If we bring a floating balloon in a accelerated train, the balloon will move forward in the same direction as the acceleration as shown in the following figure.     However if a pendulum is hung on the train ceiling, the ball moves backward. We also get moved backward in the accelerated train.  Could you explain why the floating balloon behaves differently?
I noticed that when I had a helium filled, latex balloon inside of my car, it moved forward in the cabin as I accelerated forward. The faster I accelerated forward, the faster the balloon went from the back of the car to the front of the car. The balloon didn't have a string.  This became a game with my 4 year old as we drove home. We figured out where the balloon would go based on how fast I accelerated, turned corners etc.  I expected that it would act a lot like the water in a cup does, but it was the total opposite it seemed.  What forces caused this behavior?  I assumed it has something to do with the fluid dynamics in the closed cabin, but I can't figure it out.
Android: Overlay on Android Camera Preview Even though I have the latest Adobe Flash player 11.2 for Linux in Firefox -   - a particular online flash game still requests that I update to the latest flash player.  I've tried this online game on my laptop (Windows 8 with Flash Player 11.8) and it has no problems.  Is there a way to trick Ubuntu or this game into thinking Flash Player 11.8 is "installed"? For a presentation with Beamer, I would like to have a slide where a long list of formulas (maybe mixed with text) scrolls automatically within a certain part of the slide. This should look like e.g. closing credits in movies.   I have tried the idea from  based on animateinline from the , but whenever I use environments like \begin{equation} ... \end{equation} or commands like \textcolor{red}{...} I get an error:  TeX capacity exceeded, sorry [main memory size=3000000]. \end{frame}   Ideally, the formulas/the text should be given within the document itself, but if a solution with an external PDF works fine, I'll take it!  Any ideas how that might work? Ideal column width for paragraphs online There is nothing worse than coming across a website with paragraphs that span the width of your screen resolution. They are usually so hard to read, I don't even bother.  A lot of web designers use generic grid and column systems, but I don't feel these have been optimised for readability, they are more of design guide on general aesthetics.  I guess it comes down to words per line. Are the rules that apply to print media the same for screen media?  Are there any type of guidelines to help me size the width of paragraphs on the screen?  I want to take into consideration:   Major web font faces (i.e. Arial, Verdana, Georgia, Times) A range font sizes (i.e. 8px-24px) Space between columns I was surprised to find that standalone package can not compile a document with an equation:  \documentclass{standalone} \begin{document} \begin{equation} % not working! F(V, T) = E(V) + D(T) \end{equation} \end{document}   Is there an option or some workaround that allows this? The current error is something like:   ! Missing $ inserted.   in line 4. (The idea of course is that the including (main) document can just \input the standalone without knowing if is going to be an equation or something else) Determining functions from specifications... my high school teacher asked this question today, and I am struggling to find an answer that will work. The question is outlined below:  Give an example of a cubic polynomial, defined on the open interval (-3,3), which reaches both its maximum and minimum values. prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$ Prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$ using the fact that $\mathbb{Q}$ is dense subset  of $\mathbb{R}$  I know that $\mathbb{Q}$ is dense subset  of $\mathbb{R}$ That is, between any two real numbers, there exists a rational number  then how to prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$ We were given the following problem as an assignment, we proved the converse in class for prime numbers; however, we can't use the assumption that $\operatorname{gcd}(a,b) = 1$.  So I am struggling to think of my first possible move.  We are given $ar + bs = 1$, the only think I can think of is let $d$ be a common divisor or $ar + bs$ and then show that the $d = 1$.  However, I am not really sure how to do that.  If anyone could just give me a hint or two to nudge me in the right direction I would be appreciative. launchd plist format for running a command at a specific time on a weekday How do I parse command line arguments in Java? What is a good way of parsing command line arguments in Java? Remove items from one list in another Contradicting Fubini's theorem I have a function defined as follows: $f(x,y)= \dfrac{x^2-y^2}{\left(x^2+y^2\right)^2}$, if $(x,y)\neq (0, 0)$ and $f(x,y)=0$ if $(x,y)=(0,0)$.  Now, $$\int_0^1\int_0^1 f(x,y)\,\text{d}x~\text{d}y=-\frac{\pi}{4}$$ and $$\int_0^1\int_0^1 f(x,y)\,\text{d}y~\text{d}x=\frac{\pi}{4}.$$   The question I have is this: why does this not contradict Fubini's theorem?    thanks. vim and system clipboard I can cat a file, copy and paste text with the middle button or shift-insert.  How can I copy text in vim and paste it from the system clipboard? Subject-Verb Agreement For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$ Well I attempted to try this but I failed to solve it: So $$\Phi_{p^{n}}(x)= \frac{x^{p^{n}} - 1}{\Phi_{1}(x) \Phi_{p^{2}}(x) \dots \Phi_{p^{n-1}}(x)}$$  Now I'm just stuck here. I saw a result somewhere on the net that said $\Phi_{p^n}(x) = \Phi_p(x^{p^{n-1}})$. I would just use that, but I don't see why that result is true or know how to show that's true.  How do I approach this? In the movie Interstellar,  Cooper (played by ) enters a black hole and sends a message to Murph (his daughter). Later, he is found by rangers, but I don't understand how he gets out of the black hole?  As far as I know, nothing can get out of a black hole, as it has extremely high gravity. How to create two classes in C++ which use each other as data? Show that $\mathbb{Q}\times \mathbb{Q}$ is denumerable No option to create a new Managed Path inside Office 365 SharePoint online 2013 I am working on an Office 365 SharePoint online 2013. Now when I wanted to create a new private site collection, inside the online SharePoint admin center, I did not find the option to create new managed path, as I use to get when creating a site collection inside SharePoint on-premise. So how do I create a new managed paths inside SharePoint online? Why don't we include $\rho g h$ in a hydraulic jack below? Consider a hydraulic jack with massless pistons as follows.    The famous equation for this system is   $$ \frac{F_1}{A_1}=\frac{F_2}{A_2} $$  My question is why isn't the equation as follows?  $$ \frac{F_1}{A_1}=\frac{F_2}{A_2} + \rho g h $$  It is based on  my understanding that any points in the same horizontal line have the same pressure.  Could you spot my misconception?