For example, in a hanging massless rope, or in a massless rope hanging   over a frictionless pulley, the tension must be the same at all  points, because otherwise there would be a net force on at least one tiny piece, and then $F = ma$ would yield an infinite acceleration for    this tiny piece.   What happen if the tension is different at some point?How it yields an infinite acceleration?
Suppose I have an Atwood machine, that is, two different masses connected with an inextensible, massless rope over a pulley. Assuming no friction between the rope and the pulley, the heavier mass will accelerate towards the ground, the lighter mass will accelerate towards the pulley, and the rope will accelerate towards the heavier mass. These three accelerations will be equal in magnitude. But this makes no sense to me. Force causes acceleration. But there is no force acting on the rope. And even if there was, the acceleration of the rope would be infinite because its mass is 0. So why does the rope accelerate? And how can the magnitude of this acceleration be finite?
A teacher wants to randomly form two teams of 5 students from a group of 5 girls and 5 boys for a sports activity. A teacher wants to randomly form two teams of 5 students from a group   of 5 girls and 5 boys for a sports activity. Two of the girls, Ann and   Alice, are selected as team leaders. Find the probability that one   team has exactly 3 girls.   If i do this way $$\dfrac{{3 \choose 2}{5\choose 2}{1\choose 1}{3\choose 3} \times 2!}{{8 \choose 4}{4 \choose 4}} = \dfrac{6}{7}$$  Which turns out to tally with the answer. But i got one big question, is my way correct. Do i really need to times $2$ here? Please see my link below to my previous question cause the previous question make me doubt if i should times $2$. I work in D8, I create a custom module first_module. By modules create a url and display all nodes by *.html.twig file.  Write code in controller.php  public function contentthree() {    $connection = Database::getConnection();    $query = $connection-&gt;select('node', 'n');   $query-&gt;fields('n', ['nid', 'type']);    $groups = $query-&gt;execute()-&gt;fetchAll();    foreach ($groups as $group) {     $events[] = [$group-&gt;nid, $group-&gt;type];   }    return [     '#theme'  =&gt; 'first_module_display',     '#events' =&gt; $events,   ]; }   In *.module  function first_module_theme($existing, $type, $theme, $path) {    return [     'first_module_display' =&gt; [       'variables' =&gt; ['events' =&gt; NULL],       'template'  =&gt; 'first-module-list',     ],   ]; }  function _get_node_details() {    $output = 'Welcome D8';    $output .= 'Node Details';    return $output; }   and create templates first-module-list.html.twig and display data  {%for key, data in events %}  {%for key1, data1 in data %}     {{ data1 }}  {% endfor %}  {% endfor %}   work fine and showing data correct. But, my question is how to call function _get_node_details() and how to render node details in first-module-list.html.twig files? Where is log file from rc.local? I have some commands to in my rc.local. I know that they are failing. How can I get log file with messages produced by executing rc.local? Where is it located?  I have checked the /var/log/boot.log. I know my messages are not there because I know already what is the reason of failure. But I still want to make sure from log file.  Note, I don't want to run script again, I could but I don't want. I would rather analyse wht happened during startup.  Thanks for any help.  Ubuntu 12.04 Desktop (if it matters) 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? QGIS ->ArcGIS Server configuration possible? Are you less likely to down-vote someone whose gravatar is a photograph of them? I know this is hard to answer since, to the extent that anyone does this, they likely don't do it consciously. In the spirit of Richard Wiseman and  I just wondered what were people's thoughts on it.  Please bear in mind that that's me in the picture, and if you down-vote this, that'll be a real person hurtin', not some abstract symbol. Selenium 2: Open link in new tab and close tabs How do you change from icon to list view in 20.4 Calling the base constructor in C# If I inherit from a base class and want to pass something from the constructor of the inherited class to the constructor of the base class, how do I do that?  For example, if I inherit from the Exception class I want to do something like this:  class MyExceptionClass : Exception {      public MyExceptionClass(string message, string extraInfo)      {          //This is where it's all falling apart          base(message);      } }   Basically what I want is to be able to pass the string message to the base Exception class. Draw Lewis structures like a book I want to draw a Lewis structure as in the picture. I tried to do with chemfig but does not perform the separation of the points and a minus in the superscript. What's the maximum value for an int in PHP? Ignoring the special libraries that allow you to work with very big numbers, what's the largest int value you can store in PHP? C# - Keyword usage virtual+override vs. new Show that $\ker \hat{T} = \text{ann}(\text{range } T)$ This is an old exam problem: Let $V$ and $W$ be finite dimensional vector spaces over a field $F$ and let $T: V \to W$ be a linear transformation. Define $\hat{T}: W^* \to V^*$ by $(\hat{T}(f))(v)=f(T(v))$. Here, $U^*$ denotes the dual vector space $U$. Since $\hat{T}$ is a linear transformation prove $\ker \hat{T} = \text{ann}(\text{range } T)$ where $\text{ann}(Y) = \{g \in U^* : g(y)=0 \text{ for all } y \in Y \}$ for a subspace $Y$ of vector space $U$.  I'm really not sure how to start this problem. Any advice would be great! Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$? Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ that is $a^{2n-1}\mid b^{2n} ; b^{2n}\mid a^{2n+1} , \forall n \in \mathbb Z^+$ , then is it true that $a=b$ ? How can I serialize an object to JSON in JavaScript? Can PHP PDO Statements accept the table or column name as parameter? Why can't I pass the table name to a prepared PDO statement?  $stmt = $dbh-&gt;prepare('SELECT * FROM :table WHERE 1'); if ($stmt-&gt;execute(array(':table' =&gt; 'users'))) {     var_dump($stmt-&gt;fetchAll()); }   Is there another safe way to insert a table name into a SQL query? With safe, I mean that I don't want to do  $sql = "SELECT * FROM $table WHERE 1" How to draw a border around character in a formula? So far everything I found on the matter of borders only applies to the text mode.  I want to be able to do something like  $x_i = y$   so the result will be like the ordinary "xi = z" formula with the border around "i"?  The common answers seems to be the fbox or boxed commands. Yet they render their argument in the standart mode, unless specified to do otherwise with the specific mode. For example, the following code  \[ x_i, \boxed{x}_i, x_{\boxed{i}}, \boxed{x}_{\boxed{i}} \]   produces two normal xi figures, and another two with an oversized i. Script to remove certain span elements from an HTML file I am having trouble loading csv files into layers using QgsVectorLayer().  I know this looks like a repeat, but I have carefully read     and    but still cannot get it work.  An example of my data file, test.csv:  Index,y,x 0,37.7646618,-122.4960858 1,37.777494,-122.416311 2,37.717707,-122.3997056 3,37.732284,-122.498118 4,37.749998,-122.392333   My code:  import os import urllib  import pathlib from qgis.core import QgsVectorLayer  local_path = 'C:\dev\FCMS_conflation\data\TMC_nodes.csv' node_layer = 'test'  abspath = os.path.abspath(local_path) params = {'delimiter': ',',           'decimalPoint': '.',           'xField': longitude,           'yField': latitude}  uri = "%s?%s" %(pathlib.Path(abspath).as_uri(), urllib.unquote(urllib.urlencode(params)))  layer = QgsVectorLayer(uri, node_layer, "delimitedtext")   The formatted URI looks like:  [] uri &gt;&gt;&gt; 'file:///C:/dev/FCMS_conflation/data/TMC_nodes.csv?decimalPoint=.&amp;delimiter=,&amp;xField=longitude&amp;yField=latitude'   I have tried many variations of the parameters, including the crs and type. But no matter what I try, I cannot create a valid layer.  [] layer.isValid() &gt;&gt;&gt; False   I have verified that I can add the file using the QGIS gui. I even tried using the uri provided by layer.metadata from within the Python plugin.   I am using QGIS 2.10.1 on Windows 7 64-bit machine. maximize volume of triangle in given perimeter