Expansion Definition and 1000 Threads

Homework Statement https://holland.pk/uptow/i4/d6adf6b4297ef9c8c20c3e58ec66535d.png Homework Equations integration The Attempt at a Solution [/B] https://holland.pk/uptow/i4/36ea9fcf0a17f1ea8137f0140c881289.jpg I have got stuck at this step... And have no idea on how to go on to the...

I read Chris Hirata's paper on gravitational waves (http://www.tapir.caltech.edu/~chirata/ph236/lec10.pdf) where he performs a multipole expansion of the gravitational source. I got most of it, apart from the part where he expands the inverse distance function into a series : More specifically...

We are told that space is expanding and that the rate of expansion is speeding up. However, as relativity shows that space and time are inextricably linked, does this mean that time is expanding too?

Hi, I am trying to work out how much each dimension of a solid (for instance an annular disc) made out of steel changes assuming that the solid is heated uniformly and is not constrained at any of its boundaries. Am I right in saying that, the linear expansion equation L = L_0 (1+ α ΔT) can be...

Homework Statement The 40 ft long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap in inches so that the rails just touch one another when the temperature is increased from -20 F to 90 F. The cross sectional...

In two papers of Terrel and Penrose, the concept of Terrel effect were presented. Both of the papers say that "the plane of projection is expanded by a certain factor, which is equal to Doppler factor for certain cases." Now does it mean the area of the projected plane is expanded by that...

Hi guys, I need to determine the performance of a single expansion ramp nozzle (SERN) from CFD results with different nozzle pressure ratios (NPR). For some NPR the nozzle is overexpanded and for some underexpanded. Now the impact of the control volume definition on especially the axial thrust...

I am interested in whether it might be possible to select a more efficient heat expansion media for nuclear power plants than water, which has a very specific heat and a very high heat of vaporization. The high value of the specific heat and the heat of vaporization of water requires much...

If a particle can potentially be transported to any place in space limited only by the speed of light, does that potential amount to an expansion of space? And another question: Does it make sense to define space as any place a particle could go to?

I'm having a hard time understanding some fundamental properties of our expanding universe. It seems reasonable that globally the size of the universe increases bc of the expansion. However the size of each causal patch/observable universe stays the same. Following this logic it would seem that...

Homework Statement I need to expand this piecewise function f(x) = h for a<x<L and f(x) = 0 for 0<x<a. I am told that this is a square wave so ao and an in the expansion are 0 (odd function). Therefore I only need to worry about bn. The limits on the integral are from a to L, but what about the...

I began thinking about the problem I describe below from trying to understand the discussions in another thread. https://www.physicsforums.com/threads/concordance-cosmology-paper.909603 This problem is about the expansion behavior of a “simple” universe model that might demonstrate a distinction...

My question is very simple but it is something I have been thinking about for some time. Every time a person needs to have the expansion of the Universe explained or the question "What does the Universe expand into?", people who know a bit about the topic answer that it expands into and onto...

Homework Statement Show that ##\displaystyle \frac{1}{1+x^2} = \frac{1}{x^2} - \frac{1}{x^4} + \frac{1}{x^6} - \frac{1}{x^8} + \cdots## Homework EquationsThe Attempt at a Solution I know that the power series expansion of ##\displaystyle \frac{1}{1+x^2}## about ##x=0## is ##1-x^2 + x^4 - x^6 +...

Homework Statement Four particles are each placed a distance a from the origin 3q at (0,a) -2q at (a,0) -2q at (-a,0) q at (0,-a) find the simple approximate formula for the potential valid at points far from the origin. Express in Spherical coordinates Homework Equations P=qr ##V =...

Is it true for all material that if young's modulus is high then melting point will be high and coeff of thermal expansion will be lower? Any example that doesn't follow the above statement. Many Thanks

Homework Statement I'm stuck on part (c) of this question. Homework Equations $$T\frac{d}{dT}\bigg(\frac{L}{T}\bigg) \equiv \frac{dL}{dT} - \frac{L}{T}.$$ Clausius-Clapeyron equation: $$ \frac{dp}{dT} = \frac{L}{T\Delta V} \approx \frac{L}{TV_{vap}}.$$ The Attempt at a Solution My approach...

Would you explain what "mechanical expansion or compression of a material" is? It makes no sense to me I only know thermal expansion or compression. https://www.google.tl/patents/US5004946 Thank you.

MENTOR NOTE: NO TEMPLATE BECAUSE SUMITTED TO WRONG FORUM. 3.1) A quantity of 0.10 mol of an ideal gas A initially at 22.2 degrees C is expanded from 0.200 dm3 to 2.42 dm3 . Calculate the values of work (w), heat (q), internal energy change (delta U), entropy change of the system (deltaSsys)...

Hi! Dealing about wave propagation in a medium and dispersion, wavenumber k can be considered as a function of \omega (as done in Optics) or vice-versa (as maybe done more often in Quantum Mechanics). In the first case, k (\omega) \simeq k(\omega_0) + (\omega - \omega_0) \displaystyle \left...

If the Universe is expanding, wouldn't it be common sense to think everything inside it is expanding too?

We all know BigBang theory, which states that the universe is continuously expanding, my doubt is the term expanding, does it mean the expansion of galaxies as a whole or including the planets in it?.

Since the universe is expanding, photons emitted by distant stars are red-shifted, having their wavelengths stretched out. But, since the energy of a photon is dependent on the inverse of its wavelength, doesn't that mean that the expansion of the universe is causing photons to lose energy? How...

Hi, I stamped at a series expansion. It is probably Taylor. Would you explain it? It's in the vid. https://confluence.cornell.edu/display/SIMULATION/Big+Ideas%3A+Fluid+Dynamics+-+Differential+Form+of+Mass+Conservation I understand equation 1 in the picture but I do not understand 2. I...

For this question imagine an balloon that will never pop and contains infinite mass. This balloon materializes inside a perfect vacuum with no boundary. Is there a terminal velocity of the expansion of the balloon? If so, does the balloon gradually accelerate to this velocity or does it hit...

<Moderator's note: moved from a technical forum, so homework template missing> Hi. I have solved the others but I am really struggling on 22c. I need it to converge for |z|>2. This is the part I am really struggling with. I am trying to get both fractions into a geometric series with...

I have a question about thermal expansion of liquid into a gas void. Imagine a closed upright cylinder filled mostly with water – say 99%, and the remaining 1% is gas. Now imagine that you heat the cylinder and its contents. The water will expand by ΔV owing to thermal expansion. The gas...

Hi! I'm trying to show how the chemical potential depends on the temperature and I'm advised to use the Sommerfeld expansion. I'm using it on the density of charge n=\int^{+\infty}_{-\infty} \rho(\epsilon)n_Fd\epsilon , which gives n=\int^{\mu}_{0} \rho(\epsilon)d\epsilon...

Hello all! This is my first post on the forum. As some background, this issue pertains to the IB Physics Internal Assessment that I am in the process of writing. Thanks in advance for your help! Homework Statement My research question is: How does the drop height of a consistent-size clay ball...

Homework Statement A vertical heat-insulated cylinder is divided into two parts by a movable piston of mass m. Initially, the piston is held at rest. The top part is evacuated and the bottom part is filled with 1 mol of monatomic gas at temperature 300 K. After the piston is released and the...

I have a PVC fitting that keeps cracking. The fitting consists of 2 parts. One piece is placed over the end of a flexible PVC ribbed hose, and the other is inserted inside the hose. The 2 parts act as a compression fitting to attach to the end of the hose. The hose typically has an outside...

Homework Statement Find the common temperature at which the inner diameter of the ring is 0.05% larger than the diameter of the sphere. Given: Lead sphere d = 5cm To = 70°C ∝ = 29x10-6/C° Steel ring d = 4.9975cm (the sphere is 0.05% larger than the inner diameter of the ring, hence this value)...

"How it can be explained mathematically by dP/dV = -gammaP/V

Since there are no bonds at the other side of the surface, external layers of solids are usually closer to the next layer. This process is called relaxation. (Example in picture a here). However, at a lecture I attended the other day it was mentioned that some surfaces present expansion...

ΔL=LαΔT The concept is interesting and applying its formula isn't even tedious, but what are the real factors that determine α here? I understand that thermal expansion is a direct consequence of the average separation between atoms. And that the coefficient can be found through different...

Before the period of the the accelerated expansion started about 5 billion years ago.. where was the dark energy and what was it doing. Or could it only got produced 5 billion years ago and non-existent before that?

With the LDCM, cosmological constant, model I understand that the scale factor of the Universe grows more rapidly than the Horizon. I believe the correct horizon I need to be considering is the Hubble Horizon and the point when objects recessional velocity hits the speed of light they disappear...

@phinds noted in a recent thread that energy is not conserved on a cosmological scale, which hadn't occurred to me before, so I did some reading and happily the concepts were easy to digest and things I already understood but just hadn't connected the dots myself on regarding the implications...

Homework Statement Let v(0) = [0.5 0.5 0.5 0.5]T, v(1) = [0.5 0.5 -0.5 -0.5]T, v(2) = [0.5 -0.5 0.5 -0.5]T, and z = [-0.5 0.5 0.5 1.5]T. a) How many v(3) can we find to make {v(0), v(1), v(2), v(3)} a fully orthogonal basis? b) What are z's coefficients of expansion αk in the basis found in...

Hunt & Ott 2015, Defining Chaos NB: For a more introductory version, phys.org ran a piece on this article two summers ago This paper was published as a review of the concept of chaos in the journal Chaos for the 25th anniversary of that journal. The abstract is extended with a clearer...

Homework Statement 1 mole of ideal gas with internal energy U= 3/2 RT , expands from initial volume Vi = 1/10 Vo following the equation p=(− po / Vo ) V +po . Find (a) the highest temperature reached by the gas during the expansion and (b) the maximum amount of heat taken in by the gas...

Homework Statement A rectangular windshield is to be assembled by installing a glass plate on a 3 ft by 1 ft frame at 60°C. The glass plate is cut at 68°F in such a way that its length is three times its width. The linear expansivity of glass is 5 x 10-6 /C°. (a) What area of the glass plate at...

isn't expansion essentially making more space rather than moveing us in it? So why does it redshif light? Or is that just a super facile explanation of expansion that they explain people like me who wouldn't get it?...

Hi everyone I would love to get some feedback on this silly idea I had when thinking of the balloon analogy. Another way to achieve the same effect - at least in 2 dimensions - is to move a projector further away from a screen - everything expands relatively. If the universe is a 2d hologram...

1. ... Expand the Eigenvalue as a power series in epsilon, up to second order: λ=[3+√(1+4 ε^2)]V0 / 2 Homework Equations I am familiar with power series, but I don't know how to expand this as one.[/B]The Attempt at a Solution :[/B] I have played around with the idea of using known power...

Friedmann's Eq can be viewed here https://ned.ipac.caltech.edu/level5/March08/Frieman/Equations/paper1x.gif What I don't get is that all the texts/analyses of Friedmann's equation say that if the right hand side is negative it means that the universe will expand reach a critical point and then...

I have just found this paper that states the universe is expanding faster the further we look back, Different than the Hubble measured.? https://www.sciencedaily.com/releases/2017/01/170126132624.htm The new measurement is completely independent of -- but in excellent agreement with -- other...

I am trying to find examples problems on thermal expasions related to the subject of measurement technique Google but I can't find them.. I don't know exactly what could be asked but the problem will be related to: "expansion of measurement device" is given, and "expansion of measured...

Homework Statement Ok, so if the universe is expanding, and the scale of space itself is changing, then that means that even humans and the Earth is expanding right? But is the reason why we don't notice this effect the slowness of it? So v=Hd, where H is Hubble's constant, which has a value of...

Homework Statement Fourier series expansion of a signal f(t) is given as f(t) = summation (n = -inf to n = +inf) [3/(4+(3n pi)2) ) * e j pi n t A term in expansion is A0cos(6 pi ) find the value of A0 Repeat above question for A0 sin (6 pi t) Homework Equations Fourier expansion is summation...