Normal Definition and 1000 Threads

Homework Statement If \sigma_{ij} = \begin{pmatrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \end{pmatrix} represents a stress tensor, on what plane(s) will the normal stress be a minimum? On what plane(s) will the shear stress be a maximum? Homework EquationsThe Attempt at a Solution The first...

I know that normal force is a reaction force. http://www.sumoware.com/images/temp/xzhhpaacgkdktjna.png In the leaning ladder problem, the normal force is perpendicular to the floor and the wall. But, in the cable and beam problem, why isn't the normal force perpendicular to the wall ...

Homework Statement A hollow cone is put upside-down with its symmetry axis vertical. The surface of it makes an angle of theta with the vertical direction as shown in the figure . A small puck of mass m slides without friction on the inner side of this cone and remains within a horizontal plane...

What fraction of adult human cells are not replaced over a normal lifetime ?. see ... http://en.wikipedia.org/wiki/Ship_of_Theseus / [ aka "Trigger's broom" ]. I'm guessing it's a minority : brain and heart only account for about 3% of body weight.[ skeleton is replaced every decade , but...

I am studying to be a pilot and something I've read in the book confuses me. It is that Vertical Takeoff and Landing (VTOL) engines need to be heaver than their corresponding traditional takeoff/landing counterparts. Wikipedia says the same thing here. I am going to interpret "larger" and...

Homework Statement A small block is shot into each of the four tracks as shown below. Each of the tracks rise to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal Reaction is maximum in which track? 2...

i have a 3d vector, and i want to draw a circle with a specified radius around the vector (for computer programming) so i have the location of the center of the circle(first point of the vector) but i also want the circle to be at a right angle to the vector my approach: the equation of a...

Water is a conductor of electricity. So if i throw a normal clock or tv remote battery in a bucket of water, will it conduct the electricity, allow a short circuit between the + and - ve terminals and cause some minor explosion? I wanted to try it but got scared. What will happen if i connect...

Homework Statement Given a uniform plane wave in air as: E_i=40cos(wt- Bz)a_x +30sin(wt- Bz)a_y (a) Find H_i (b) If the wave encounters a perfectly conducting plate normal to the z axis at z = 0, find the reflected wave E_r and H_r. (c) What are the total E and H fields for z < 0?Homework...

Let G be a group of order pm where p is a prime and p > m. Suppose H is a subgroup of order p. Show that H is normal in G. There is a very similar problem Let |G| = p^nm where p is a prime and n \ge 1, p > m. Show that the Sylow p-subgroup of G is normal in G. Proof: Let n_p be the...

Homework Statement Consider the real scalar field with the Lagrangian \mathcal{L}=\frac{1}{2}\partial_\mu \phi \partial^\mu \phi - \frac{1}{2} m^2 \phi^2. Show that after normal ordering the conserved four-momentum P^\mu = \int d^3x T^{0 \mu} takes the operator form P^\mu = \int...

Homework Statement Okay so there is a wall that has a mass of 150 kg and I am pushing it but the wall does not move. The coefficient of friction is 2 and I am trying to find the frictional force using the frictional force formula. Although, I need the normal force in which I am using to push...

Dear all: The boundary condition of electric field is well know for us which illustrates that the normal component of the electric field will not be continuous across the interface between 2 dielectric material with different dielectric functions. (There is no extra fixed charge on the...

All degrees are measured from the positive x-axis. FG = Force of gravity FN = Normal force FT = Force of tension Problem: A skier is being pulled up a 15° incline by a rope. I'm solving for FT. The only forces acting on the skier are FG, FN, and FT. Attempt at a solution: Initially, my...

Radiance is defined as radiant flux per solid angle per projected area normal to the beam direction: ##L = \frac{d^2 \Phi}{d \vec\omega \cdot d A_\perp}## where ##A_\perp = A \cos \theta## and ##\theta## is the angle between the beam direction ##\vec\omega## and the surface normal. I kind of...

Let H subgroup in G. Prove H is normal in G iff for all g in G and for all h in H, there exists an h1 and h2 in H such that hg=gh1 and gh=h2g.Completely lost on this. All I know for normal is that gH=Hg. Where else do I go from here? Help a brother out! Thanks :)

Can you guys show me how to calculate the normal vector n, given that i know the coordinates of the center c (c1,c2), the side of the square (let's call it s), and the length of the plank (l) below the square? i am taking the assumption that n is (0,1), which seems to be incorrect, because the...

Two clocks in a spaceship floating though space at 99% the speed of light. One is a atomic clock and uses light and mirrors to measure time, the other clock uses cogs and gears like a conventional clock. From the perspective from inside the ship both clocks tick and tock at the usual rate...

This number is rational and normal, right? http://www.wolframalpha.com/input/?i=0.01234567890123456789... edit - You'll have to edit in the ".." because the forum doesn't recognize it as part of the link.

Why are they important? I've been learning about them quite a bit and have no idea why they are significant. What is the motivation for their discovery, their use, or even their mention in physics for that matter. All I really know is that when you look/have solutions with the same angular...

Homework Statement $$f:\mathbb{R} \rightarrow \mathbb{R},$$ $$ f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{\frac{-(x-\mu)^2}{2 \sigma ^{2}}}$$ What are the roots of this equation? Homework EquationsThe Attempt at a Solution The roots of an equation are the values of x such that f(x) = 0. This...

is there a difference between natural frequencies, normal frequencies, and resonant frequencies? Any subtle differences? I've seen them used at different times, and I've also seen at least two used in a single sentence implying some kind of difference. For example, "[FONT=Book Antiqua]Natural...

I'm studying statistics from the book "design of experiments" by Montgomery and about the t-test it's stated it is necessary to check the samples are described by a normal distribution throughout a normal probability plot and I have noticed the y-scale is not familiar to me, it's neither linear...

Homework Statement Grammar 'G' is any context-free grammar without any λ productions or unit productions. Let k be the max number of symbols on the right side of any production in P. Prove that there's an equivalent grammar in Chomsky Normal Form with no more than (k − 1)|P| + |T| production...

Homework Statement The physics of circular motion sets an upper limit to the speed of human walking. (If you need to go faster, your gait changes from a walk to a run.) If you take a few steps and watch what's happening, you'll see that your body pivots in circular motion over your forward foot...

Homework Statement A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of...

So if I understood well, Normal ordering just comes due to the conmutation relation of a and a⁺? right? Is just a simple and clever simplification. Wick Theorem is analogue to normal ordering because it is related to the a and a⁺ again (so related to normal ordering, indeed). However I do not...

Homework Statement A 65 kg airplane pilot pulls out of a dive by following at constant speed, the arc of a circle whose radius is 300 m. At the bottom of the circle her speed is 180 km/h. a.) Calculate net force on pilot at bottom or circle. b.) Calculate force exerted on pilot by seat at top...

I don't know if this is possible or not, let's see if this is a fun problem. Let X_1 and X_2 be 2 independent normal random variables. They have different means and variances, and they are independent. I want to have a function that inputs X_1 and X_2, and it has a F distribution with degree of...

I am trying to understand wick's theorem and normal ordering mostly from Peskin and Schroeder. Now I have this problem with how normal ordering is defined. It seems to me that if you take the normal ordering of a commutator it should always be zero. Here is what I understand normal ordering to...

am a bit confused, if i want to find out for example the P(Having the disease among everyone) , using conditional, would it be total people Having the disease over total population?Prescreening Positive and Have the disease is 66 Prescreening Positive but does not the disease 150 prescreening...

Homework Statement If the normal to the parabola y^2 = 4ax at the point (at^2 , 2at) cuts the parabola again at (aT^2, 2aT), then minimum value of T^2 is ans: 8 I got the answer but I don't know why it should be the answero_O? Homework Equations Equation of normal to the parabola in parametric...

Homework Statement This involve testing population proportion. (either small or big sample) this question is done by my lecturer by using binomial , i am wondering could it be done using normal distribution? because the np is 20(0.45) = 9 which is greater than 5 ...

Homework Statement Find the equations of the tangent line, normal plane and osculating plane to the curve r(t) = -2sin(t) i + 2cos(t) j + 3 k at the point corresponding to t = π/4. Homework Equations T[/B]^(t) = r'(t) // ||r'(t)|| u = a i + b j + c k, ||u|| = √(a^2 + b^2 + c^2) N^(t) =...

Hello everyone! Here is a question I am working on: Consider the context-free grammar G = ( { S, B, E }, { 0, 1, i, e, s }, R, S ), where R is: S --> iBSE | s B --> 0 | 1 E --> lambda | eS Convert this to Chomsky Normal Form, showing all steps. Alrighty, so I removed the lambda and got: S0...

Let \text{ } H \text{ }be \text{ }a \text{ } Hilbert \text{ } space, \text{ }K \text{ }be \text{ }a \text{ }closed\text{ }convex\text{ }subset \text{ } of \text{ }H \text{ }and \text{ }x_{0}\in K. \text{ }Then \\N_{K}(x_{0}) =\{y\in K:\langle y,x-x_{0}\rangle \leq 0,\forall x\in K\} .\text{...

Hey guys, I'm trying to understand the properties of normal modes of the electromagnetic field inside an arbitrary cavity, but I'm having some trouble. By definition, for a normal mode we have \mathbf{E}(\mathbf{x},t) = \mathbf{E}_0 (\mathbf{x}) e^{i \omega_1 t} and \mathbf{B}(\mathbf{x},t) =...

Homework Statement An airplane of mass 25,000 kg (approximately the size of a Boeing 737) is coming in for a landing at a speed of 72 m/s. Calculate the normal force on the landing gear when the airplane lands. Hint: You will use 0.92 m as the compression (vertical displacement) of the landing...

Homework Statement The problem motivating this post is: "An out-of-gas car is rolling over the top of a hill at speed v. At this instant, a. n > FG b. n < FG c. n = FG d. We can't tell about n without knowing v." (Associated figure attached.) Homework Equations [/B] Newton's second law The...

Hello Mathematicians! I'm doing some work on obtaining true measures of ability for students, and am trying to find a simple mathematical example that would show that a student's true ability is obtained by having a few equally weighted tests rather than one big test. The example I'm thinking...

Consider a pulley fixed to the ceiling. A mass-less string is wrapped around it, with each side of the string hanging down either side of the pulley. Since the pulley has friction with the string, tension along the string will vary. Let's say the string is attempting to move clockwise, so the...

SU(2) matrices act isometrically on the Riemann sphere with the chordal metric. At the same time the group of automorphisms of the Riemann sphere is isomorphic to the group SL(2, C) of isometries of H 3(hyperbolic space) i.e. every orientation-preserving isometry of H 3 gives rise to a Möbius...

I need help with the proof of an apparently simple Proposition in Aigli Papantonopoulou's book: Algebra: Pure and Applied. The proposition in question is Proposition 5.2.3 and reads as follows:Can someone please help me and provide an explicit and formal proof of this proposition.Since...

Hi all, I'm struggling with the concept of angular frequency in the context of sinusoidal waves. We describe sinusoidal waves with equations like y(x,t) = Asin(kx-\omega t) , where \omega is the angular frequency, yes? But what does this quantity physically represent? The rate at which...

A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force, FN, and the coefficient of kinetic friction, µk. So, I know I have to find the vertical and parallel forces Vertical: Fn and 250 sin of...

Homework Statement I need to show that any normal matrix can be expressed as the sum of two commuting self adjoint matrices Homework Equations Normal matrix A: [A,A^\dagger]=0 Self Adjoint matrix: B=B^\dagger The Attempt at a Solution A is a normal matrix. I assume I can write...

Homework Statement Homework Equations An = mv^2 / r The Attempt at a Solution I get the 2D free body diagram, and how the vertical components are resolved, but how is Nc sin θ = mv^2 / r when they both are in the same direction? Also another related problem is this diagram...

Homework Statement In Griffiths, the following boundary condition is given without proof: ∂Aabove/∂n-∂Abelow/∂n=-μ0K for the change in the magnetic vector potential A across a surface with surface current density K, where n is the normal direction to the surface. A later problem asks for a...

A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force, FN, and the coefficient of kinetic friction, µk. FN µk (a) 330 N 0.31 (b) 310 N 0.33 (c) 250 N 0.27 (d) 290 N...

I'll be going into first year of a physics degree in early September and I was looking at the module list and noticed that the university I will be going to does quantum mechanics in fourth year. I've since looked at other universities in the area and noticed that they all seem to do it in third...