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### Approximate formula for the volume of water at a given temperature

Sorry for asking this kind of question. Do you recongnize this formula? $$V(T) = 0.0000679T^3+0.0085043T^2- 0.0624T+999.87$$ when $V$ is volume of water in $\mathrm{ml}$, $T$ is temperature in ...
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### In geometrical optics, how can we say that rays coming from a distant object are parallel to one another?

If two rays are not parallel in the start, how can they become parallel at the instant when they strike the lens of a telescope? If they don't become parallel, why do we consider them to be, in the ...
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### How to choose basis functions that contribute most efficiently per term? [closed]

I would like to approximate some positive, scalar function $f(x,y) > 0$ on a 2D field of finite size i.e. $x\in [a,b],y\in[c,d]$ I am familiar with the set of basis functions used in the Fourier ...
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### There isn't really an isolated system so why sometimes we consider a system to be isolated?

In real life, there's nothing to be called an isolated system then why at some applications do we assign isolated systems?
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### Approximating Gallons of Gas Needed for Trip (read: physics grad. with too much free time)

My departure from college has left me with an itch for physics-y problems to solve, and my boredom and free time gave way to this approximation of the gallons of gas I use for the trip to my ...
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### Help understanding expansion for following $\sin(\theta)$ [closed]

my professor posted a solution to a problem that I am having trouble understanding. This is the question: Find the frequency of small oscillations about the stable equilibrium position. And this is ...
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### Hyperfine structure in hydrogen

Consider the Dirac equation for bounded electron in hydrogen atom. I am trying to get a clear physical explanation for all mathematical terms that appear in the Hamiltonian and energy spectrum. ...
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### Are some laws in physics really as simple as they seem?

For example, is $F = ma$ really an exact formula, or is it an approximation? I know a lot of formula's come from taking the first few terms of a Taylor expansion, so I was wondering if the simple ...
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### Why Earth is considered to be an inertial frame? [duplicate]

Earth rotates about its axis and also revolves around the Sun at the same time. So why Earth is considered as an inertial frame in Newtonian Physics. So technically, I'm effectively asking why the ...
This may just be a simple Misconception Question, here goes: Definition for Gravitational Potential Energy: The work done by gravity to pull an object to the ground. $E=-(\frac{GMm}{r}-\... 1answer 35 views ### In perturbation theory, how do I determine the order of an approximation? The title says it all: I'm confused about the various approximations and their orders. In time-independent perturbation everything is quite explicit and obvious, but, for example, how would it be with ... 0answers 27 views ### Systems with elements having size which tends to zero [Question] If I have an element whose size(as in physical dimensions) tend to 0 but is NOT 0 (very very very small). If I create a system from these elements based on (say) the fractal concept (... 1answer 46 views ### Is “approximative reduction” general knowledge to physicists? I came across this concept called "approximative reduction", about which there are some papers, e.g. in this collection called Structure and Approximation in Physical Theories. Very briefly, it ... 0answers 104 views ### Fresnel diffraction approximation (parabolic waves) The Huygens-Fresnel principle (Introduction to Fourier Optics, Goodman), $$U(x,y)=\frac{z}{i\lambda}\int_\Sigma U(\xi,\eta)\frac{e^{ikr}}{r}d\xi d\eta\,,$$ where$\cos \theta=\frac{z}{r}$, shows ... 5answers 3k views ### Is there a rigorous definition of 'much greater than'? I have encountered$\gg$in many physics text books where it's used as a relation between constants or functions but in none of the text books I have read is it properly defined anywhere. If$A \gg ...
Problem Statement: Imagine a spherical ball is dropped from a height $h$, into a liquid. What is the maximum average height of the displaced water? For instance, although one particular drop of water ...