question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>I'm looking at amplitude decrease of a seismic pulse as a result of geometrical spreading.</p>
<p>Starting with the energy contained in a unit area, $I = E / (4 \pi r^2)$, where $E$ is the original energy from source, we know that energy falls off as $1/r^2$, thus amplitude falls off as $1/r$.</p>
<p>From Wikipedia: </p>
<blockquote>
<p>"The energy or intensity decreases (divided by $4$) as the distance $r$ is doubled"</p>
</blockquote>
<p>This makes sense to me, as when $r$ is doubled we have the energy divided by $(2r)^2 = 4r^2$ (which is $4 \times r^2$).</p>
<p>From this same principle, I would expect that the amplitude is divided by 2 when the distance is doubled as we have $1/2r$ instead of $1/r$.</p>
<p>However from a Louisiana State University website:</p>
<blockquote>
<p>Geomteric spreading makes the amplitude of a signal falls off in proportion to the distance traveled by the ray. So that if the path of flight is doubled the amplitude will decrease by a factor of ${\sqrt 2}$.</p>
</blockquote>
<p>I can't see how they got their factor of $√2$ instead of $2$.</p>
<p>Is there a mistake or am I missing something?</p> | g11763 | [
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<p>It is known that good DI water have resistance ~20 MΩ·cm
But how can I measure that? Using good vanilla ohmmeter (with 2000 MΩ range) showed crazy results (too low, not much dependent from distance between probes).
I need that to compare DI water from 2 sources.</p> | g11764 | [
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<p><img src="http://i.stack.imgur.com/TgQNG.jpg" alt="enter image description here"></p>
<p>The picture is an emission spectrum of Helium. The spectrum has sharp lines (peaks) at certain wave lengths characterizing it as helium. Agreed that it characterizes Helium as atomic spectral line characterize gases and they are based on allowed energy states of electrons in an atom.</p>
<p>Well and good, but what i don't know is the $y-axis$. what does it represent? It is shown as intensity (counts) but I want to know what it is and how does it vary from element to element. Does this count also characterize the elements, or is it same for all elements? Appreciate if you could throw some light on it.</p>
<p>Question : I mean if i keep the position of lines(pulses) same but change their relative amplitudes, what happens? does it represent a different gas?</p>
<p>Picture taken from the internet.</p> | g11765 | [
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<p>Why does it take a lot of energy to heat metals? And to do it quicker it requires much more energy? What about the use of lasers would that be an efficient process that is quicker and requires less? </p> | g11766 | [
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<p><img src="http://i.stack.imgur.com/H2nRB.jpg" alt="enter image description here"> </p>
<p>Is it possible for the curled dimensions described in superstring theories to become uncurled and open up. I have read that the big bang could have been the uncurling over 3 dimensions through collisions of branes: <a href="http://universe-review.ca/I15-39-collision.jpg" rel="nofollow">http://universe-review.ca/I15-39-collision.jpg</a>. Is their any theoretical mechanism that causes this uncurling of dimensions?</p> | g11767 | [
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<p>The wave is</p>
<p>$\bar{E} = E_{0} sin(\frac{2\pi z}{\lambda} + wt) \bar{i} + E_{0} cos(\frac{2 \pi z}{\lambda}+wt) \bar{j}$</p>
<p>Let's simplify with $z = 1$. Now the xy-axis is defined by parametrization $(sin(\frac{2\pi }{\lambda}+wt), cos(\frac{2\pi }{\lambda} + wt)$ where $t$ is time and $\lambda$ is wavelength. This parametrization satisfy the equation $1^2=x^{2}+y^{2}$, a circle. </p>
<p>Now, let's variate the value of $z$. We know now that it cannot move into x or y coordinates or do we? Not really, the latter simplification is naive -- $x-y$ parametrization depends on the dimension $z$ -- but can we see something from it? If so, how to proceed now?</p>
<p>The solution is that the wave moves along the $z$ -axis to the negative direction as $t$ increases, a thing I cannot see.</p>
<p>The way I am trying to solve this kind of problems is:</p>
<ol>
<li>Parametrize the equation</li>
<li>suppose other things constant and change one dimension, observe</li>
<li>check other variable</li>
</ol>
<p>...now however I find it hard to parametrize the $z$ so a bit lost. So how can I visualize the wave with pen-and-paper?</p> | g11768 | [
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<p><a href="http://physics.stackexchange.com/questions/38837/spaghettification-of-humans-near-black-holes">THIS POST</a> does a pretty good job of giving an idea as to what the differences in forces becomes as you approach a black hole.</p>
<p>For a small enough black hole, you would reach the dangerous tidal force distance before you reached the event horizon, which means you could have a stable orbit around the black hole near that dangerous distance. So to prevent from getting torn apart, you could lay down like a plank, facing the black hole while orbiting in the danger region, the differences in force on different parts of your body would be uncomfortable but survivable. But if you suddenly extended an arm towards the black hole, that arm would have a dramatically different force acting on it.</p>
<p>Assuming you are far enough so it doesn't quite rip your arm off, would this sudden change in forces acting on your body change your orbit? My initial thought was that since you haven't changed your momentum or center of mass at all, your orbit would remain the same. Then I realized that since the gravitational force is proportional to 1/r^2, that means that even though your COM is the same, the total force acting on your body has increased by stretching your mass out perpendicular to the gravitational body, which means your orbit would change right? How would it change your Apoapsis and Periapsis, if you started in a perfect circular orbit?</p>
<p>As a follow up question IF you can change your orbit this way: Could you build a machine(and thus higher tolerances than any human) that could orbit a black hole, and just by moving its mass around at the right times in orbit, change its orbit dramatically?</p> | g11769 | [
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<p>In Hamiltonian mechanics, we show $\{H,L_z\}=0$, which can be interpreted as the conservation of angular momentum around $Oz$. Following the same idea, how can we interprete $\{H,L^2\}$?</p>
<p>Is the interpretation the same (or <em>only</em> similar) as in quantum mechanics for $[H,L_z]$ and $[H,L^2]$?</p> | g11770 | [
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<p>Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels.</p>
<p>$$
f(x,y)= ∑_(u=0)^(U-1)∑(v=0)^(V-1)\ |F(u,v)| exp^(1j*2Π*xu)/M) * e^(1j*2Π*(vy)/N) /
$$</p>
<p>Figure 1.(d) shows the Test image reconstructed from PHASE spectrum only. We can say that intensity values of HIGH frequency (edges,lines) pixels are comparatively more than LOW frequency pixels.</p>
<p>Why this magical contradiction of intensity change (or exchange) is present between Test image reconstructed from MAGNITUDE spectrum only and Test image reconstructed from PHASE spectrum only, which when combined together form the original Test image?</p>
<p>$$
f(x,y)= ∑_(u=0)^(U-1)∑(v=0)^(V-1)\ exp(j*angle(u,v)) *exp^(1j*2Π*xu)/M) * e^(1j*2Π*(vy)/N)
$$</p>
<p><img src="http://i.stack.imgur.com/nIRwF.png" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/J5Xlb.png" alt="enter image description here"></p> | g11771 | [
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<p>In the book <em>Quantum Mechanics - Volume 1</em> written by Albert Messiah, page no. 142-143, author says: </p>
<blockquote>
<p><em>...But the diaphragm is a quantum object, just like the electron. Its momentum is not defined to better than dp....</em></p>
</blockquote>
<p>I did not understand why diaphragm is a quantum object ?</p>
<p>Also, it is not clear to me what author says below, </p>
<blockquote>
<p><em>....One must postulate that the measuring apparatus is a quantized object which also obeys uncertainty relations....."</em></p>
</blockquote>
<p>On the other hand, N. Bohr says that measuring apparatus is always a classical object (i.e. instrument which follows rules of classical mechanics).</p>
<p>Any CLEAR explanation?</p> | g11772 | [
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<p>At what pressure will be particles in a medium be unable to form a sound wave when disturbed? How can this pressure be described mathematically?</p>
<p>My guess is that this would correspond to the point at which the restoring force due to pressure is unable to create a transverse wave and the disturbed particles travel infinitely far away before the hypothetical wave reaches it's amplitude. But I have no idea how you would even begin to start finding a quantitative value for this point.</p> | g11773 | [
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<p>In the theory of non-abelian <a href="http://www.quantiki.org/wiki/Anyons" rel="nofollow">anyons</a>, essential information is stored in the fusion multiplicities or Verlinde coefficients $N_{ab}^c$.</p>
<p>Having the <a href="http://www.math.brown.edu/~brock/home/text/papers/pdwp/www/pdwp.pdf" rel="nofollow">Pants Decomposition</a> in mind, it is possible to use these coefficients to calculate the dimension of the topological/fusion Hilbert space for $p$ anyons <a href="http://quince.leeds.ac.uk/~phyjkp/index_files/JiannisPachosLecture.pdf" rel="nofollow">3</a>, which is</p>
<p>$${\rm \ dim} H= \sum_{\{a_i\}}N_{b_1 b_2}^{a_1} N_{a_1 b_3}^{a_2}...N_{a_{p-3} b_{p-1}}^{b_p}$$.</p>
<p>My question is: What is the effect of braiding of , for example, anyon 1 with anyon 2 on the dimension? What is the effect of a twist?</p>
<p>Knowing that $N_{ab}^c=Z(S^2\times S^1; R_a, R_b, R_c)$ (Witten `89) braiding of anyons $a,b$ should give rise to a phase, when considering subsections 4.4 and 4.6 of <a href="http://projecteuclid.org/download/pdf_1/euclid.cmp/1104178138" rel="nofollow">4</a> or chapter 18 of <a href="http://books.google.com/books?id=xXzguxNfno4C&pg=PA248&hl=de&source=gbs_toc_r&cad=3#v=onepage&q&f=false" rel="nofollow">5</a>. Can this affect the overall dimension $dim H$?</p> | g11774 | [
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<p>I'm a novice to physics, so maybe it's rather stupid.</p>
<p>According to <a href="http://en.wikipedia.org/wiki/Tractrix#Basis_of_the_tractrix" rel="nofollow">wiki</a>, the tractrix could be considered a trajectory:</p>
<p>Suppose $AB$ is a stick on a smooth plane $\pi$, and the initial position of $AB$ is $A_0B_0$. $\mathbf v$ is a vector on $\pi$ such that $\mathbf v\perp \overrightarrow{A_0B_0}$ (It's not necessary, but it simplifies the problem). Now let's drag $B$ side of the stick $AB$ such that the speed is constantly $\mathbf v_B=\mathbf v$, then the locus of $A$ is a tractrix.</p>
<p>I tried to solve out the equation of that locus and then prove that it's a tractrix, but failed because I don't know the exact properties of a stick. Somebody told me that $\mathbf v_A\parallel\overrightarrow{AB}$ any time the stick is moving, but I can't prove that.</p>
<p>Can anybody help me formulate all the properties of sticks (just as properties of $\mathbb N$ in Peano's axiom system), well, there're something trivial, for example, $\left\lvert\overrightarrow{AB}\right\rvert$ is constant, and prove that $\mathbf v_A\parallel\overrightarrow{AB}$?</p>
<p>Thanks!</p> | g11775 | [
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<p>Can anyone explain why fast neutron reactor designs use sodium/lead/salt cooling, instead of water (heavy/light)?</p>
<p>Is that because neutron absorption by water would not allow to break even in fuel cycle?
Will heavy water help here?</p>
<p>Or water slows neutrons so efficienly so that even if we reduce amount of water inside the reactor (by increasing flow speed) - it still will significantly lower neutron energy, while sodium does not slowdown neutrons at all?</p> | g11776 | [
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<p><a href="http://en.wikipedia.org/w/index.php?title=Automatic_quartz&oldid=432281459" rel="nofollow">Wikipedia article on automatic quartz watch</a> describes the watch mechanism as follows: a rotating pendulum is attached to a pinion and when the wearer moves his hand the pinion is rotated at <strong><em>up to 100 thousand revolutions per minute</em></strong> and that pinion rotates an electric generator.</p>
<p>AFAIK the fastest hard disk drives currently reach only 15K RPM and they have serious problems with heat dissipation - a fan is required for cooling the drive.</p>
<p>How can a miniature pinion inside a watch be rotated at such speed without the whole assembly being worn out by friction in no time?</p> | g11777 | [
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<p>Moments after the Big Bang, the universe was expanding at an incredible rate, (I've heard) faster than the speed of light. Due to dark energy, scientists predict the rate of expansion will pick up again. Space itself will be expanding faster than light speed. Someday, we will not be able to see other galaxies because they'll be moving away so fast that the light they produce will never reach us. Nowadays, though, we can see other galaxies, which means the expansion of the universe slowed down.</p>
<p>What caused the expansion of the universe to accelerate more slowly? If dark energy is causing the acceleration to increase, wouldn't the universe continue to expand faster after the big bang?</p>
<p>Is there a <strong>minimum rate</strong> of acceleration? If so, what is it, and what determines it?</p> | g11778 | [
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<p><code>5 x 10^7 kg of radioactive material emits energy in the form of photons of red light (700 nm). (Note: photons have no mass.)
What is the momentum of each photon?</code></p>
<p>We just started a new chapter, and in the process of learning it, I came across this question in the back of our book, which I am really having trouble understanding right now. Can anyone suggest how I can go about solving this (note, I would like to actually work out the problem myself; however, I need a sufficiant place to start.) Obviously, the Newtonian equations like <code>p =m/v</code> will not apply here, so I'm somewhat stuck at the moment...</p>
<p>Any help is much appreciated, thank you. </p> | g11779 | [
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<p>I'm trying to solve the equation:</p>
<p>$$
\frac{\partial^2 v_z(x,y)}{\partial x^2} +
\frac{\partial^2 v_z(x,y)}{\partial y^2} =
\frac{\Delta P}{\mu \Delta X}
$$</p>
<p>This flow is supposed to be flowing in a square channel (laminar,steady,fully developed).</p>
<p>I know I need to solve it numerically and if there was no source term I could just take the average of all four points around each node and get my answer. The problem is that I need to find the appropriate source term and I honestly don't know how to start. I also know I need to make the equation dimensionless. I know the source term can't be found analytically and I honestly am lost there. Can someone explain what the source term is and how I can start my quest to find it?</p> | g11780 | [
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<p>Is there any experiment conducted to prove Many world interpretation of Quantum mechanics?</p>
<p>If it can't be proved why we should take MWI seriously? Recently I read some papers of Max Tegmark who is an advocate of MWI and avoids the lack of experimental prove.</p>
<p>I think <a href="http://physics.stackexchange.com/questions/97991/are-there-any-non-interpretational-arguments-in-favour-of-everetts-many-worlds?rq=1">this</a> is the same question as mine.</p>
<p>What about the two arxiv papers <a href="http://arxiv.org/abs/0809.4422" rel="nofollow">this</a> and <a href="http://arxiv.org/abs/quant-ph/9510007" rel="nofollow">this</a>?</p> | g11781 | [
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<p>For example use p-form for p identical fermion system?</p>
<hr>
<p>The Maxwell equations can be rewritten as a single function using forms plus an intrinsic equation showing the Faraday tensor is a two form. This happens because forms are antisymmetric and we can construct an antisymmetric Faraday tensor which contains all the information we need to describe a pure electromagnetic system.</p>
<p>In quantum mechanics, we use tensor product space to describe some many-particle or many-freedom systems. Sometimes it is cute to use forms to describe an antisymmetric quantity such as the wave function of fermions.</p>
<p>So do we use wedge product and forms massively in some quantum mechanics topics? </p> | g11782 | [
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-0.022349126636981964,
0.003839836921542883,
-0.032383158802986145,
0.059480030089616776,
0... |
<p>The atomic theory as first theorised by Democritus has been successfully applied to matter and to energy (quanta).</p>
<p>Space-time is still generally seen as a continuum. What arguments are there (if any) in support of there being a particulate structure of space-time?</p> | g11783 | [
0.05280083790421486,
0.020083637908101082,
-0.008056535385549068,
-0.04678880795836449,
0.0004125257255509496,
0.06522994488477707,
-0.017334282398223877,
-0.018063778057694435,
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0.016532504931092262,
0.07804560661315918,
-0.01683703064918518,
0.025575170293450356,
-0... |
<p>As far as I understand Everett's <a href="http://en.wikipedia.org/wiki/Many-worlds_interpretation" rel="nofollow">Many-Worlds Interpretation</a>, he makes the case for a realist theory of QM at the enormous cost of many-worlds.</p>
<p>Are there any arguments in favour of Everett's interpretation that makes the case for his theory one a purely instrumental or operational view - in that certain calculation look easier or more 'elegant'?</p> | g11784 | [
0.009565341286361217,
0.052785780280828476,
-0.022985026240348816,
-0.08482350409030914,
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0.023763323202729225,
0.0215073823928833,
0.04390091449022293,
0.005450013093650341,
0.06928617507219315,
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0.0... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/3468/what-would-happen-if-you-put-your-hand-in-front-of-the-7-tev-beam-at-lhc">What would happen if you put your hand in front of the 7 TeV beam at LHC?</a> </p>
</blockquote>
<p>Not a terribly scientific question, but one that I'm sure many people have thought about :)</p> | g372 | [
0.02410569041967392,
0.03874390944838524,
0.024629559367895126,
-0.023410752415657043,
0.02423594519495964,
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-0.014309248887002468,
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0.034666553139686584,
-0.03906562924385071,
0.04... |
<p>If we were trying to figure out the time scale for a gas-phase reaction between two hydrogen atoms in a molecular cloud (which has density $~10^4/$cm$^3$), apparently the reaction would happen on a time scale proportional to the inverse of the density multiplied by $10^{15}$ years. Aside from the cloud not being dense and the probability that a collision will surpass the activation energy is small, is the time elongated because you need to induce a dipole moment between two hydrogen atoms to actually bind them together?</p> | g11785 | [
-0.010847164317965508,
0.07235182821750641,
-0.006997521501034498,
-0.038014378398656845,
0.04504027217626572,
0.0010081144282594323,
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0.04158724844455719,
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-0.03438257798552513,
-0.026891596615314484,
-0.027416573837399483,
-0.026544855907559395,
... |
<p>I once saw a statement about the relation between division algebra(which means you can define a division in this algebra, there is a theorem saying we only have 4 kinds of division algebra, real R, complex C, quaternion H and octonion O) and discrete symmetries, saying that the number of discrete symmetries(I mean time reversal, charge conjugate and parity) is limited because we only have 3 kinds of associative division algebra(octonion O is not associative, I guess the associativity is related to physical operation, since all physical operation is associative, I mean ABC=A(BC)). </p>
<p>This statement seems to be very interesting and deep, however, I don't know much about this. Just want to attract you physicists attention and give some comments or explanation about this.</p>
<p>Thank you very much!</p>
<p>For more about division algebra: </p>
<p><a href="http://en.wikipedia.org/wiki/Division_algebra#Associative_division_algebras" rel="nofollow">http://en.wikipedia.org/wiki/Division_algebra#Associative_division_algebras</a></p>
<p><a href="http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(normed_division_algebras)#Hurwitz.27s_theorem" rel="nofollow">http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(normed_division_algebras)#Hurwitz.27s_theorem</a></p> | g11786 | [
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0.036524057388305664,
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-0.... |
<p>I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics: </p>
<p>Is there a set of axioms to which it adheres? In Mathematics, we have given sets of axioms, and we build up equations from these sets.</p>
<p>How does one come up with seemingly simple equations that describe physical processes in nature? I mean, it's not like you can see an apple falling and intuitively come up with an equation for motion... Is there something to build up hypotheses from, and how are they proven, if the only way of verifying the truth is to do it experimentally? Is Physics rigorous?</p> | g11787 | [
0.06683582067489624,
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0.00... |
<p><img src="http://i.stack.imgur.com/B7pBq.png" alt="enter image description here"></p>
<p>I have no idea what formula I'm supposed to use.I just want to know the concept that would allow me to get the answer. I know basic concepts of electricity like charge, currents, etc., but as far resistances go I know only about series and parallel. I tried looking for resistances in a circular loop but I didn't understand what was being explained. Also I didn't find any concept that helped me understand what was to be done, probably because I didn't understand them.I used some help from a different question and got the resistances but my answer wasnt correct. </p> | g11788 | [
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0.03... |
<p>Is it an accurate statement to say that free electrons in a metal experience NO restoring force when they interact with electromagnetic waves? I understand that the electrons exist in a space filled with ions, and doesn't the cumulative potential that is present due to the presence of the ions exert an electric field on the electrons. Even in the case of simple metals, where you can say that the nucleus is shielded by the valence electrons, so called Coulomb shielding, how significant is the shielding. Naively, it seems to me that because the charge in the nucleus is not balanced by the charge in the bound electrons, there should be some net potential that the free electron sees. </p> | g424 | [
0.05160939320921898,
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-0.03583551198244095,
-0.003508... |
<p><img src="http://i.stack.imgur.com/X9MiJ.png" alt="enter image description here">is it possible to find to resistance without knowing the length?
i am tryigng to solve a problem that requires me to find the resistance.I cant seem do so without knowing the length of the circuit which is not given.Is there something that shows resistance without knowing the length or am i just looking at problem all wrong?other details include: resistivity of the upper resistance=4ohm metre,resistivity of the lower resistance=2ohm metre,battery emf V=10pi ohm, radius of the circle=1m,angle between A and B is 60.is there a special relation between resistances in parallel? </p> | g11789 | [
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0.04903978109359741,
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0.03378128260374069,
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0.0... |
<p>I would like to know whether anyone has seen a boundary condition used in a fluid flow problem, of the following type. Suppose viscous incompressible fluid is to the left of a plane $x_1=a$, so the outer normal to the fluid region is $n=(1,0,0)$. The condition specifies that the $x_1$ momentum flux is a nonnegative multiple of the velocity:
$$
m\begin{bmatrix}
u_1\cr
u_2\cr
u_3\end{bmatrix}
=
\begin{bmatrix}\rho u_1^2+p-2\mu u_{1,1} \cr
\rho u_2u_1-\mu(u_{1,2}+u_{2,1}) \cr
\rho u_3u_1-\mu(u_{1,3}+u_{3,1}) \end{bmatrix}
$$
where $m$ could be a number $\ge0$ or even a nonnegative 3 by 3 matrix.
(This is connected with my question at <a href="http://www.mathoverflow.net/q/163772/" rel="nofollow">http://www.mathoverflow.net/q/163772/</a>)
Thanks for any references.</p> | g11790 | [
0.026856152340769768,
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0.020444391295313835,
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<p>I've seen videos of people in space (on ISS) who squeeze a bottle or something and liquid comes out, it then separates into smaller balls.</p>
<p>Why is this surely it should stay pretty much together because theres no gravity from the Earth so the liquid should attract itself?</p> | g264 | [
0.005319444462656975,
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0.042187873274087906,
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0.034399744123220444,
0.... |
<p>The process is the following:
$$e^-e^+ \rightarrow photon \rightarrow quark + antiquark$$</p>
<p>Regarding the momentum conservation law, how come we have a photon of spin 1 and at the end some meson with spin 0?
Are gluons "behind this"? If this is correct, at which point are they radiated? From quarks? Or? Is this photon a virtual photon or not? I'm a bit confused here.</p> | g11791 | [
0.007418712601065636,
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0.030858632177114487,
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0.05018975958228111,
0.002569477539509535,
0.01296... |
<ol>
<li><p>In correspondence to AdS black hole solutions, what does it mean by Misner string singularities? And when there are no Misner string singularities, what does this mean in terms of curvature singularities and event horizons and the black hole in general?</p></li>
<li><p>A related question (as far as I'm aware), what do we do if our solution contains closed timeline curves (CTCs)? Should we really only consider cases when our solution doesn't contain closed timelike curves and strictly impose restrictions on our parameters that ensure this? </p></li>
<li><p>(While on this topic, an elementary question, why does $g_{\phi \phi}<0$ imply CTCs, if we're in hyperbolic 4d space?)</p></li>
</ol> | g11792 | [
0.036774035543203354,
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0.07415355741977692,
0... |
<p>In <a href="https://en.wikipedia.org/wiki/ENDF" rel="nofollow">ENDF</a> there are cross-sections given for different types of nuclear interactions. For example, <a href="http://t2.lanl.gov/nis/data/endf/endfvii.1-n-pdf/u235.pdf" rel="nofollow">this file</a> gives the cross-sections for different neutron energies. However, it is not clear, which temperature of the medium itself (not the neutron gas) is implied.</p>
<p>Is there a way to know, for which temperature are those cross-sections given. Or maybe to know the
cross-section values for different temperatures of the medium.</p> | g11793 | [
0.0342211052775383,
-0.0013558876235038042,
-0.009157218970358372,
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0.0333525724709034,
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0.024897707626223564,
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0.011466769501566887,
0.04005451872944832,
0.012162786908447742,
-0.0076195355504751205,
0.... |
<p>I'm reading Goldstein's Classical Mechanics and he says the following:</p>
<blockquote>
<p><em>A <a href="http://en.wikipedia.org/wiki/Virtual_displacement" rel="nofollow">virtual (infinitesimal) displacement</a> of a system refers to a change in the configuration of the system as the result of any arbitrary infinitesimal change of the coordinates $\delta \mathbf{r}_i$, *consistent with the forces and constraints imposed on the system at the given instant $t$*. The displacement is called virtual to distinguish it from an actual displacement of the system ocurring in a time interval $dt$, during which the forces and constraints may be changing.</em></p>
</blockquote>
<p>Then he discusses <a href="http://en.wikipedia.org/wiki/Virtual_work" rel="nofollow">virtual work</a> and so on. Now, I can't grasp what this thing of virtual really is. By this text there's a diference between one infinitesimal change and one virtual change and I really don't get what this virtual really is.</p>
<p>Also, this is based on infinitesimals. How can this be expressed rigourously without refering to infinitesimals? I tried looking on Spivak's Physics for Mathematicians where he considers these virtual displacements as tangent vectors to a certain manifold, but I'm not sure this is the most "standard" way to do it rigorously.</p> | g11794 | [
0.030398830771446228,
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0.004960217513144016,
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0.038196347653865814,
0.03233916684985161,
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0.01893734745681286,
-0.01925325207412243,
-0.030007382854819298,
0.03550814837217331,
-0.0... |
<p>This was a practice test question.</p>
<blockquote>
<p>Consider the following figure. (If the frictional coefficients are unclear, between A and B we have $k_1 = 0.3$, B and platform is $k_2 = 0.2$. If you further doubts about the diagram ask me in the comments below and I will clarify.)</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/PRMA5.jpg" alt="enter image description here"></p>
<blockquote>
<p>The blocks are resting on the rotating platform (bold) attached to the rod which is rotating at constant angular velocity $\omega\ \mathrm{rad/s}$. The masses of blocks and distances from the pulley are as given in the figure. The distance of the pulley from the rod (axis) is negligible. Block B is on verge of slipping. Find $\omega$.</p>
</blockquote>
<p>What I did :</p>
<p>Let mass of $A = m_1$. Distance of $A$ from axis = $r_1$. Mass of $B = m_2$. Distance of $A$ from axis = $r_2$.</p>
<p>If block $B$ is on verge of slipping $A$ is also on the verge of slipping. Questionable observation. But leads to correct answer. Anyway, we consider a rotating frame attached to the rod. So we give a centrifugal force to $A$ = $m_1 \omega^2 r_1$ and to $B$ equal to $m_2 \omega^2 r_2$. Tension in string $ = T$. We check two cases. Let $B$ slip inwards. Then $A$ slips outwards. So $A$ slips rightwards relative $B$. $A$ was on verge of slipping. Static friction on $A = k_1 m_1 g$. Static friction on $B = k_2 (m_1 + m_2) g$. Then equating forces and solving the system and putting values we get $ \omega = \sqrt{22}\ \mathrm{rad/s}$. The other case ($B$ goes outwards) leads to contradiction.</p>
<p>Though the result is correct, I have a few questions. Why does the fact that $B$ is on the verge of slipping imply that $A$ is also on the verge of slipping. I mean, suppose we just eliminate the rotation and add an external force on $B$ instead. Let the magnitude of force reach $k_2 (m_1 + m_2) g$. Then why is it necessary that the force of static friction between $A$ and $B$ is $k_1 m_1 g$ ? Am I wrong, and is it just that the answer matched, without correct physics?</p>
<p>A detailed explanation of a solution to this problem would be very helpful as I'm a beginner, and I intend to clarify these essential concepts.</p> | g11795 | [
0.00901162251830101,
0.009566315449774265,
0.015585627406835556,
-0.019790994003415108,
0.05229576677083969,
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0.12258582562208176,
-0.03156433627009392,
-0.065592460334301,
-0.012256392277777195,
-0.018235299736261368,
0.00804905965924263,
-0.029732907190918922,
0.013... |
<p>I have read that the total magnetic field of a ferromagnet, $\vec{B} = \mu_0\vec{H}+\mu_0\vec{M}$ where $\vec{H}$ is an external magnetic field and $\vec{M}$ is the magnetic field of the ferromagnet due to the alignment of its dipoles to $\vec{H}$. </p>
<p>On the other hand, I have read that ferromagnetic materials tend to "channel" and "concentrate" field lines. See, for example, the image below. With the solenoid alone, the shape of the magnetic field would be very different than the shape with the magnet included. The magnet has "channeled" the magnetic field lines of the solenoid.</p>
<p>What explains this "channeling" behavior of ferromagnetic materials? In other words, is this explainable using the normal methods for magnetic field calculations such as Biot-Savart and treating the ferromagnet as consisting of infinitesimal dipoles or does the dynamic process of domain alignment need to be considered in calculating the final magnetic field? </p>
<p><img src="http://i.stack.imgur.com/TIlBw.png" alt="Magnet has affected the shape of the field due to the solenoid."></p>
<p>Edit: In order to explain myself better, I have included two simulations from <a href="http://www.femm.info/wiki/HomePage" rel="nofollow">FEMM</a>. One is a selenoid wrapped around an iron core which has geometry chosen to emphasis the channeling behavior I mention above. The second is identical to the first, with iron replaced with air. From the equation $\vec{B} = \mu_0\vec{H}+\mu_0\vec{M}$ I would expect the two simulations to have magnetic fields that have identical directions $(\vec{B_{iron}}/|\vec{B_{iron}}| = \vec{B_{air}}/|\vec{B_{air}}|)$ but these simulations show they do not. Why is this?</p>
<p><img src="http://i.stack.imgur.com/thqhb.png" alt="Iron Simulation"></p>
<p><img src="http://i.stack.imgur.com/FHSbF.png" alt="Air Simulation"></p>
<p>Note the simulations are axisymmetric which means that they are treated as if the entire configuration is rotated around the left axis to form a three-dimensional problem.</p> | g11796 | [
0.020411236211657524,
0.05208932235836983,
-0.012523293495178223,
0.045640572905540466,
0.08156237006187439,
0.013128782622516155,
0.06335543841123581,
0.026075739413499832,
-0.0161651112139225,
-0.018940502777695656,
-0.00030486061586998403,
0.01600196771323681,
0.01689896173775196,
0.012... |
<p>In our aerodynamics class we recently discussed the concept of static and dynamic pressure and discussed their application to aircraft instruments. However, I do not understand properly how the altimeter can work.</p>
<p>First of all a small recap of Bernoulli's law. The total pressure is given by $p_t = \frac{1}{2} \rho V^2 + p_s$ and is constant along a streamline. Consequently, the static pressure is given by $p_s = p_t - \frac{1}{2} \rho V^2$.<br>
Now imagine a low speed windtunnel. In a reservoir the speed is so low that it can be assumed to be $V=0$ m/s. Hence here the static pressure equals the total pressure, $p_t = p_s$. Now the fluid is accelerated along a streamline, and hence the static pressure should drop according to the relation given above.</p>
<p>Now this is where my problem is. I read that the altimeter just measures the static pressure at flight level to obtain the pressure altitude. According to the explanation given above, however, this can not be, as the static pressure in the flow will be lower than the static pressure at the same altitude at zero velocity.</p> | g11797 | [
0.05209873989224434,
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0.04629583656787872,
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0.007070375140756369,
-0.026940440759062767,
0.04502295330166817,
0.033274851739406586,
0.01... |
<p>If electrons in an alternating current periodically reverse their direction, do they really flow? Won't they always come back to the same position?</p> | g124 | [
-0.0037038486916571856,
-0.011458317749202251,
-0.0009302961407229304,
-0.022720571607351303,
0.08513780683279037,
0.005428464617580175,
0.00959642231464386,
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0.020291652530431747,
0.018089013174176216,
-0.006655502133071423,
0.10739558935165405,
-0.02799796499311924,
... |
<p>In mechanical engineering, the torque due to a <a href="http://en.wikipedia.org/wiki/Couple_%28mechanics%29" rel="nofollow">couple</a> is given by $\tau = P\times d$, where $\tau$ is the resulting couple, $P~$ is one of the force vectors in the couple and $d$ is the arm of the couple. A couple is made up of two forces of the same magnitude.</p>
<p>On the other hand, a <a href="http://en.wikipedia.org/wiki/Moment_%28physics%29" rel="nofollow">moment</a> is also given by $M = P\times d$. However, there is only one force involved! How can the resulting <a href="http://en.wikipedia.org/wiki/Torque" rel="nofollow">torque</a> be of the same magnitude if in one case two, in the other case only one force is involved?</p> | g11798 | [
0.04950520396232605,
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0.056359998881816864,
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0.008070642128586769,
0.014371627941727638,
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0.01981896534562111,
-0.031083062291145325,
0.026888903230428696,
... |
<p>In working through a rigorous derivation of the compressible Navier-Stokes equations, I find that the momentum flux in the X-direction should be driven not only by the normal pressure gradient $\frac{\partial p}{\partial x}$ and shear stress terms $\frac{\partial(\tau_{yx})}{\partial x}$ and $\frac{\partial(\tau_{zx})}{\partial x}$, but also by the gradient of the normal stress $\frac{\partial(\tau_{xx})}{\partial x}$. It's intuitively clear to me how adjacent lamina moving at different speeds can transfer momentum across their interface, and so the shear stress terms in the momentum equation are readily intelligible. The normal stress term, on the other hand, is far less intuitive because I cannot see how a freely-deforming fluid can support tensile stresses. Positive normal stresses (i.e. compression) are not that hard to understand, but it's proving exceedingly difficult to fully envisage an element of a fluid "pulling on" an adjacent element in a way even remotely analogous to the behavior of a solid under the same conditions. I am also unclear on the difference between "pressure" and "normal stress" in the fluid. How exactly are these terms different? I am interested primarily with gases not liquids.</p> | g11799 | [
0.00495876744389534,
0.02304246462881565,
-0.03207455947995186,
-0.02707485668361187,
0.005507220048457384,
0.0060131181962788105,
0.03375007584691048,
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-0.03879261016845703,
-0.02268308401107788,
-0.03691345825791359,
-0.03219084069132805,
-0.04... |
<p>The cosmological constant (dark energy) is often described in terms of empty space having a non 0 energy value and this energy being the source of the accelerated expansion of the universe. If space is expanding, what does this imply for energy conservation? Is this energy conserved by being more thinly distributed as space expands? Does this question make any sense or am I just crazy?</p> | g11800 | [
0.059548329561948776,
0.0034384329337626696,
0.01364136952906847,
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-0.03974130377173424,
0.025736013427376747,
-0.04549173265695572,
0.01618173159658909,
0.0213... |
<p>I understand water boils at different temperatures depending on altitude.</p>
<p>I am seeking to get an illustrative explanation for this, including a diagram if possible.</p> | g11801 | [
0.04261390119791031,
0.0002808122371789068,
-0.029012978076934814,
0.06977017968893051,
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0.0010898385662585497,
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0.05... |
<blockquote>
<p><em>The small, hot, dense early universe the size of an atom was made up entirely of energy, it wasn't until after the expansion began and the universe cooled down some of that energy began converting into the first atomic nuclei.</em></p>
</blockquote>
<p>This quote seems a little dubious but I think this is worth asking anyway:
Can someone explain the atomic process, if it even exists, of how this would work to convert energy in to matter, and what form of energy was initially present, and what is required to cause this change?</p> | g67 | [
0.06481523811817169,
0.028787458315491676,
0.029610905796289444,
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0.02824406698346138,
0.037775278091430664,
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0.0303477980196476,
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0.010162577033042908,
0.03433195874094963,
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<p>As I understand, in physics, 'information' is closely tied to thermodynamic entropy. Does this relationship imply that if the Universe expands and ends in 'heat death' (maximum entropy?) that it reaches a state of maximum information (so at the Big Bang it had very low entropy and information content)? I sense this is incorrect given the principle of conservation of information, so what does an increase in entropy in the Universe imply for its information?</p> | g11802 | [
0.0428742989897728,
-0.029767503961920738,
0.015211127698421478,
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0.030276108533143997,
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<p>My lecture script of Quantum Field Theory states that " the state space contains states with negative norm ".</p>
<p>Why does it have to be like this and what would be an example fo such a state?</p> | g11803 | [
-0.010300219058990479,
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<p>According to quantum theory,Einstein said that light waves have small packets called photons and they are said to have no mass and charge but having energy E=hv and they behave has both particle and wave character.</p>
<p>And they travel with certain velocity.</p>
<p>How photons have momentum and energy if they said to have no mass?</p>
<p>Momentum = p=mv ,where m= mass v=velocity.</p> | g195 | [
0.01683492213487625,
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0.035296231508255005,
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0.006103426218032837,
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0.0240... |
<p>On a test, we had a question where there are 4 point charges at the vertices of a square. The 2 charges at the upper vertices have charges of <code>+q</code> and the 2 charges at the lower vertices have charges of <code>-q</code>. The magnitude of the charges are equal. According to the answer sheet, the electric potential is 0 along a horizontal line halfway between the 2 upper and 2 lower charges. Why is it 0? Shouldn't the test charge be attracted to either to top or the bottom depending on its charge?</p>
<pre><code>+q +q
------------ <--- 0 electric potential
-q -q
</code></pre> | g11804 | [
0.06105342507362366,
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0.06512602418661118,
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0.02... |
<p>So I have a triangle Wavefunction defined as:</p>
<p>$$\psi(x)=\begin{cases}x &0<x<\frac{L}{2} \\ L-x &\frac{L}{2}<x<L\end{cases}$$</p>
<p>When I try to find the uncertainty in momentum, I find that it is zero. This cannot be possible by Heisenberg. So I am wondering if I have to (or how to) account for the discontinuity in the wavefunction when using the $\hat p$ operator.</p> | g11805 | [
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... |
<p>It is known the fact that there is no way to extract energy (in any form) from any system without introducing some energy. The Earth for example, gets energy from the Sun, from nuclear fusion of hydrogen. But, what if the Earth would be isolated (there is neither an energy gain, neither loss), it would be possible for our lives to continue (without using an fuel on the Earth)? </p>
<p>The idea of this question started from the quote "Nothing is lost, nothing is created, everything is transformed". As the energy remains inside the system, may it be transformed to be reused?</p> | g11806 | [
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... |
<p>Does the knowledge of the material absorption coefficients aids engineers in determining which material to use in their solar cell designs? If yes, how?</p> | g11807 | [
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<p>What is <a href="http://www.encyclopediaofmath.org/index.php/Elliptic_genera" rel="nofollow">elliptic genera</a> in physics?
Reading many relevant papers, they just defined <a href="http://ncatlab.org/nlab/show/elliptic+genus" rel="nofollow">elliptic genus</a> as sort of partition function.
I try to find useful materials to explain it, but I couldn't find it.
Can you give some intuition for this terminology in physical view? </p> | g11808 | [
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<p>In a video (<a href="https://www.youtube.com/watch?v=KfyWWv5GCzM">Here</a>), I saw crocodiles jump vertically about three meters without using any solid surface. The wonderful thing is that when they start to jump, their vertical velocity is approximately zero, unlike fish who jump using initial velocity. It seems that crocodiles create an upward force that counteracts gravity, because when they are rising, their velocity seems to be constant.</p>
<p>How is this possible? Could anyone explain this phenomenon using physics laws?</p> | g11809 | [
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0.010203186422586441,
-0.0080346... |
<p>If we write the Klein-Gordon equation in this form
\begin{equation*}
c^2 \hbar^2 \nabla^2 \Psi = \hbar^2 \ddot{\Psi} + 2i\hbar (U - mc^2) \dot{\Psi} + U (2mc^2 - U) \Psi
\end{equation*}
we have a pleasant sense of continuity from the non-relativistic to the relativistic treatment of quantum particle (we use the Schrödinger formalism, and to get the NR solutions we only have to put $c\to\infty$). The (not Lorentz invariant) equation has to be handled with care because the manipulations I used in order to obtain it, included squaring conservation of energy, so we can get spurious solutions too. But I think that for zero-spin particles it works, because I found it in page 42 of <a href="http://books.google.lu/books/about/Relativistic_Quantum_Mechanics.html?id=NjZogv2yFzAC&redir_esc=y" rel="nofollow">Wachter's <em>Relativistic Quantum Mechanics</a></em> (written slightly differently). </p>
<p>If we suppose that $|\Psi|^2$ is stationary (i.e. the solution has the form $\Psi (\mathbf{r},t) = \psi (\mathbf r) e^{Ct} $ with $C$ purely imaginary) the equation takes the time-independent form:
\begin{equation*}
-c^2 \hbar^2 \nabla^2 \Psi = [U^2 - 2(E+mc^2)U + E^2+2Emc^2] \Psi
\end{equation*}
(if you are interested in the proofs search <em>sr.pdf</em> in my Home Page, I don't transcribe here because, more than a question, this should become an article)</p>
<p><strong>My question:</strong> </p>
<p>Suppose using this equation with a finite monodimensional hole:
\begin{equation*}
U(x) = \left\{
\begin{array}{ll}
-V_0 & \quad \textrm{if }-a<x<a\\
0 & \quad \textrm{if }|x|>a
\end{array}
\right.
\end{equation*}
In the internal region $\Psi$ is sinusoidal (with the not restrictive condition $E>-V_0$), but in the external region we get
\begin{equation*}
\Psi'' = k^2 \Psi ;\qquad k = \frac{\sqrt{-E (E + 2 mc^2)}}{c \hbar}
\end{equation*}
If $-2mc^2 <E <0$, $k \in \mathbb{R}^+$, otherwise $k$ is purely imaginary, the wave function is sinusoidal and the normalization is impossible. Not surprising that for $E>0$ we don't have stationary states with that finite hole, but:</p>
<ul>
<li>what about the case $E<-2mc^2$? What does it mean?</li>
</ul>
<p>The only reasonable interpretation I found, is that in this case the particle is totally confined into the hole.
- Is this wrong?</p> | g11810 | [
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0.02994408644735813,
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0.... |
<p>firstly I am a Grade 12 Physics student currently doing my final experimental investigation which I decided to do on double pendulums. Before I got into this, I was under the impression that there was some equation I could use which I could plug in my starting conditions such as starting angle, weight of pendulum arms, their lengths, and gravity to pull out a function of x and y against time. Now I am writing the report, it seems it isnt that simple and there is a lot of terminology used on sites that I am unfamiliar with and I really don't know what I am looking for.</p>
<p>My maths/physics knowledge extends to know about integral/differentials, but nothing as complex as these Lagrangians, Hamiltonians or other university-level mathematical principles.</p>
<p>I have researched many sites, such as <a href="http://en.wikipedia.org/wiki/Double_pendulum" rel="nofollow">Wikipedia</a>, <a href="http://scienceworld.wolfram.com/physics/DoublePendulum.html" rel="nofollow">Wolfram ScienceWorld</a>, and other <a href="http://physics.stackexchange.com/questions/54835/double-pendulum">physics stack exchange questions</a>. However, I still have only a vague idea of what I am looking for.</p>
<p>On the stack exchange question I linked, I became familiar with the dot notation. I guess my question is, what is the equation/function which I can use to find the path of a double pendulum given starting conditions. Looking at the wikipedia page shows me many equations of motion. Do I need the hamiltonian equations? The one linked on that stack exchange? The one on that stack exchange question uses $p_{\theta1}$ and its $p_{\theta2}$ equivalent which I don't know what they are either.</p>
<p>Sorry if my question is not clear enough. Also, my teacher told me that I do not need to know the proof for the equation of motion, only that I include the final equation in my report to show how accurate my data is (which I know is off due to the chaotic motion).</p> | g11811 | [
0.05356895178556442,
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0.007979984395205975,
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0.01584065705537796,
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<p>I get confused about two things when deriving the time-dependent <a href="http://en.wikipedia.org/wiki/Perturbation_theory_%28quantum_mechanics%29" rel="nofollow">perturbative</a> approach. </p>
<p>We have the Hamiltonian<br>
$$H = H_0 + \lambda H^{(1)}$$
and we have solved (from Schroedinger)<br>
$$\dot{C_f(t)} = - \frac{i}{\hbar}\sum_{k}\lambda C_k(t)H^{(1)}_{f,k}e^{i\omega_{f,k}t} $$<br>
with the usual<br>
$H^{(1)}_{f,k} = <f|H^{(1)_{f,k}}|i> $ and $\omega_{f,k} = \frac{E_f-E_i}{\hbar}$.</p>
<p>Ok. Next I expand $$C_k(t) = C^{(0)}_k(t) + C^{(1)}_k(t)\lambda + C^{(2)}_k(t)\lambda^2 +...$$
Substituting that I get
$$\frac{d}{dt}(C^{(0)}_k(t) + C^{(1)}_k(t)\lambda + C^{(2)}_k(t)\lambda^2 +... )= - \frac{i}{\hbar}\sum_{k}\lambda (C^{(0)}_k(t) + C^{(1)}_k(t)\lambda + C^{(2)}_k(t)\lambda^2 +...)H^{(1)}_{f,k}e^{i\omega_{f,k}t} $$ </p>
<p>From this I am unable to see<br>
<strong>1) Why does the zeroth order correspond to $\lambda = 0$?</strong><br>
To me this would feel like we have a situation where we have a variable, and for some reason we would be allowed to choose its value for the first term of the series? [As, it stays as a coefficient in the right side of the previous equation]<br>
2) Ok, then if I set $\dot{C}^{(0)}_k = 0$ then I get the recursion relation
$$\dot{C}^{(n)}_f(t) = - \frac{i}{\hbar}\sum_{k} C^{(n-1)}_k(t)H^{(1)}_{f,k}e^{i\omega_{f,k}t} $$
<strong>Did we substitute $\lambda = 1$ in the last</strong>, or what happened to lambda if not? (This is not stated in the sources that I try to study, but it's the only explanation I come up with right now)</p> | g11812 | [
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0.06745312362909317,
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0.04313117638230324,
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0.00697982357814908,
0.007349660620093346,
0.... |
<p><img src="http://i.stack.imgur.com/4Zvo3.jpg" alt="Question"></p>
<p>My question is above. Firstly, I don't actually know whether it is true or not (!). Secondly, if I were to try to prove it, then I have very little idea how to. The potential steps that I have always done are steps from a constant level to another constant level (Heavyside), whereas this is different.</p>
<p>I would imagine the answer is yes, but I'm not sure how to show it.</p>
<p>Can I approximate the curve by small steps (/sums of Heavyside functions), and then show that a larger Heavyside step gives a larger probability?</p>
<p>Thanks,
Sam</p> | g11813 | [
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0.007704260293394327,
0.020524021238088608,
-0.01008577086031437,
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-0.037338968366384506,
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0.009182642214000225,
0.005018118768930435,
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<p>I have some questions about the $i\epsilon$ factor in <a href="http://en.wikipedia.org/wiki/Feynman_diagram" rel="nofollow">Feynman diagrams</a>. First, what is the physical meaning of $i\epsilon$ in loop amplitudes. Second, how does it ensures unitarity?
And third, <a href="http://en.wikipedia.org/wiki/Dyson_series" rel="nofollow">Dyson series</a> assume that incoming and outgoing particles are free, this can be implemented by assuming that the interaction Hamiltonian switches off adiabatically, $e^{-\eta\,t}H_{I}(t)$. Is this $\eta$ related with the $i\epsilon$?</p> | g11814 | [
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0.03155798465013504,
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0.08806172758340836,
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-0.001521049765869975,
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0.06003720685839653,
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0.005... |
<p>A and B are connected to a rope. A constant upward force 86.0N is applied to box A. Starting from rest, box B descends 12.1m in 4.70s . The tension in the rope connecting the two boxes is 32.0N.</p>
<p>What is the mass of B?
What is the mass of A?</p>
<p><img src="http://i.stack.imgur.com/g90hu.jpg" alt="enter image description here"></p>
<hr>
<h2>My work and what I am struggling with:</h2>
<p>I am trying to find the acceleration experienced by B, with that I will find the mass.
I find the acceleration using:
$$2\Delta_y/t^2=a$$
$$a=1.0955m/s^2$$</p>
<p>Then I have a problem for B do I use this equation:
$$\sum F_y =32-M_b*g=M_ba$$
$$Or$$
$$\sum F_y =86-M_b*g=M_ba$$</p> | g11815 | [
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0.027423065155744553,
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-0.040901146829128265,
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-0.002935145748779177... |
<p>Can we divide two vector quantities? For eg., Pressure( a scalar) equals force (a vector) divided by area (a vector).</p> | g11816 | [
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0.04586613550782204,
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... |
<p>I live in Louisiana these days, in an area that is known for its numerous antebellum plantation homes (circa early 1800s). While touring one of these homes it was clear that almost everything about the house was designed around keeping cool in the summer. Some examples:</p>
<ul>
<li>4 meter high ceilings to allow hot air to rise to the ceiling.</li>
<li>Floor to ceiling windows to allow hot air at the top to escape and cool air to be drawn in at the bottom. </li>
<li>Porches on the sunny sides of the house to prevent sunlight from entering the windows.</li>
<li>Large central staircases to allow hot air to rise to the second floor, drawing cool air in on the bottom floor.</li>
<li>Some have a cupola, a central observation room at the top of the house, again to allow hot air to escape at the top of the house and draw air in from the bottom.</li>
</ul>
<hr>
<p>My question is: Given our modern understanding of thermodynamics, how could one design a home today to be cooled passively? Could we do any better than the plantation owners of the 1800s?</p>
<p>Lets define cooling as making the house more comfortable for humans. This means that it is not only important to reduce the temperature, but also to block sunlight and maintain airflow. Also, if possible, it would be very beneficial to extract moisture from the air. </p> | g11817 | [
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0.08553439378738403,
... |
<p>Would an airplane flying through superfluid helium experience lift and drag? The airplane is presumed cold enough to not heat up the helium.</p> | g11818 | [
-0.005450261291116476,
0.05409061163663864,
0.0258196871727705,
-0.0011754647130146623,
-0.020201917737722397,
0.04850573465228081,
-0.023839328438043594,
0.05424497649073601,
-0.03510873019695282,
-0.04797332361340523,
-0.015960760414600372,
-0.05036238953471184,
-0.041258662939071655,
0.... |
<p>When light rays reflect off a boundary between two materials with different indices of refraction, a lot of the sources I've seen (recently) don't discuss the relation between the amplitude (or equivalently, intensity) of the transmitted/reflected rays and the original ray. Mostly they just discuss the phase difference induced by the reflection, for instance to calculate thin film interference effects.</p>
<p><img src="http://i.stack.imgur.com/W8fL3.png" alt="reflection/refraction diagram"></p>
<p>Is it possible to calculate the <a href="http://en.wikipedia.org/wiki/Transmission_coefficient" rel="nofollow">transmission coefficient</a> $T$ and <a href="http://en.wikipedia.org/wiki/Reflection_coefficient" rel="nofollow">reflection coefficient</a> $R$ based on other optical properties of the materials, such as the index of refraction? Or do they need to be looked up from a reference table?</p> | g11819 | [
0.001125712995417416,
-0.02384823001921177,
0.012527265585958958,
-0.0011128535261377692,
0.005367199424654245,
-0.049018681049346924,
0.011219051666557789,
0.022932808846235275,
-0.016505885869264603,
0.01145683228969574,
0.006141801830381155,
0.05981520190834999,
0.04400522634387016,
-0.... |
<p>My question is basically what exactly is electricity? I've simply been told before that it's a flow of electrons, but this seems too basic and doesn't show that electricity is instant. What I mean is turning a switch has no delay between that and a light coming on. Is it really instantaneous? Or is it just so fast that we don't notice it?</p> | g988 | [
0.05328460410237312,
0.035159606486558914,
-0.001120558357797563,
-0.019138725474476814,
0.029222266748547554,
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0.03604309633374214,
0.04388239607214928,
-0.03884345293045044,
-0.020407361909747124,
-0.004759101662784815,
-0.009488769806921482,
0.008498700335621834,
-0... |
<p>Why turning velocity of star towards point "A" makes it's satelites, change their apoapsis to side opposite of velocity vector?</p>
<p>Sentence above turned a bit crazy or not understandable (possible reasons: my vocabulary isn't that good; I don't know what the heck I am talking about).</p>
<p>So I mean this: <a href="http://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html" rel="nofollow">http://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html</a> The first you get is star (yellow) and planet (purple). If you closely, you notice circle around star. It's velocity, if you move it in direction opposite to purple star. Purple planet get's crazy and flies away, as if star turns it's magnetic polar towards that planet.</p> | g11820 | [
0.001584221376106143,
0.06503269821405411,
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0.008986380882561207,
0.05466138944029808,
0.006341670174151659,
0.007077701855450869,
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-0.04941811412572861,
0.02052568644285202,
0.0831698477268219,
0.0683203861117363,
-0.00171783... |
<p>I'm trying to find the period of precession for a gyroscope. Now I was able to find the angular precession rate, which was 1.132 rad/s, but I have no idea how to convert this to a 'period', and google didnt find me anything useful. How do I do this?</p> | g11821 | [
0.07049711793661118,
0.0010275413515046239,
0.016998780891299248,
-0.08926717936992645,
0.05470980703830719,
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-0.008714239113032818,
-0.007889222353696823,
-0.023071015253663063,
0.04307159036397934,
-0.0... |
<p>Let's say you have a garden hose connected to an ordinary water tap which is opened fully. If you pinch the end of the hose, water leaves the hose at a higher speed (and this can be useful while watering plants, to reach pots which are further away). However when a tap (with no hose connected) is opened only slightly, water flows out at a low speed, possibly even in drops.</p>
<p>The actions of pinching the end of a hose and of almost-closing an open tap seem similar, so why the difference in behaviour?</p> | g913 | [
0.0180828794836998,
-0.04456452280282974,
0.0038447596598416567,
0.03473958373069763,
-0.00720912916585803,
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0.07689019292593002,
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0.007453819736838341,
0.025857388973236084,
-0.032208867371082306,
0.028667612001299858,
0.098... |
<p>I'm having trouble with a boundary condition. In a fluid mechanics problem, I have flow at $z = \infty$ flowing into a solid plate at $z = 0$ and then flowing radially, and the problem is given as axisymmetric. I know that the velocity field has $v_r$ and $v_z$, and $v_\theta = 0$. How in the world would I express the symmetry boundary conditions without $\theta$?</p> | g11822 | [
0.08222673833370209,
0.012178403325378895,
0.00577550008893013,
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0.050539810210466385,
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-0.013574478216469288,
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0.... |
<p>Related: <a href="http://physics.stackexchange.com/questions/92960/why-is-stainless-steel-a-poor-conductor-of-electricity">Why is stainless steel a poor conductor of electricity?</a>
I recently had a metal implant, and I'm psyching myself out- should I be considered at all with eddy currents in the implant? I feel like the steel must be somewhat of a better conductor than my body, indeed in the above question it appears to be so. Couldn't eddy currents get painful?</p> | g11823 | [
0.04701371118426323,
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0.043199390172958374,
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0.05157758295536041,
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0.08431771397590637,
-0.0627049133181572,
0.0107... |
<p>Help, I am terribly confused about entropy. On the one hand, I am taught at school that a substance such is an ice/solid has a lower entropy than its gaseous equivalent and that a process such as solidification reduces entropy, which is justified with the explanatory premise that the solid is more "ordered". </p>
<ol>
<li>All this seems dogmatic to me, and it somewhat conflicts with my own intuition (probably means I am wrong). For one, if a change of entropy is measured with the equation (delta)S = q/T (btw, can anyone justify this equation / show its derivation?), take solidification - the heat content (q) falls so its exothermic, hence q is a knowable negative value (the enthalpy of fusion, if I am not wrong?) and T is the critical temperature at the given atmospheric pressure - however how about the entropy change when the temperature changes too - what if the change in the heat content results in a change in temperature - how is that measured.</li>
<li>
Another idea that conflicts with my mind is why are solids/colder things said to have lower entropies at all? I understand from a statistical point of view why overall entropy increases, as things progress to chaotic, and this entails that the heat death of the universe will see maximum entropy - or another to express it: no work will be attainable from the system/universe. However, I am told that colder things have LOWER entropies? I can only intuitively understand entropy from a complete picture - where hot and cold mix to increase overall entropy - how can a part - like the cold area by itself (given it is uniformly cold so that its own potential energy, by itself, is null) even be given a entropy value? The same goes for the hot part - it only makes sense to be if we consider the entropy of the system as a whole when hot and cold are separate or mixed - but obviously, there must be something i don't get.</li>
<li>
Could it be that I am confusing different kinds of entropies - btw (final point) if (in Chemistry at least) entropy is defined by change in heat content / temperature (in kelvins), then how could overall entropy ever decrease as the loss of entropy over there (via loss of heat content) would increase the entropy here (which compensates) and so on. This definition (for me) entails that entropy simply is transformed/passed on like energy. This clearly even conflicts with my own intuitive view of entropy as more of a measure of order, and hence attainable work from a system.
You can see, I have many questions and if you know the answers but can't be bothered, do not hesitate to answer only a fraction of it all, I am grateful for anything. Thank you very much.</li>
</ol> | g11824 | [
0.020954761654138565,
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-0.036545198410749435,
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0.06646890193223953,
0... |
<p>When graphing the induced current in a coil while a magnet is dropped through it why is the total area equal to 0?
The area represents the charge in the coil but why must the resultant flow of charge be 0?</p> | g11825 | [
0.0779060572385788,
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0.0321... |
<p>For a charge moving in an electric field $\vec E$, its equation of motion is given by the electric part of the Lorentz force $$\frac d {dt}\gamma m \vec v = e\vec E$$This comes from the conservation of relativistic energy in a static electric field. But a magnetic field would still make this conservation law true since the magnetic force is always orthogonal to the velocity of the charge and therefore doesn't change its energy.</p>
<p>Is there a simply physical argument that shows why a static charge doesn't create a magnetic field?</p> | g346 | [
0.03413381427526474,
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0.01500630285590887,
0.008457639254629612,
-0.013613021932542324,
0.02423018030822277,
-0.00... |
<p>A terrifying idea I think, to be so utterly alone.</p>
<p>Do you recon life could exist in intergalactic space? A lot of cosmic radiation is shielded from us by the Milky Way's magnetic field, but the stars of galaxies also create a lot of radiation, so maybe it would cancel out for a planetary system floating in intergalactic space.</p>
<p>Don't really see why not if its star is a high energy yellow dwarf.</p>
<p>I'm talking if about if the system was magically transported to intergalactic space, but as a second part to this question, how could such a system be ejected out into the void in the first place? Super nova?</p>
<p>Could life survive its planet being blasted out into intergalactic space? Could intelligent, advanced life, with foresight, be able to survive? What would they have to do to achieve this? Or could such a phenomenon happen gradually?</p> | g11826 | [
-0.010097753256559372,
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0.01138047780841589,
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0.013850858435034752,
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-0.08642777800559998,
-0.015833212062716484,
0.0470866896212101,
0.0418052151799202,
-0.0... |
<p>I'm interested in the existence of a Lagrangian field theory description of Bronwnian motion, does such a thing exist? Given a particle of some spin $\sigma$, which has a Lagrangian associated with it $\mathcal{L}_{\sigma}$ (which, using the Euler-Lagrange equations, produces Klein-Gordon for $\sigma$ = 0 etc) is there a way I can allow for Brownian type freedoms in this description? Hopefully such a stochastic freedom is allowed in the Lagrangian description.</p>
<p>Any references would be warmly welcomed. Thanks!</p> | g11827 | [
0.0326932892203331,
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0.02647041343152523,
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0.0054391538724303246,
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0.05007953941822052,
0.039604298770427704,
0.021... |
<p>I been reading: <a href="http://www.mth.uct.ac.za/omei/gr/chap5/node2.html" rel="nofollow">http://www.mth.uct.ac.za/omei/gr/chap5/node2.html</a>. The website seems credible with its contact details & location being extremely accurate and easily verified, and its mathematics seem correct so I have no doubt about it however in this thought experiment it devises a object falling then </p>
<blockquote>
<p>observer has some magical method of converting all this energy into a photon of the same energy [ this is a thought experiment after all! ]</p>
</blockquote>
<p>That seems slightly over-the-top expectations even for a thought experiment or is it perfectly credible and possible on contrary to my belief?
I previously assumed thought-experiment had to be realistic yet this seems very un-realistic. Don't get me wrong I'm confident on this University and am sure that they have intelligent people but anyway is this though experiment for Red-Shift allowed even with its "magic" as some may call it?</p> | g11828 | [
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0.02887554094195366,
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0.07417316734790802,
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-0.024167312309145927,
0.05856335535645485,
0.00995502807199955,
0.024702271446585655,
-0.001... |
<p>We know there are rouge stars floating in intergalactic space, thought to be caused by galactic collision. What other other classes of celestial object could be found floating around in intergalactic space?</p>
<p>Within galaxies there are the following types of object:</p>
<ul>
<li>Nebulae </li>
<li>Stars</li>
<li>Brown Dwarfs</li>
<li>White Dwarfs</li>
<li>Black Holes</li>
<li>Neutron Stars</li>
<li>Comets</li>
<li>Asteroids</li>
<li>Interstellar rogue planets</li>
<li>Planetary Systems</li>
<li>Star Systems</li>
<li>Star Clusters</li>
<li>Debris Disks</li>
</ul>
<p>Which of these can possibly exist in intergalactic space? Asteroids and comets are probably quite common, but is it known for entire planetary systems to exist in intergalactic space? Even star clusters?</p>
<p>Out of all the possible types, could I also have a link / designation to each object thats been observed, floating in intergalactic space.</p>
<p>For example, here's an intergalactic star <a href="http://en.wikipedia.org/wiki/HE_0437-5439" rel="nofollow">HE_0437-5439</a></p> | g11829 | [
-0.027019033208489418,
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0.042153846472501755,
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0.0019929674454033375,
-0.08923324197530746,
0.042351093143224716,
0.06026793271303177,
0.009160950779914856,
... |
<p>For a planet which has a temperature gradient, hot in the center and cooler on the surface, why do we see absorption lines?</p>
<p>Similarly, why do we see emission lines if the planet is hot on the surface and gets cooler as you move to the center?</p>
<p>Note, for this question I am only thinking of the planet as a black body, not as something, for example, transiting a star and observing the spectra (transit spectra) of the light that shines through the planet's atmosphere. The source of the spectra is the planet itself.</p> | g11830 | [
0.003155731363222003,
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0.04729361832141876,
0.07808799296617508,
0.05037393... |
<p>I have a goal to educate myself up to the current level of knowledge we possess about the universe.</p>
<p>I've tried textbooks, wikipedia, lectures, but i find each of them fundamentally flawed in different ways.</p>
<p>Textbooks tend to be incredibly bloated, and I become unable to "see the forest for the trees"
Wikipedia seems to be too technical/mathematically rigorous for my level of understanding
Lectures feel very time consuming and i dont really feel as though i get a structured sense of how everything fits together.</p>
<p>I feel as though all mathematical and physical concepts can be explained in simple terms, yet i cant find resources which present concepts like this.</p>
<p>I don't want explanations that are completely dumbed down or necessarily lacking in math, but i would prefer explanations which give math intuition and take time to explain what the variables and symbols mean in laymen's terms.</p>
<p>If anyone knows any resources similar to what i described, or has any advice it would be greatly appreciated!</p>
<p>Edit: I should also mention that i had been referred to Hooft's outline of learning, as seen here:
<a href="http://www.staff.science.uu.nl/~hooft101/theorist.html#ssphysics" rel="nofollow">http://www.staff.science.uu.nl/~hooft101/theorist.html#ssphysics</a>
Which i find to be a trememndous help, but I'm still struggling as to the ideal places to find clear resources in regards to these subjects.</p> | g98 | [
0.02293081395328045,
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0.0013814350822940469,
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0.003908119630068541,
0.06194761022925377,
-0.05386506766080856,
0.06266080588102341,
0.0... |
<p>I have a Celestron Firstscope telescope and like it overall for my location and the amount of observing I do. I am disappointed in my view of the planets with the scope. What would be a good eye piece to purchase for this telescope to improve planetary observing. In keeping with my limited budget, it should not cost more than the telescope.</p> | g11831 | [
-0.028335103765130043,
0.039283737540245056,
-0.005111546255648136,
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0.0077229891903698444,
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0.024108942598104477,
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0.0... |
<p>I understand what an <a href="http://en.wikipedia.org/wiki/Hanbury_Brown_and_Twiss_effect" rel="nofollow">Hanbury Brown and Twiss</a> (HBT) interferometer <em>does</em>, but how can this be used to measure the apparent angular diameter of some object? </p>
<p>What is the mathematical explaination?</p> | g11832 | [
-0.005572499241679907,
0.0024221609346568584,
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0.02089843340218067,
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-0.04898082837462425,
-0.012089354917407036,
0.01656314544379711,
0.07428348809480667,
0.01... |
<p>Could you recommend some good books on physics? I found out that some books on physics are not good, especially about Einstein's Relativity and quantum mechanics. Here is an example which makes me think so: <a href="http://physics.stackexchange.com/questions/110207/while-space-man-lives-for-1-day-then-how-long-does-earth-man-live-1000-years/110294#110294">While Space-man lives for 1 day, then how long does Earth-man live ? 1000 years or 1 second?</a></p>
<p>A bad book makes my head spin for hours , it may be a good thing(I have some joy in it！）, but maybe it's a bad thing too sometimes.</p>
<p>Someone says that "Michael Berry, Principles of Cosmology and Gravitation" is a good book. Any other good books ?</p> | g98 | [
0.02342226356267929,
0.04504843056201935,
0.017581894993782043,
-0.0038071060553193092,
0.005129098426550627,
0.01873558573424816,
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0.02969122678041458,
0.05211854726076126,
0.11613589525222778,
-0.04250127077102661,
0.026915738359093666,
-0.0166... |
<p>Is there a detailed description for a <a href="http://en.wikipedia.org/wiki/Hartmann_mask" rel="nofollow">Hartmann mask</a> based collimation process?</p>
<p>I've been told by a friend that is possible to collimate an <a href="http://en.wikipedia.org/wiki/Schmidt%E2%80%93Cassegrain_telescope" rel="nofollow">SCT</a> by placing a three round holes Hartmann mask at the secondary and then covering one hole at a time. Unfortunately the guy did not clearly describe the full procedure and what I should try to obtain looking in the eyepiece (or looking at an attached webcam video).</p> | g11833 | [
0.024384506046772003,
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0.0065552410669624805,
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0.011123953387141228,
0.024331822991371155,
0.0066606951877474785,
0.04774320498108864,
0.... |
<p>We have seen birds sitting on uninsulated electric wires of high voltage transmission lines overhead without getting harmed, because sitting on only one wire doesn't complete any circuit. </p>
<p>But what about the potential difference between their legs? Is this not a small complete circuit? Because the wire has a potential gradient, there should be a potential difference between the bird's feet. Is this potential difference so very small that we can say the bird is sitting at a single point on the wire? If a bird of a sufficiently large size, with a wide gap between its feet, sits on a single wire, shouldn't the bird receive a shock if the potential difference is sufficient?</p> | g11834 | [
0.012118719518184662,
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0.025042906403541565,
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0.05896352231502533,
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0.029314791783690453,
-0.07650697231292725,
-0.024514244869351387,
-0.0748511552810669,
0.0199... |
<p>A reservoir contains a fluid, and there is an aperture at the bottom through which the fluid flows out as shown in the illustration:</p>
<p><img src="http://i.stack.imgur.com/Ne3dy.gif" alt="enter image description here"></p>
<p>I understand that the rate of flow is based on at least these parameters: the amount of fluid in the reservoir due to the weight of the fluid, the size of the apperture, and the density of the fluid. But how exactly do these relate to the flow rate? That is:</p>
<p>$$Q=f(V,A,\rho)$$</p>
<p>What is $f$?</p> | g11835 | [
0.07593415677547455,
0.008062941953539848,
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0.0475720576941967,
0.01484604086726904,
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0.0735853910446167,
0.028039... |
<p>Problem:</p>
<blockquote>
<p>$1.0 \text{ kg}$ of air at pressure $10^6 \text{ Pa}$ and temperature $398 \text{ K}$ expands to a five times greater volume. The expansion occurs such that in every instance the added heat is a quarter of the work done by the gas. Calculate the final pressure. $1 \text{ kmol}$ has a mass of $29 \text{ kg}$ and $C_V = \frac 52 R$.</p>
</blockquote>
<p>I solved the problem but I have some questions regarding the approaches I made. I interpreted heat being a quarter of the work done every instance as $\text{d}Q = \frac 14 \text{d}W$. By the 1st law of thermodynamics ($Q = W + \Delta U$), this yields $-\frac 34 \text{d}W = \text{d}U$. </p>
<p>But for molar heat capacity we know that $\text{d}U = nC_V\text{d}T$, hence $-\frac 34 \text{d}W = nC_V\text{d}T$. By definition, $\text{d}W = p\text{d}V$ and therefore $-\frac 34 p\text{d}W = nC_V\text{d}T$. We treat the gas as ideal and thus we can substitute $\frac {nRT}V$ for $p$, arriving at $-\frac 34 \frac{nRT}V \text{d}V = nC_V\text{d}T$.</p>
<p>Separation of variables yield $-\frac 34 \frac{nR}V \text{d}V = \frac {nC_V}T \text{d}T$. We take the definite integrales</p>
<p>$ \displaystyle \int_{V_1}^{5V_1} \!\!\!\!\! -\frac 34 \frac{nR}V \text{d}V = \int_{398}^{T_2} \frac {nC_V}T \text{d}T$</p>
<p>and can then finally solve for $T_2$ (it turns out to be approximately $245 \text{ K}$). At last, we can determine the final pressure from</p>
<p>$\displaystyle \frac {p_1V_1}{T_1} = \frac {p_2V_2}{T_2}$.</p>
<hr>
<p><strong>(1)</strong> My main question is whether you guys know of a different way to solve this problem not involving having to solve differential equations?</p>
<p><strong>(2)</strong> I've seen the 1st law written as $\text{d}U = \text{d}Q + \text{d}W$ but if we use that expression we definitely won't get the right answer; what's up with the inconsistency?</p>
<p><strong>(3)</strong> I saw no other option than having to use the molar heat capacity equation $\text{d}U = nC_V\text{d}T$ but doesn't this assume constant volume? In our problem the volume is definitely changing, so is it not contradictory to use that very equation?</p> | g11836 | [
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... |
<p>If faster than light travel is impossible, how is it that light emitted from matter so close together in the time soon after the Big Bang is only now just reaching us? I would assume that there would be a "limit" to how far back we can see, but exactly how long after the Big Bang are we able to observe? I'm sure there's an easy explanation, but it has been bugging me for a while... I am aware of how this works, but I am curious as to how long after the Big Bang are we able to see in images such as the Hubble Deep Field? If light travels at a constant speed no matter the conditions the observer is experiencing, then why would there be a <em>longer</em> stretch of time for light to travel through as the universe expanded? Please let me know if I should elaborate more on my question because I do feel like my writing is a little bit hard to understand...</p> | g11837 | [
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<p>I've been working on some exercises and I'm in doubt if my procedure with this one is correct. We have a hollow cylinder with internal radius $r_a$, external radius $r_b$, resistivity $\rho$ and length $L$. A difference of potential $V$ is then applied on the extremes paralel to the axis of the cylinder.</p>
<p>First I'm asked to find the resitance. Well, for this one I've just used that $R=\rho L/A$ and calculated $A=\pi(r_b^2-r_a^2)$. Second, I'm asked to find the current density when $V$ is applied. Well, what I did was suppose that the cylinder is an ohmic resistor so that $V=Ri$ holds, and then I've got $i=V/R$. Then the current density should be $J=i/A$ and so we have $J=V/RA$ which gives $J=V/\rho L$. Is this correct? Can I assume that the cylinder is ohmic?</p>
<p>Third I'm asked to find the electric field. Now I've used that $\rho = E/J$ so that we must have $E = \rho J$ so that $E = V/L$, this says tha that the field is uniform, but I'm a little unsure about it. Finally the fourth one asks to find the resitance again if now the current flows radially from inside to ouside. In this final case I think that it'll change just the cross sectional area, but I didn't find some easy way to write this down.</p>
<p>Can someone give a little help with this?</p> | g11838 | [
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<p>I am asked to show that an new defined operator:</p>
<p>$$U_{\beta} = \exp(\displaystyle\frac{i\beta L_z}{\hbar})$$</p>
<p>is unitary, where $$L_z = -i\hbar\,\,(x\displaystyle\frac{\partial}{\partial y} - y \frac{\partial}{\partial x }).$$</p>
<p>I tried the following: </p>
<p>$$ U_{\beta}^{\dagger} U_{\beta} = \exp \left( \frac{i\beta(-L_z^{\dagger}+L_z)}{\hbar} \right)$$</p>
<p>So I couldn't make the inside of exponential zero.</p> | g11839 | [
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<p>For example, there's a very simple circuit which only contains on resistor. So according to Ohm's law, we have: $\mathrm{emf} = IR$</p>
<p>As we know when time $t = 0$, the current must be $I = 0$. However, how do I describe how the current really behaves just after I switched on the circuit?</p>
<p>You may ask why I care about that. </p>
<p>Since I'm learning self-inductance. The most torturing part of it is understanding the "back Emf" induced by changing magnetic field. Every textbooks in which I've looked up this part dismiss the detail of how the "back Emf" really impact on the varying current, instead, they just say "back Emf" pulled the current and "slowed" it down, which is quite vague and obscure.</p>
<p>And I devised a situation where this vaguely described intuition really burns out my head:</p>
<p>In LR circuits, we have the following differential equation:</p>
<p>$$\mathrm{emf}-L \frac{dI}{dt}-IR = 0$$</p>
<p>Let's take $ t = 0$ to see what is going on.</p>
<p>At the time $t = 0$, obviously we have $I = 0$, which indicates "no current" at all.
So $IR$ must also be zero, we therefore have:</p>
<p>$$L \frac{dI}{dt} =\mathrm{emf}$$</p>
<p>which means the inductor has produced a "back emf", that is to say, there exists a magnetic field in the inductor. But how? Since there's no current at all.</p>
<p>Furthermore, can anyone help me understand the very first moments when an LR circuit is switched on? Thanks in advance.</p> | g11840 | [
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<p>My understanding is that the Casimir Effect is caused by vacuum energy. Quantum mechanics (QED) predicts vacuum energy, but gets the value grossly wrong, by a factor of $10^{120}$. On the other hand, from what I have read, Dark Energy is understood to be caused by vacuum energy.</p>
<p>Has anyone checked whether the measured value for the Casimir Effect fits the value required for Dark Energy to make up 70% of the energy in the universe? If it did, that would be an excellent validation of Dark Energy.</p> | g11841 | [
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<p>I'm writing a script involving physics equations, and someone complained that my script outputs $F = m a$ as $F = a m$, as well as outputting $E_p = m g h$ as $E_p = g h m$; another example would be $E = m c^2$ vs $E = c^2 m$. I've obviously opted for displaying the variables in the equations in alphabetical order, and it looks wrong because it's against convention - but why are the variables ordered in the way they conventionally are in the first place?</p>
<p>From what I can see of all the examples I've just given, the out-of-place variable is <em>mass</em>, so perhaps the convention is to put mass first? I don't see any reason why that would be the case though.</p> | g11842 | [
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<p>I'm tough in school that a reference frame must be non-moving; For example if I take as reference frame the waves of the ocean, i will have the impression that i'm moving, but I'm not. But if movement is relative, how to distinguish between a reference frame that is not moving and one that is moving? It is impossible i think!</p> | g11843 | [
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<p>Is it reasonable to assume that de Sitter temperature will stop growing when it reaches equilibrium with the temperature of CMB?</p>
<p>Currently the de Sitter temperature (the temperature of the Universe's boundary) is $$T_{dS}=2.67\times10^{-30}\,\mathrm K$$</p>
<p>and rises.</p>
<p>At the same time, the temperature of CMB is $$T_{cmb}=2.7\,\mathrm K$$</p>
<p>and falls.</p>
<p>I wonder, does it mean that at the moment they will equate, the de Sitter temperature will stop growth, and so the expansion of the universe will also stop accelerating, thus reaching the thermodynamic equilibrium?</p>
<p>In other words, whether the excessive temperature of CMB compared to the de Sitter temperature is the main source of the accelerated cosmic expansion?</p> | g11844 | [
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0.... |
<p><em>"The electron around the nucleus is in a quantized energy level and can change it only if an external interaction intervenes."</em> That is OK but when there is a magnet, it has energy of attracting iron particles for months and years (natural magnet) just by right order of atoms. Where this energy come from? In nature we have to spend one sort of energy to gain another form, but in a magnet what is spending? Thanks</p> | g202 | [
0.010833702981472015,
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<p>When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.</p>
<p>However, how can the body exert a force on the ground when it does not have any acceleration? Since force equals mass times acceleration how does a body without acceleration experience a force?</p> | g63 | [
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0.06414328515... |
<p>I just wanted to know whether time dilation is different from time travel or not. Personally I believe both are different. If they are the same things I just wanted to know why. According to me time dilation is something that applies for every object, while time travel particularly applies for humans. Moreover I feel that travelling through time also in a sense means being able to control time. Time dilation is just an effect due to special relativity and I think it is often confused with time travel. Time travel can be based upon time dilation but I do not think that it completely implies the same thing.</p>
<p><strong>EDIT</strong>
By time travel I mean like exact travelling. Like you can go in any direction. Similarly I mean into the past as well as the future. But I just wanted to know if there is a general difference since everyone could define time travel in a separate manner.</p> | g11845 | [
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<p>I just wanted to understand the following. Let's stay with the harmonic oscillator in QM, just to have an example at hand.
First, there are all the different states for $n=1,2,...$. (Let's call them $\psi_n$).</p>
<p>Then, the superposition of a state, for example $$\frac{1}{\sqrt{2}}(\psi_1+ \psi_2)$$ is also a solution to the Schrödinqer equation.</p>
<p>But then, there is also the concept of a <a href="http://en.wikipedia.org/wiki/Density_matrix" rel="nofollow">density matrix</a>, for example</p>
<p>$$\rho= \frac{1}{2} |\psi_1 \rangle \langle \psi_1| + \frac{1}{2} |\psi_2 \rangle \langle \psi_2|.$$</p>
<p>My question is: What is the meaning of the concept of superposition and this density matrix state? </p>
<p>What I know so far is somewhat vague:I would say I can only measure whether a particle is in one of the $\psi_i$. The density matrix tells me that the particle is equally likely in one of the two states written down there, but if I would measure, then I would get one of them. But I don't really know what the superposition tells me? Which experimental setting corresponds to a superposition and what is the meaning of it?</p>
<p>If anything is unclear about my question, please let me know.</p> | g11846 | [
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<p>From a physicist's perspective there are several situations in which somehow arbitrary choices of mathematical structures can be made. One can describe a system from different perspectives, etc. without changing anything in the physical properties. (see gauge invariance, picture changing etc.)
In the situation when these choices impose a mathematical structure one has limitations in the subsequent choices (are these limitations physical???). However, there are situations when this prescription does not hold. The best example is in this case the Black-Hole complementarity principle (if it is well defined in the first place).
So, the question about how mathematical structures "interact" in a logical way is not a bad one. Again: what is the interaction between, say, locality and Hausdorff-ity in the case of a black hole? Or what is the true relation between metrizability and hausdorff-ity of a space in the context of a black hole? The question about how mathematical structures assigned (innocently) at some point interact in different situations is in my opinion a quite relevant one... </p> | g373 | [
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0.00... |
<p>Is there any physical significance of the fact that the group manifold (parameter space) of $SO(3)$ is doubly connected?</p>
<p>EDIT 1: Let me clarify my question. It was too vague. There exists two equivalence classes of paths in the group manifold of SO(3) or in other words, $\Pi_1(SO(3))=Z_2$. This space is therefore doubly connected. There are paths which come back to initial configurations after a rotation of $2\pi$ and others after a rotation of $4\pi$, with proper parametrization of angles.</p>
<p><strong>Using this fact</strong>, is it possible to show that such a topology admits the existence of half-integer spins and integer spins? I understand spinors as objects <strong>whose wavefunctions</strong> pick up a -ve sign after a rotation of $2\pi$, and comes back to itself after a rotation of $4\pi$. Right? But from the topological argument given above, it is not clear to me, that how does it lead to two kinds of <strong>wavefunctions</strong>, spinor-type $(j=\frac{1}{2},\frac{3}{2},\frac{5}{2}...)$ and tensor-type $j=0,1,2,...$? It is not explicitly clear <em>how these two types of paths in SO(3) group manifold will lead to such transformation properties on "the wavefunctions"</em>?</p>
<p>EDIT 2: <a href="http://en.wikipedia.org/wiki/SO%283%29#Topology">http://en.wikipedia.org/wiki/SO%283%29#Topology</a>. </p> | g11847 | [
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<p>I think I am currently making a mistake regarding my interpretation of Faraday's Law.</p>
<p>$\vec{\nabla}\times\vec{E}=-\frac{\partial\vec{B}}{\partial t}$</p>
<p>Assuming we have an electric field $\vec{E}$ in the plane between 2 particles given by:</p>
<p>$\vec{E}=(\frac{x}{x^2+y^2}+\frac{1-x}{(x-1)^2+y^2}, \frac{y}{x^2+y^2}-\frac{y}{(x-1)^2+y^2})$</p>
<p>Then $\vec{\nabla}\times\vec{E}=(0,0,\frac{y\cdot(2\cdot x-2)}{((x-1)^2+y^2)^2}+\frac{(2\cdot(1-x))\cdot y}{((x-1)^2+y^2)^2}) = (0,0,0)$</p>
<p>As expected, now, if there's an electric field through a coil due to potential difference, then why will the curl be non-zero only when the electric field is initiated and closed off from the coil (e.g. connected/disconnected from a power source)?</p>
<p>Currently; I assume that the derivative of the magnetic field converges to 0 over time - because it can not grow indefinitely if we simply have a potential difference (coil connected to a power source).</p>
<p>So my question is:
How does the electric field (I am correct in that E indeed stands for the electric field, right?) change over time in the time we connect the coil (get potentials at both ends, and a current), until the coil's E curl has stabilized (becomes 0)?</p>
<p>It'd be great if someone had an example of an $\vec{E}(\vec{r}, t)$ that changes with time so that $\vec{\nabla}\times\vec{E}$ converges to 0. Where $t_0$ is the connection time and $t_1$ the stabilization time, and $\vec{r}$ the position in space.</p>
<p>Are my questions based on false premises? I feel really confused, I've tried my best to look for answers but I can not seem to find them.</p> | g11848 | [
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