Lets assume that the red ball is more dense than the white fluid and less dense than the blue fluid. The fluids are of very low viscosity and the machine can be of any height. The flaps open when pushed from the bottom and after the ball goes through then they close hermetically(some magnets perhaps).  My understanding is as follows:  The ball needs a finite velocity to open the flaps. Since H1, H2, can be of any height that is not a problem.  The ball needs a finite velocity to jump off the water high enough. That is not a problem since H3 can be of any height.  The ball needs a finite velocity to get into the water. That is not a problem since H1+H2+H3 can be of any height.  If it worked it would be a perpetuum mobile. Please help me find out why it won't work.
I realize this isn't possible, but I can't see why not, especially if you change the model a little bit so that the balls simply travel through a tube of water on the way up, rather than exactly this model.  Please be clear and detailed.  I've heard explanations like "the balls wouldn't move" but that doesn't do it for me - I really do not see why the balls on the right would not be pulled/pushed up, and the rest of the chain wouldn't continue on.
This is something that has long bothered me, and I have asked a few physicists and chemists and never gotten a very satisfying answer. Why are particles charged? And I'm not asking (and this is the answer you often get) why some molecule might be negatively charged because the answer to that is simply is that there was one more negatively charged particle than positively charged particle. That doesn't answer my question, however, of why there are charged particles at all?  So, on a fundamental level, what makes one particle charged and another one neutral.  For instance, protons and neutrons have almost exactly the same mass, which I'm assuming that means they have very similar internal compositions, yet one is positively charged and the other neutral. What is going on that makes these particles different?  On a similar note, and I'd really like to know this, how is it that a proton and an electron have exactly equal and opposite charge, yet an electron is about 1000 times less massive than a proton?  I have particular trouble with this question because if the answer were something along the lines of "particle X which composes protons all have partial positive charges of n amount..." I would just ask why particle X has any charge and we'd be in the same predicament.  I'm sure there is a satisfactory answer to my question, I just can't find it and don't know what resources are reliable or detailed enough to be satisfactory. What's the limit on the no. of partitions I can have? I would like to know how many Primary and Extended Partitions I can create on a x86_64 PC with Linux running on it?     Update  : If there is a limit to the number of partitions, why is that the limit? When do you use Java's @Override annotation and why? Linux command line. 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However I'd have to find some function $h(x)\in A$ such that $h(x)(ag+f) = 1$, but this function $h$ has to be different from 0 for all x $\in \mathbb{R}$, so I don't know how to find this function.  My second idea to solve this problem was prove that the quocient $A/M$ is a field. We have that $$A/M = \{h(x) + M; h(x) \in A\},$$ but again I have the problem to show that all elements of $A/M$ are units.  If someone could help, I would be really grateful (: In the cases of black holes that form from supernova and collapse of a massive star, I understand that in most of these cases, the star loses significant amounts of mass from the explosion. Presumably, after this point as the remaining mass becomes more dense as it further collapses unto itself, it eventually becomes a black hole with gravitational force greater than that of its parent star. But, if gravity is based on mass, how can the black hole have greater gravitational force than the star from which it is formed? My Ubuntu 16.04 keeps disconnecting from the Wi-Fi (eduroam). Why? The relationship between the eigenvalues of matrices $XY$ and $YX$ If $X \in \mathbb{C}^{m \times n}$ and $Y \in \mathbb{C}^{n \times m}$ ($m \geq n$), how to prove the following?  $$\sigma (XY) = \sigma(YX) \cup \underbrace{\left \{ 0, ..., 0 \right \}}_{m-n}$$  Here, $\sigma$ denotes the set of eigenvalues/spectrum. Is there a way to step between 0 and 1 by 0.1?   I thought I could do it like the following, but it failed:  for i in range(0, 1, 0.1):     print i   Instead, it says that the step argument cannot be zero, which I did not expect. When does $\lim_{n\to\infty}f(x+\frac{1}{n})=f(x)$ a.e. fail How was the Cloak of Invisibility Created? Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction. How to show/hide a column at runtime? I'd like to show/hide a column at runtime based on a particular condition. 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Well the question is to solve for $x$ in $$a^x+b^x=c \tag{a,b,c are constants}$$   Well as of me, I tried to put $\ln{}$ on both sides which does not seem to help. Apart from this I don't seem to have any other way to solve it.   I turned to WolframAlpha and the solution which was given was : $$x=\dfrac{-i(2\pi n +\pi)}{\ln{a}-\ln{b}} , {n \in \mathbb{Z}}$$  And if $n=0$ $$x=\dfrac{-i\pi}{\ln{a}-\ln{b}}$$  The only thing I am able to recognize is $e^{i\pi}=1$ ... i guess is used.  Link :   So I see that $x$ is independent of the constant $c$.  So how to solve it? Please help...Thanks!    EDIT - It seems that WolframAlpha is taking $c=0$ as suggested by Donkey_2009. And when i write "Solve for x in a^x + b^x = k" it is not returning anything. So are you guys aware of a method to solve this? Also are you guys aware of any other website/software like WA?    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Error handling in C code