Relation Definition and 1000 Threads

Homework Statement Homework EquationsThe Attempt at a Solution [/B] Apologies for a bit hazy picture .Let the three particles be in a line after time 't' . If the inclined line (path of v) from the origin is perpendicular to the hypotenuse then we could write vt= v1cos45°t = v2cos45°t . But...

Homework Statement Let ##x_1=1## and ##\displaystyle x_{n+1} = 3 x_n^2## for ##n \ge 1##. a) Show if ##a = \lim x_n##, then ##a = 1/3## or ##a = 0##. b) Does ##\lim x_n## actually exist? Homework EquationsThe Attempt at a Solution I have proven before that, in general, ##\lim s_{n+1} = \lim...

Hello - I am having a tough time understanding the problems in the attached picture (Problem 13). My issue is understanding how I plug in the proposed solutions, specifically those that include n. I am able to solve A and B but unable to solve the rest. For instance, how do I plug in C or...

I'm in the process of learning special relativity (SR), and I'm a bit confused as to why the relativistic energy dispersion relation ##E^{2}=m^{2}c^{4}+p^{2}c^{2}## gives the energy for a free particle? I get that it is the sum of (relativistic) kinetic energy plus the rest mass term (a...

Why can sometimes entropy remain constant with increase of temperature and vice versa?Entropy implies transfer of heat and heat must increase with temperature.I am unable to intuitively understand.

Homework Statement apparently your effective power is V_maxI_max * cos(x) where x is the phase angle. So I must consider only real power Homework Equations power = VI current = I sin(wt) The Attempt at a Solution Let impedence be = e^ix . I'll write current as Ie^i(wt) consideronly the real...

I am reading a book of General Relativity and I am stuck on a demonstration. If I consider the FLRW metric as : ##\text{d}\tau^2=\text{d}t^2-a(t)^2\bigg[\dfrac{\text{d}r^2}{1-kr^2}+r^2(\text{d}\theta^2+\text{sin}^2\theta\text{d}\phi^2)\bigg]## with ##g_{tt}=1##, ##\quad...

Homework Statement What is the relationship of charge polarity and voltage polarity? I understand an anion has negative charge and cation ion has negative charge, but does an anion have a positive voltage and the cation have a negative voltage? Given the above is generally true, when is the...

Power is measured in watts and lightbulbs are rated in watts. P = W/t and W = Fd What is being displaced? electrical current?

Do all observables which do not commute generate an uncertainty principle ?

Where can I find strict mathematical proof of the relation between antenna aperture and gain which is applicable to any type of antenna ? Aeff = Gain * (lambda^2) / (4*Pi) Aeff - Antenna Effective Aperture Gain - Antenna Gain lamdda - wavelength Pi - 3.14159 Many textbooks just show the...

hi, do the translation operator commute with parity operator?

How should power be calculated in a situation where distance and time are both given, as well as mass. At first, I was thinking of just using W=Fx (force as mass x 9.8) to solve for work, and then I would take the solution for work and put it into P=wt. Does this make sense? That's my best...

New to set and graph theory and need help on how to approach these exercise questions: For each of the following relations, state whether the relation is: i) reflexive ii) irreflexive iii) symmetric iv) anti-symmetric v) transitive Also state whether the relation is an equivalence or partial...

Hi, what is the true meaning and usefulness of the commutator in: \begin{equation} [T, T'] \ne 0 \end{equation} and how can it be used to solve a parent ODE? In a book on QM, the commutator of the two operators of the Schrödinger eqn, after factorization, is 1, and this commutation relation...

Hi all, A happy 2018 for all PF members. I have a question. I am trying to understand some basic principle of thermodynamics. My book tells me tge following: "Heating of a gas at a constant pressure uses more heat as when heating the same gas a constant volume" How do i interpret this? I...

I'm reading about star spectra, color, and temperature and have a question... I understand that very hot stars burn blue because a lot of the radiation is on the UV end so it appears more blue when its ran through several color filters. and the opposite applies for cool stars that are skewed...

Homework Statement Homework EquationsThe Attempt at a Solution ## v = \frac { \omega } k ## ## \omega = \sqrt{ kg \tanh (k) } ##I have no idea to guess the graph. I put g = 9.8 and tried to calculate ## \omega ## for different values of k. ## \omega (0 ) = 0, \omega (30) =...

Homework Statement In hydrogen atom ionization H→p+e show that ##μ_H=μ_p+μ_r## Homework Equations G=μN (N is the number of particles) The Attempt at a Solution (1) I think the question should say "Find chemical potential relation AT EQUILIBRIUM", don't you think? (2) My professor said that...

Hi everyone, I just have some confusion regarding Planck's and Einstein's equation. The following is an explanation of the photoelectric effect using Einsteins theory: Light is composed of photons. Each photon has energy hf and mass hf/c^2. When ultraviolet photons are brought to rest by zinc...

Homework Statement Homework EquationsThe Attempt at a Solution From the equation it is clear that the wave is propagating in y direction. So, the magnetic field is along z- axis. ……….(1) Dimensionally B = E/v……….(2) According to the above two conditions , the correct option is (c). Is this...

Homework Statement Homework EquationsThe Attempt at a SolutionChemical potential is defined as ## \mu = Gibbs potential per particle ##. So, is the system consists of N particles, ##\mu = \frac { G } {N } ##. Now, dG = VdP – SdT ## \frac {dG } { N } = \frac { VdP } { N } - \frac { SdT }...

Hi! Above is a screenshot of logger pro that I'm currently using. I need to linearise this graph and draw a best fit linear line but I have no clue how to do it. What should I do? The table on the left shows the raw data. The first column is showing the values for x-axis, and the second is for...

Hello, I am a Mechanical Engineering student but I am a TA for an electricity and magnetism course, and I had a student ask a question that's a little bit outside my understanding. The question was related to the equation for a radiating electric field from an accelerating charged particle...

Hi, I have an assignment to derive the two following expressions: R(J)-P(J)=2B'(2J+1) R(J-1)-P(J+1)=2B''(2J+1) where Bis the rotational constant and prime ' stands for upper level and bis '' for lower level. Bv=Be-α(v+1/2) using the selection rules (I guess in this case ΔJ=±1) and...

Does centrifugal force generate in increase in overall speed? For example, if I am driving down a highway on-ramp which goes in a circular fashion, with my speed slowly increasing, does my overall speed increase because of the centrifugal force generated from the circular on-ramp? Is more force...

Can the wave function in four dimensions be expressed as e^i(kx+ky+kz-wt)?

1. Homework Statement I've been using a recurrence relation from "Adv. in Physics"1966 Nr.57 Vol 15 . The relation is : where Rnl are radial harmonic oscillator wave functions of form: The problem is that I can't prove the relation above with the form of Rnl given by the author(above). I've...

I am reading the book: "Discovering Modern Set Theory. I The Basics" (AMS) by Winfried Just and Martin Weese. I am currently focused on Chapter 2: Partial Order Relations ... I need some help with understanding the meaning of "nonreflexive relation"... The section from J&W giving the various...

Hi everyone! Sorry for the bad English! Please, I learned that a wave is something the photons "surf" on, like, in one electromagnetic wave, can have many photons. So, is this true? Like, I though that one gamma ray and an infrared photon would ride different waves... More: the light from the...

Hey! :o We have an electromagnetic field. The relation between energy and momentum of a particle with charge $q$ is $$\left (\frac{E-q\phi}{c}\right )^2=m^2c^2+\|p-\frac{q}{c}A\|^2$$ where $c$ is the velocity of light and $\phi=\phi (x,t), A=A(x,t)$ are the scalar and vector potential of the...

Is anyone familiar with a way to determine the half-life of a protein from its melt temperature (Tm)? It seems like there ought to be some sort of correlation, be it theoretical or empirical.

Homework Statement I am having a slight issue with generating function of legendre polynomials and shifting the sum of the genertaing function. So here is an example: I need to derive the recurence relation ##lP_l(x)=(2l-1)xP_{l-1}(x)-(l-1)P_{l-2}## so I start with the following equation...

Homework Statement the file given Homework Equations F=mv^2/r The Attempt at a Solution I do not understand why the centripetal force is 2a and not 2/a since the radius of X is twice longer. When I use the equation above, raidius is inversely proportional to the acceleration. Is radius...

Homework Statement Find the expression for c_p - c_v for a van-der-waals gas, with the equation of state \Bigg{(}p+\dfrac{a}{V^2}\Bigg{)}(V-b)=RT Homework EquationsThe Attempt at a Solution Basically I've proved c_p - c_v = \Bigg{[} p + \Bigg{(}\dfrac{\partial E}{\partial V}\Bigg{)}_T...

Homework Statement By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny. Homework Equations $$G=U-TS+PV$$ $$dG=\mu...

By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny. My working:

Hello Everyone, Question about the centripetal force: the centripetal force is the name given to the component of the net force acting on the object in a direction perpendicular to the object's trajectory and directed towards the center of the osculating circle. This net force component causes...

My main question is regarding whether the membership relation is taken as an undefined concept (as is usually hinted in set theory books) or if the membership relation can be defined within the language of first order predicate theory. Let me describe a method to define the membership relation...

In the picture above, there are three balls in separated small elevators. Elevator A lifts the ball upwards, elevator B stays still, elevator C moves the ball downwards, all in constant speed. (And this is a model, a simplification of the reality, we assume no other forces on the balls other...

Hi all - forgive me, I'd asked a series of questions in a previous post that was deemed to be circular, but I still didn't obtain a satisfactory answer to the question I was asking. In this post, I'm going to try to be very careful to use terms that are at least less 'misplaced', per se...

I am in a chemistry class, and there was an in class example on how to do this type of problem, but then when I looked in the book, there wasn't an equation. the questions are related to what the wavelength will be when electrons are moving between orbitals.

Hello, I may working through attached paper and really need help with deriving equation in appendix - A4 to give A10. http://iopscience.iop.org/article/10.1088/0004-637X/744/2/182/pdf Any help would be greatly appreciated. thanks, Sinéad

Homework Statement Homework Equations $$\frac{\partial S}{\partial u}\Bigr|_{v} = \frac{1}{T}$$ $$\frac{\partial S}{\partial v}\Bigr|_{u} = \frac{-P}{T}$$[/B] The Attempt at a Solution a.) $$\frac{S}{R} = \frac{UV}{N} - \frac{N^3}{UV}$$ $$\frac{S}{R} = \frac{UV}{N} - \frac{N}{uv}$$ $$...

I need a clear-cut explanation of vacuous truth, as I can't seem to wrap my head around it. I guess this more precisely comes down to why we organize the truth table for the conditional statement the way that we do. Also, in connection to this, I'm wondering why the empty set is a subset of all...

Hi! In school I was thaught that magnet doesn't have anything to do with the motion of electrons, but then when you see the way electromagnetic induction work, it seems like the magnet move the electrons somehow. How is that possible and can we control the movement? Thanks a lot and sorry for my...

I have information about temperature, pressure, normal and shear stresses, viscosity, conductivity, density, heat capacity and adiabatic heating for a particular area of mantle in the form of 2D matrices. I want to show phase relation for this region of mantle. Is there an equation (group of...

My book says that the real numbers are complete in the sense that they satisfy the least upper bound property. So it is the case that completeness and satisfying the l.u.b. property are equivalent by definition, or is it the case that satisfying the l.u.b. property implies completeness, meaning...

Hi, say for example we have a magnetic core with a coil wound around, and if we introduce an airgap (i.e. increasing the reluctance), how is inductance reduced? I read on some forum (see source below) that inductance scale inversely with reluctance. So I do not have the mental picture of why...

It's pretty easy to explain why objects appear small as the distance from them increases, if we use ray theory: as the distance increases, the angle become smaler. But I know the ray theory is far from being a accurate theory of light. My question is then, How can we explain the phenomenon of...