Fundamental Definition and 907 Threads

Homework Statement Compare the magnitude of the Coulombic fundamental force to the Gravitational fundamental force. Explain similarities/differences between the 2 types of forces. You have 2 protons separated by 1*10^-4 meters. Calculate the gravitational force of attraction between the two...

A lot of times I read that "Field is more fundamental than particles". This comes from QED. I read some explanations, but I do not understand precisely, what aspect of particles is mentioned. If we say that elementary particles are black holes (let us assume that BH exists smaller than the...

Homework Statement Let f(t) = sin(6t) + cos(8t). (a) What is the fundamental period of f(t)? T= 2pi/\omega I know the fund. period of sin is pi/3 and cos is pi/4, and the definition of fundamental period saids that f(t + T ) = f(t) for the smallest T in the function, so would pi/4 be my...

1. what's the fund. period of f(t)= sin6t + cos8t? 2. the fund period of the first term is pi/3, the second pi/4 3. do i just add the 2 fundamental periods up to get the whole fund period? also for the Fourier coefficients of this function, should i use euler's to make it into exponentials...

Homework Statement Si(x) = \int_{0}^{x}{\frac{sin(t)}{t} dt At what values of x does this function have a local maximum? 2.Solutions [PLAIN]http://img833.imageshack.us/img833/701/27444263.png The Attempt at a Solution So I took the derivative and applying FTC and I got sin(x)/x = 0 sin(x)...

As mass is independent of the period for SHM?

Homework Statement If I post this question in the wrong section please forgive me and direct me to the correct place. I want to ask about how electric circuit works. Let's use a basic circuit, which has a battery, wire, and resistor, for the problem. From what I learned, the electrons move...

Homework Statement The fundamental frequency of a vibrating stretched string of length 1.0m is 256Hz.When the string is shortened to 0.4m with the same tension,the fundamental frequency now become how many Hz? Homework Equations The Attempt at a Solution

Just curious who wrote the first proof of the fundamental theorem of calculus. Thanks.

I'm confused, by composite particle we probably mean when we use something to smash it, something new will come up, right? Then what's so different about fundamental particles? For example if we "smash" a electron with a positron, we also get something new--photon. I guess I am making some...

Why must the 4-momentum for photons p^\mu =(\frac{h\nu}{c},\frac{h\nu}{c} \textbf{e}) transform as a 4-vector in Special Relativity?

Suppose the functions f(t) and g(t) are periodic with periods P and Q, respectively. If the ratio P/Q of their periods is a rational number, show that the sum f(t)+g(t) is a period function. How to prove this?

Hello, I'm following an introductory course in modern physics. So I understand there's a chance the particle appears on the right side of the barrier, and this has been experimentally verified. Now I was wondering: can the particle also appear in the barrier? If so: is this directly...

curved or non-curved space, what is more fundamental? By intuition it seems that non-curved space is more fundamental. By general relativity and difeomorphism it seems that no one is more fundamental. But how it is with this?

Is it just as fundamental as Newtons Law of Motion or it is deeper than that? I mean, is it like- No matter what invention and discoveries you come up in future, no matter which theories fail and which emerge, this Law of Conservation of Energy shall always stand above all.

why is S^n/S^m homotopic to S^n-m-1. the book just made this remark how do you see this geometrically. how do you compute fundamental groups of matrices like O(3) and SO(3) or SL(2) and whatnot.

Homework Statement Use Your Phi(from part 1) and the fundamental theorem of line integrals to evaluate the same line integral. (should get the same answer!) The Attempt at a Solution Phi from part 1: Phi = xy+ y^2 +C The line from before go from (0,2) to (-2,0) r(a) = (0,2)...

Homework Statement A very tall pipe is partially filled as shown. (A vertical pipe is filled with water about halfway, and .85m of air is in the pipe to the open end. The bottom is closed). |**| ^ |**| | |**| .85m |__| _|_ |__| |__| |__| |__| |__| ^^ My attempt at a drawing, where...

So I've read through beginning alg topology really fast and there are a lot of theorems and methods for computing fundamental groups but what are the most useful tools? When asked to compute the fundamental group what should one do? try to find a deformation retract and compute the fund group...

Hi, everyone: Given a top space X, and a homeo. h: X--->X , we get an induced map (by functoriality ) h_*: Pi_1(X)---> Pi_1(X) . We can also write the map as a map g: Aut(X) --->Hom(Pi_1(X),Pi_1(X)) Is the map g always surjective.? . Almost definitely...

Hi Everyone, I have very fundamental question on Acceleration. I can understand that a moving body accelerates or de-accelerate when its velocity goes up and down. But I couldn't understand; when we say a moving body accelrates or de-accelerates when the direction of moving body changes(with...

FTC "fundamental theorem of calculus Homework Statement Homework Equations FTC The Attempt at a Solution well i have not used FTC in a long time this is from my old lecture notes...how do i show that using FTC(the question show above)

Compute the fundamental group of the space X:=((S^1\times S^1) \sqcup (S^1\times S^1))/\sim where ~ is the equivalence relation (e^{it},e^{it}) \sim (1,e^{2it}) meaning the diagonal of the first torus is identified and wrapped around twice the second generating circles. Call T_A the...

Basic question, but nevertheless. In a non-Abelian gauge theory, the fermions transform in the fundamental representation, i.e. doublets for SU(2), triplets for SU(3), while the gauge fields transform in the adjoint representation, which can be taken straight from the structure constants of...

Upon feeding the IFFT block with the mapped date elements, shouldn't the binary data be upsampled by a sampling frequency that is equal to twice the highest subcarrier frequency (nyquist criterion)? I have written a code for a complete OFDM trasceiver system and I have not upsampled my binary...

Homework Statement A uniform string of length 2.5 m and mass 0.01 kg is placed under a tension of 10 N. 1. What is the frequency of the fundamental mode? 2. If the string is plucked and is then touched at a point 0.5 m from one end, creating a node, what frequencies persist? Homework...

Is the fundamental frequency considered an odd harmonic? Thanks for any clarification

Fundamental Frequency (String Resonance) - velocity problem! Homework Statement Hey guys, i just started working on Fundamental Frequency but am getting confused! A string that is 6.0m long is vibrating with three loops in it. The frequency of the source is 16.5Hz. A)What is the...

Homework Statement prove that the limit of anxn + an-1xn-1 + ... + a1x1 + a0 as x goes to infinity equals infinity ** I forgot to mention that n is an odd number and this is for n>0 otherwise yes your counter example would be correct** Thanks for the quick responses by the way Otherwise, that...

This question may be one of those questions that is hard to talk about because it seems so obvious that a certain thing has to be a certain way that it becomes impossible to figure out how you know that it has to be that way. When you derive the Lorentz transformations from a certain set of...

I am curious how exactly fundamental measurements are made for subatomic particles. I am hoping someone who knows can point me to some references as to the following: 1) How is the position of a photon measured? 2) How is the position of a subatomic particle measured? 3) How is the momentum...

Hello all, I am going through some sample problems exercises in Paul Sally's Tools of the Trade, and am being asked to prove the Fundamental Counting Principle. That is, If A has m elements and B has n elements, then A X B has mn elements. Sally goes on to write that "this is simple to prove...

Homework Statement I am familiar with the following kind of conditional expectation expression: \mathbb{E}[Y|X=x], where X and Y are random variables. I am wondering what the following conditional expectation stands for: \mathbb{E}[Y|X] How these two are related? How the second...

How to find the fundamental frequency of the component(let it for engine)? How the orders of that frequency is approximated while FEA?

Homework Statement A license plate has three letters followed by three numbers. Suppose the digits from 0...9 can be used, except all three digits cannot be zero, and that any letter from A-Z with repeats can be used. How many plates are possible? Homework Equations My question is on...

Hi, how can i derive this fundamental identity "without using entropy"? \left(\frac {\partial U}{\partial V}\right)_T = T\left(\frac {\partial P}{\partial T}\right)_V - P I believe the above equation is purely thermal and has nothing to do with entropy and statistical mechanics but...

If Quantum mechanics theory is the most fundamental theory of nature that explain it at the smallest scale then it should explain Consciousness . I think that there may be deeper level of physics that can explain it . If consciousness is merely a quantum effect , it may be not only limited to...

So I was thinking about the question "What if Boltzmann's constant k were different?" but then I got thinking about the nature of the question. What is the significance of a constant? Can you say one dimensioned constant is more fundamental than the other one? For example, I can imagine...

All the fundamental forces are acting all the time, weak decays etc. So we need colliders so we will have more events per unit time for better analysis? What is the higher energy for? Proton collison of 14 TeV should "blow" the Higgs out for us to see? In general, how does higher energies...

Can we apply the fundamental theorem of calculus to an integrand that's a function of the differentiating variable? For example, can one still use the fundamental theorem of calculus when trying to find the derivative of this function: f(x) = \int_{0}^{x} \frac{cos(xt)}{t}dt

Homework Statement When a 70kg aluminum (density = 2.7 g/cm3) sculpture is hung from a steel wire, the fundamental frequency for transverse standing waves on the wire is 250.0 Hz. The sculpture (but not the wire) is then completely submerged in water. What is the new fundamental frequency...

The fundamental group of a torus is Z*Z,then the fundamental group of a punctured torus is Z*Z*Z. But I've ever done a problem,it said a punctured torus can be continuously deformed into two cylinders glued to a square patch.Really? If that is right,then the fundamental group of punctured...

Homework Statement Theorem. (Fundamental Theorem of Arithmetic) Ever positive integer n has a prime factorization, which is unique except for reordering of the factors. Homework Equations 6.8 Definition. A prime factorization of n expresses n as a product of powers of distinct primes; the...

Quantum mechanics is a very powerful and accurate method of describing the actions of small particles in space but it has its limits. On the large scale, QM cannot explain relativistic effects. On the smallest of scales, the theory starts to become nonsensical. QM is based on events whch are...

Everyone knows by now that a conic section is the figure formed when a plane intersects a right circular cone. Most everyone also knows that there are many different ways to describe a conic, geometrically and algebraically. What one seldom sees is the derivation of those descriptions from the...

Almost all physics or engineering textbooks have a table of the SI units that are based on six fundamental quantities. The one that is listed for the quantity "electric current" is always "ampere". However, usually a few pages past this fundamental table lies a definition of the ampere. 1...

To proove the inequality: \left | \int_a^b f(t) dt \right | \le \int_a^b | f(t) | dt for complex valued f, use the following: \textrm{Re}\left [ e^{-\iota\theta}\int_a^b f(t) dt\right ] = \int_a^b \textrm{Re}[e^{-\iota\theta}f(t)] dt \le \int_a^b | f(t) | dt and then if we set: \theta =...

I am seeking to understand the relationship of energy within a standing wave vs. the energy in its first three harmonics. Is the energy latent within the fundamental wave the same as the energy in its first three harmonics, or is the energy and exponential increase. IE How much energy is...

How were the masses of fundamental particles(electrons,protons,neutrons) determined?

Hi. So I have learned that this holds for the trace if A and B are two operators: \text{Tr}(AB)=\text{Tr}(BA). Now I take the trace of the commutator between x and p: \text{Tr}(xp)-\text{Tr}(px)=\text{Tr}(xp)-\text{Tr}(xp)=0. But the commutator of x and p is i\hbar. Certainly the trace of...