr-x)    ls -al shows:  mvl1014@FX6800:/media/My Book/Videos$ ls -al   total 88  drwx------ 1 mvl1014 mvl1014     0 Aug 28 15:17 .   drwx------ 1 mvl1014 mvl1014 20480 Sep  3 14:29 ..  drwx------ 1 mvl1014 mvl1014  8192 Aug 28 15:18 xxxx drwx------ 1 mvl1014 mvl1014 49152 Aug 16 14:02 xxxx drwx------ 1 mvl1014 mvl1014  8192 Aug 27 21:36 xxxx drwx------ 1 mvl1014 mvl1014  4096 Jul 23 19:09 xxxx   I apologize if this has been asked. I looked through this place plus at all the suggested "Similar Questions". The closet thing I got to an answer , but running the provided code with my own UID didn't work either. In set theory, if natural numbers are represented by nested sets that include the empty set, how are the rest of the real numbers represented as sets?    Thanks for the answers. Several answers basically said for irrational numbers that  A Dedekind cut is a pair of sets of rational numbers $\{L, R\}$. The set of real numbers is defined to be the set of all Dedekind cuts, where a Dedekind cut is a pair of sets of rational numbers $\{L, R\}$ which have no elements in common, and where all the elements of $L$ are less than any element of $R$.  Each Dedekind cut is a real number. This is where I have a problem - surely that can’t be correct. The set $L$ is a set of all rationals, and there must be a rational in the set $L$ that is greater than all other rationals in that set, even if we have no method of determining it. And similarly, there must be a rational in the set $R$ that is less than all other rationals in that set, even if we have no method of determining it. If every irrational number has a corresponding set $L$, then each irrational number has some such corresponding largest element of that set $L$, and then each irrational number has some corresponding rational number. And that would mean that the irrational numbers are countable. So, with Dedekind cuts,  the only conclusion is that there must be irrational numbers $x$ which are either greater or lesser than some irrational cut $y$ of the rationals, and between $x$ and $y$ there is no rational number.  But that is impossible, so that the Dedekind cuts cannot be the correct representation of the real numbers.  Surely the problem with Dedekind cuts is in using sets of rationals that include all rationals up to a certain rational. But there is an alternative method of representing irrationals can be defined in terms of infinite sets of rational numbers. For example, in binary notation, the non-integer part of $\pi$ is $.00100100\ 00111111\ 01101010\ 10001$. You define a set by: if the nth digit is a $1$, then  the natural number $n$ is in the set. And then we have that, for the real numbers between $0$ and $1$, that the set of real numbers is simply the set of all subsets of natural numbers. Each subset corresponds to some real number between $0$ and $1$.  And in this way, all real numbers can be considered to be some set based only on nested sets of the empty set.  But I still haven’t got a satisfactory answer for how negative numbers can be represented in terms only of sets containing the empty set. Any ideas? This question led to a new package:      I'm giving my students an old exam and barely remembered to change the date at the top. A colleague and I joked about how long we could reuse the same exam, and it made me wonder if I could use LaTeX to create an exam that looked like it was written in 1963 on a typewriter.  Here's what I'd like to see:   Typewriter font even in math mode. (Several ways to accomplish this; is there a "best" way?) Slight inconsistencies in the printing of each letter. I attempt this below adapting code taken from . Each word has a random vertical shift, though I'd like to see it reduced to each letter having its own vertical shift. Other typewriter-like irregularities would be great. It would be great if math-mode delimeters \left(, \right}, etc., can be created in a piece-meal fashion as they did in days of old. Fraction bars, tops of square-root symbols -- any horizontal line, really -- is made up of a series of en-dashes that don't quite match up.   Here is what I've come up with so far:  \documentclass[10pt]{article}% This is a document class providing more font size options \usepackage{graphicx} \usepackage{ifthen} \usepackage[textwidth=7.5in,textheight=9.5in]{geometry} \pagestyle{empty}  % thanks to Bruno Le Floch: https://tex.stackexchange.com/q/9331/4012 % and in his comments to https://tex.stackexchange.com/a/29458/4012 \usepackage[first=-1,last=1]{lcg}% you can play around with these values \makeatletter \newcommand{\globalrand}{\rand\global\cr@nd\cr@nd} \makeatother  \newcommand{\randomvshift}[1]{\globalrand\raisebox{\value{rand}pt}{#1}}  %%% thanks to Martin Scharrer: https://tex.stackexchange.com/q/11598/4012 \makeatletter \def\typewriter#1{%     \@typewriter#1 \@empty } \def\@typewriter#1 #2{%    \randomvshift{#1}\space    \ifx #2\@empty\else     \expandafter\@typewriter    \fi    #2% } \makeatother \begin{document}\tt  \typewriter{Math 101 Fall 1963}  \begin{enumerate} \item   \typewriter{$\frac{\texttt{d}}{\texttt{dx}}\texttt{(x)}^2$}  \item \typewriter{State the Fundamental Theorem of Calculus.}  \end{enumerate}  \end{document} A problem with my reasoning in a problem about combinations I was given the following problem to solve:     A committee of five students is to be chosen from six boys and five   girls. Find the number of ways in which the committee can be chosen,   if it includes at least one boy.   My method was $\binom{6}{1}\binom{10}{4}= 1260$, using the logic of choosing $1$ boy, then choosing the rest. This was wrong, as the answer was $\binom{11}{5}-\binom{5}{5}= 461$.  The correct answer's logic was committee with no restrictions – committee with no girls.  Why was my method wrong? Please help... are two consecutive numbers relatively prime? I have a question.  I have been given this proof: "For any $n$ in the integers where $n&gt;2$, show there are at least $2$ elements in $U(n)$ that satisfy $x^2=1$."  I have gone through and actually proved this, (that the numbers are $1$ and $n-1$) but i didn't' know how to prove that $n-1$ is in fact in the set $U(n)$. Is it because two consecutive numbers are always relatively prime? Make Windows 10 stop installing driver software automatically unicode-math broken Correcting for multiple kruskal wallis tests I am running a kruskal wallis test a number of times (37) and wanted to know if I have to adjust the p-values of the kruskal tests before I look any further into the post hocs? I tried logging in with a Google account, but I got the following error: Fatal error: Call to undefined function add_action() - an untouched problem The question was asked many times in many ways, but unfortunately is not covered well in most of the answers. I'm having the same issue doing things using include-files.  In my TwentyFourteen child theme's functions.php I used:  require_once get_stylesheet_directory_uri() .'/admin-panel/theme-options.php';   And I'm using . I've used it in many of my projects, the same way mentioned here, without having the error. But recently I'm having the issue in several of my projects. If I take the code to functions.php then everything's fine. But it's occurring only when I'm trying to include/require external file.  I'm having the error:     Fatal error: Call to undefined function add_action() in C:\xampp\htdocs\project\wp-content\themes\my-theme\admin-panel\theme-options.php on line 2   In this case I'm having the error using a child theme (of T14). But even in one of my parent theme I'm facing the issue. But in the same environment my other projects are running well with all the includes and/or requires (where several add_action()s are defined). I'm having issues in ALL the add_action() calls, like CPT assigning, Custom Taxonomy assigning etc. But I'm successfully developing another two projects including external files from inc/ folder where all my CPTs are assigned and their meta boxes too.  I tried reinstalling WordPress, deactivating all my plugins, tried from Child Theme, tried only the same thing by modifying TwentyFifteen (applying default theme), tried require(), require_once(), include(), include, require_once, and require one after another with failure. And I'm using WP 4.1.1 in all the good and problematic installs.  Majority of the previous questions are answered with a simple line:     As the message says, you haven defined the function add_action() and yet you're trying to use it.   But,   how come (isn't it already defined by WordPress)? and why it's differing project to project in the same environment (How come it's out of the scope now only in particular project[s])? I read on  that the netbook edition of Ubuntu was discontinued and that it is now integrated into the main distribution (as of 11.04).  I tried 11.04 on my new Samsung NC110-A06AU with 10.1" 1024x600 display. Most things worked out of the box, but some (like backlight power control) needed some  before they began to co-operate.  One thing that seems to be an ongoing problem is the resolution.  At 1024x600, most of the dialogue boxes run off the bottom of the screen, including the update manager. I have tried 11.10 beta 1 and it has the same problem.  Is there any way to fix this, or at least make it more usable? (I suspect not). Given the recent rise in popularity of netbooks, do you think Ubuntu will include a low-resolution-friendly version in the near future?  How well does KDE deal with these low resolutions? I noticed KDE Plasma has a netbook interface. Is it worth switching for that? The pronunciation of words which begins 'con' and 'com' Is there any standard that covers the portability of running a command after variable assignment on the same line?  APPLE="cider" echo hi   How portable is something like that? Where will it work and where won't it?   Also: my shell scripts start with #!/bin/sh if that makes any difference. How can I stop the symbolic x coords to be plotted twice? I would like someone to explain me how the sense of a sentence changes with using "for me" or "to me":  Some examples:     1a.  She is a good friend to me.   1b.  She is a good friend for me.        2a.  How special you are to me.   2b.  How special you are for me.        3a.  It's an interesting topic to me.   3b.  It's an interesting topic for me. I have a HP 14-AN001NA laptop. It came with Windows 10 installed on which the Wi-Fi worked fine anywhere in the house.   However I removed Windows 10 and installed Ubuntu 16.04 instead and since I have had terrible Wi-Fi anywhere aside from about three foot away from the router. I don't know if it's relevant but my Wi-Fi is not called wlan0 but wlo1 for some reason (I didn't change it).  When running lspci -knn | grep Net -A3     I get the following output:  05:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter [10ec:b723] DeviceName:   Subsystem: Hewlett-Packard Company RTL8723BE PCIe Wireless Network Adapter [103c:81c1] Kernel driver in use: rtl8723be Kernel modules: wl, rtl8723be Uninstalling Ubuntu from dual boot / changing bootloader How long can a flag remain active? I have flagged the following question as a duplicate.    Now I want to know: after how long time will it be stated as active?  I do not have problem with anything here. I just want to know after how long time the request (of a duplicate question) will automatically be rejected or approved.  OK, I got the things, so it will remain active until moderators will have a look at it...  But don't you think we should have a limit that after a certain number of days this kind of request will be dropped (or cancelled)? How to disable Windows 10 system log In Windows 10 Resource Monitor I found that the system process is constantly writing C:\ProgramData\Microsoft\Windows\wfp\wfpdiag.etl at like 30-100KB/s. This equals 1TB write/year which is not healthy for SSD. There are other log write like C:\Windows\System32\LogFiles*** too.   Although logs is needed for diagnostics, it's better to be turned on only when problem has already occured.  Is it possible to disable as much system logs as possible to decrease garbage write amoung to SSD?