I think I know where I've gone wrong, just in case someone comes across this post in the future.
The Clausius-Clapeyron equation only applies in the case of a flat boundary between two phases. In the macroscopic world, the discrepancy is so small it can be ignored. However, when deriving the...
Hey
I'm trying to derive the Gibbs-Thomson equation for the freezing/melting point depression of liquids inside a confined space, such as a cylindrical pore. This has been observed for many liquids, such as water, benzene, heptane, etc. Basically my question is, why does water, which expands...
I think it sounds just fine with the minor changes suggested by Dipole: "According to Classical Physics, at any given time you cannot be at more than one position in three-dimensional space." It's not going to be for a classical mechanics textbook, after all!
Hey
I'm writing up my thesis at the moment and I'd like to include a chapter that is a summary of my project intended for the general public. This would use simple language and probably focus more on background topics instead of my specific results. I think it would be a good exercise in...
Phrased another way, your problem is to find the lowest common multiple (LCM) of a set of numbers from 1,...,n . Luckily, there is an easy formula to get the LCM for two numbers a and b from the greatest common divisor (GCD): LCM(a,b) = |a*b|/GCD(a,b) . I say luckily because finding the GCD is...
This might be helpful: http://en.wikipedia.org/wiki/Kepler_conjecture "Experiment shows that dropping the spheres in randomly will achieve a density of around 65%". I think how much they settle down would depend on the size of the balls and the diameter of the bucket.
Sorry, one more thing. If possible, get away from Excel and learn a data analysis language/package that can make some sexy graphs. R, MATLAB, Gnuplot, Root, etc. are all excellent and are very useful to know in general anyway. Finally, I once tried to do everything in Maple (it has a worksheet...
I use LibreOffice (seems faster over OpenOffice or NeoOffice) to write up technical stuff on my Mac. It has an integrated TeX-like formula editor and is free. The drawbacks are that its spreadsheet program isn't great, and copy/paste from other spreadsheets (like Excel) don't work that well. The...
Sorry, I see that you did write \left| sin z \right| = \frac{e^{i(x+iy)} - e^{-i(x+iy)}}{2i} . However, I don't understand how you came up with your answer: where did the absolute value signs in \left| \frac{e^{y} + e^{-y}}{2} \right| emerge from? You can't just insert them. And how did you...
It will be easier to break this into two problems. First prove that \left| sin z \right| \leq \frac{e^{y} + e^{-y}}{2} , then prove that \left| sin z \right| \geq \frac{e^{\left| y \right|} + e^{- \left| y \right|}}{2}.
Also, use \left| sin z \right| = \frac{e^{i(x+iy)} - e^{-i(x+iy)}}{2i} .
This is exactly like asking:
-what is the speed of silence is and why doesn't it overtake sound?
-what is the speed of no traffic and why doesn't it overtake traffic?
etc.
This sort of analysis is carried out all the time in many subjects (physics, economics, cognitive science, etc.), hence there are multiple techniques. Generally in physics, one at least has an idea of the form of the function and therefore just plays with the parameters until a good fit to the...
I went to university right after high school because I knew exactly what I wanted to study (physics). Although I don't regret that decision, I do sometimes think that taking a year off first to travel would have been very rewarding. Working and living abroad while relying completely on yourself...