Relation Definition and 1000 Threads

hey guys, I am building an electric go kart for a final project, and I'm just trying to get my initial justifications correct, with respect to the classical physics involved. SPECS: i was the car to be able to reach 15km/h, The total weight of the car will be approx 200kgs. the size of...

As far as I know, F_ {ext} = d (\hbar k)/dt = d p_{electron} / dt + d P_{crystal} /dt. could one say that \hbar k = P_{electron} + P_{crystal}?

Say we have two vector fields X and Y and we form the projection of Y, Y' orthogonal to X. Since every vector field is associated with a curve with a corresponding parameter, is there a relation between the parameters of Y and Y'?

One of the most popular mass loss equations of a star, developed by D. Reimers, is given by: dM/dt = -(4x10^-13) * η(L/(gR)) solar masses per year Where η is a free parameter close to unity and L, g, and R are the luminosity of the star, surface gravity of the star, and the radius of the star...

Homework Statement OK so I'm doing a course on Signals and Systems and I'm taking inverse z transforms using residue integration. One particular formula in complex integration made me think a bit. \oint{\frac{f(z)}{z-z_0} dz} = 2\pi jf(z_0) This looks eerily similar to the definition...

If there is a formula relating the exponential with sine and cosine normal and hyperbolic (exp(ix) = cos(x) + i sin(x), exp(x) = cosh(x) + sinh(x)), there is also a formula relating the logarithm with arcsin, arccos, and arcsinh arccosh?

In transitions in the crystals we always use conservation of wave vector of electron, not electron momentum conservation. For example in an indirect transition from top of valence band to bottom of conduction band, the group velocity of electron and hence its momentum would not change (it is...

relation between r ,ω and θ for rotation around fixed axis. \frac{d\textbf {r}}{dt} = \textbf {ω} \frac{dθ}{dt} = ω \lvert\frac{d\textbf {r}}{dt}\rvert = \frac{dθ}{dt} bold means vector. Is this right?

I'm having trouble wrapping my head around what should be a trivial detail, but it is important, so hopefully someone else putting it in explicit words might help me understand it. What I am having trouble grasping is why do row operations preserve linear dependence relations for the columns...

Hello, I have an issue with the problem below. I have a series connection of two variable capacitances C_{1}(t) and C_{2}(t). I want to establish the differential equation between the current i and voltage V on the ports of the series connection. The capacitance of the series connection of...

Homework Statement The density of a sample of air is 1.211 kg/m3, and the bulk modulus is 1.42 · 105 N/m2. a) Find the speed of sound in the air sample. b)Find the temperature of the air sample. Give answer in °C. Homework Equations The Attempt at a Solution I found...

Homework Statement Consider x^2y''-xy'+n^2y=0 where n is a constant. a) find two linearly independent solutions in the form of a Frobenius series, initially keeping at least the first 3 terms. Can you find the solution to all orders? b) for n=1 you shouild find only one linearly...

How can I prove the following relation T(∂p/∂T)v,N +(∂T/∂V)u,N =p(∂T/∂U)v,N where p= pressure, V= volume, U=internal energy, T= Temperature. I tried by fundamental relation and Maxwell's relation but couldn't able to prove it. I would appreciate if anybody helps me out.

I believe many users here are teachers now or they were in the past and some might be working as professors at universities. I think if you teach a certain subject you understand it well day after day and you realize that you are learning new things and the concept is becoming fundamental as...

hi, in quantum physics completeness relation is often use it equals to one - what is its significance in multiplying with state vector . thanks wasi

Homework Statement For main sequence stars, the mass–luminosity relation can be approximated by L\proptoM^{3.5} f) If luminosity and mass are both measured in solar units, what is the constant of proportionality? {2} I know that the luminosity value of the sun is 4x10^{26}W and M =...

On the set of Z of integers define a relation by writing m \triangleright n for m, n \in Z. m\trianglerightn if m-n is divisble by k, where k is a fixed integer. Show that the quotient set under this equivalence relation is: Z/\triangleright = {[0], [1], ... [k-1]} I'm a bit new the subject...

Homework Statement The displacement due to a wave moving in the positive x-direction is given by ##y=\frac{1}{1+x^2}## at time t=0 s and by ##y=\frac{1}{1+(x-1)^2}## at t=2 s, where x and y are in meters. Find the velocity of the wave in m/s.Homework Equations ##...

Hello, I have recently been reading some texts focusing on modern physics. Both include sections on Planck and how he arrived at the conclusion that energy is not continuous. However I am confused as to what conditions inspired him to make this leap. I am aware of the Ultraviolet Catastrophe...

Hi. I'm working through one of my first problems on sets and relations, and I need some help understanding if I'm getting this right. Any help/suggestions on my through process is greatly appreciated. The question is: Determine whether the relation R on the set of all real numbers is...

Hey guys, I have recently performed a lab where we are to find the equation relating the magnetic field strength to a distance from a dipole in both the transverse and longitudinal direction. We did this using a Hall Effect Probe and a magnetic dipole. What I found after plotting a Log...

I just read that the definition of work is not related whatsoever to the notion of time, whereas the relation between time and work is expressed by the explicit notion of power. However, W=Fs, and F is proportional to the acceleration a, which is the change of rate of the velocity wrt time...

Homework Statement . Calculate by a line integral the following double integral: ##\iint\limits_D (y^{2}e^{xy}-x^{2}e^{xy})dxdy##, D being the unit disk. The attempt at a solution. Well, if we consider C to be the curve that encloses the region D (C is the unit circle), then C is a...

Homework Statement A man of mass m is applying a horizontal force to slide a box of mass m' on a rough horizontal surface. It is known that the man does not slide. The coefficient of friction between the shoes of the man and the floor is ##\mu## and between the box and the floor is ##\mu'##...

Homework Statement It is customary to express fibre loss in units of dB/km: \alpha(dB/km) = \frac{10log(P_{in}/P_{out})}{L(km)} where P_{in} is the power entering the fibre and P_{out} is the power leaving the fibre. Show that \alpha(dB/km) = 4343\alpha(m^{-1}) The Attempt at a Solution...

Hey, Ive a question in my textbook and I don't really know what to do! The question is: I know I need to prove that the relation is 1)Symmetric 2)Reflexive 3)Transitive But how do I prove this

I have a metric g on spacetime and a spatial metric ##\gamma## such that the components of g can be written in matrix form as $$ g_ {\alpha, \beta} = \begin{pmatrix} g_{00} & g_{0 j} \\ g_{i 0} & \gamma_{ij} \end{pmatrix} $$ where ##i,j = 1,2,3## and ##\alpha = 0,1,2,3##. Now I want to find a...

Hi all, i have a doubt. How much teeth in relationship to his radius need to have a gear to be optimal? And, if i have 2 gears with same radius and same #of teeth, to have low friction and low negative effect from weight how much teeth they need to have and with which radius? I know it's too...

Hi, Say y=x2: the solution set is equal to the relation, which is also a set. What's the difference between saying "plot the relation y=x2" and "plot the solution set of y=x2"? Thanks for help.

Please help me in in proving the relation between H2n(x) and Ln(-1/2)(x2) where Hn(x) is the Hermite polynomial and Ln(-1/2)(x) is associated Laguerre polynomial.

Hey! Maybe this is a "piece of cake" question, but here is the thing, i have the Maxwell equations in the Lorenz gauge are \begin{array}{c} \partial_{\mu}\partial^{\mu}A^{\nu}=\mu_{0}j^{\nu} \end{array} In vacuum this gets reduced into \begin{array}{c} \partial_{\mu}\partial^{\mu}A^{\nu}=0...

hi guys, i have a question about the orbit-spin relationship of the celestial objects. for example in our solar system i understand the orbital period becomes lengthy for the planets more distant than the sun, it's logical, but what happens with their spinning motion..? i don't understand why...

Homework Statement In "Methods of theoretical physics" from the authors Morse and Feshbach is writen: " The displacement (dx,dy,dz) is perpendicular to the surface if the component displacemetn satisfy the equation: How to prove this relation? Homework Equations the relevant...

Fact: The refractive index depends on the medium. Also, in general, to study the pulse propagation in a medium, there is a governing model equation (e.g. Non linear Schrodinger equation). My question is: Will there be any relation between the model equation and the refractive index? Why...

1. Homework Statement . Let A be a chain and B a partially ordered set. Now let f be an injective function from A to B and suppose that if a,b are elements of A and a≤b, then f(a)≤f(b). Prove that f(a)≤f(b) implies a≤b. 3. The Attempt at a Solution . I want to check if this proof by...

Hello, I'm having trouble calculating this commutator, at the moment I've got: \left[a_{p},a_{q}^{\dagger}\right]=\left[\frac{i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p),\frac{-i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p)\right]=i\left[\Pi(p),\Phi(q)\right]=i\int...

A particle moves such that its position vector, as a function of time is r(t) = (5*t^2)*i + (3*t^2)*j − (5*t)*k Im trying to find the unit tangent to the trajectory as a function of time. However I can't seem to find any formula of how to do this. Can someone please help me with a formula or...

Homework Statement The coplanar points A,B,C,D are (2-x, 2,2); (2,2-y,2); (2,2,2-z): (1,1,1) Homework Equations The Attempt at a Solution a(2-x, 2,2) + b(2,2-y,2) + c(2,2,2-z) = (1,1,1) Equating respective components ax=by=cz=k The answer is 1/x + 1/y + 1/z = 1 but in my case...

In relativity spacetime is usually visualized by placing something on a stretchable fabric of some sort. The object placed on the fabric will bend the fabric, just as a planet or star would in real space. Time can be manipulated when something extremely massive like a black hole is in space. But...

Several species, including the squid, cuttlefish, dragonfly fish and many microscopic organisms, move themselves around by a kind of jet propulsion. In each case the animal absorbs fluid in a body cavity and expels it through an orifice by contracting the cavity. If a squid has a mass Ms when its...

Hello I have to check if the following relation is an equivalence relation. \[m\sim n \;\;\mbox{in}\;\;\mathbb{Z}\;\;\mbox{if}\; mn > 0\] I think this relation fails to be reflexive since $(0,0)$ does not belong to this relation. Hence this is not an equivalent relation. Is this ok ? Thanks

We know that radio waves follow the curvature of the earth. Reason? Gravity (I think) The only logical thing I can think of is what Johann Heinrich Winkler discovered in mid 1800's; that when electricity is given multiple paths to choose from, it invariably chooses the best conductor (least...

Hello all, I have an equivalence relation that I need some help with. Normally I find these to be fairly simple, however I'm not sure if I'm over-thinking this one or if it's just tricky. For the relation: aRb $\Longleftrightarrow$ |a| = |b| on $\mathbb{R}$ determine whether it is an...

Homework Statement problem statement is attached as problem.pdf Homework Equations eqn are given in the pdf file The Attempt at a Solution I have tried in vain to connect Fermi energy with dispersion relation. I just don't have any clue ,I also tried to determine the effective...

Hi, I have a question about groups: What is the de Sitter group?? and how does it relate to poncaire's group? Thanks!

can you give an example of symmetric property of equality and transitive property of equality. the generalization of these properties are a bit abstract for me. thanks!

Dears, I wish to measure the entropy of visual data such as image and video. I did transform these image and videos into frequency domain such as DCT, then measured the entropy with these pdfs for each AC components of image and videos. However, when I measured the entropy over spatial domain...

Hi friends, I have a system (with unknown properties) which takes an input vector of length 10 and outputs a vector with length 6. I select Inputs vector 'I' which is a 1000x10 matrix, : 1000 samples of 10 elements. And outputs vector 'O' is a 1000x6 matrix,: 1000 samples of 6...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Hi there everybody I have a nice little problem which might not be so complicated after all. I need to push a heavy object using torque applied on a bolt. This is done manually, and the necessary torque needed is of interets. The attachment explains it quite well, I think. To overcome...