Normal Definition and 1000 Threads

I am working on a fluid mechanics problem that has a parabolic gate with equation y = x^2 To solve the problem I need two vectors namely \vec{r} \ and \ \hat{n} . Assuming origin is at x = 0, the vector \vec{r} is a vector corresponding to each point on the parabola. I calculated that to...

Within the path integral formalism, in a \phi^4 theory, the one-loop self-energy is divergent. Moreover the loop does not depend on external momenta. However, if you normal order the interaction in the operator formalism, then the one-loop self-energy is zero, since it represents a contraction...

Why are there so many physical processes which are described (with more or less accuracy) by a normal distribution?

Homework Statement Find the area of the surface generated by revolving the curve x=\frac{e^y + e^{-y} }{2} from 0 \leq y \leq ln(2) about the y-axis. The Attempt at a Solution I tried the normal route first... g(y) = x = \frac{1}{2} (e^y + e^{-y}) g'(y) = dx/dy = \frac{1}{2}...

If you are standing on the side of a mountain at a point (x,y) and you know where the peak is (Xp, Yp) and how high it is (Zp) and you have a function G(x,y) that defines the 3D normal vector to the mountain side at all points on the surface, how do you calculate your height? OK it's a simple...

What is the difference between "tangential and normal components" and "radial and transverse components" ? I mean in both cases, the two components are perpendicular to each other and one of the components causes the particle to rotated around, the other one gives it a speed to rotate with. Is...

Hi! I have a very hard time grasping the pressure concept. Look at normal air pressure (1atm) 1atm≈10^5Pa=10^5N/m^2≈10^4kg/m^2=1kg/cm^2 In other words, one whole kg per square centimeter! How can this be? I don't feel the air pressing against my body with one whole kg at each...

http://www.bbc.co.uk/news/uk-england-cumbria-25975785 They have/had "above normal levels" at a perimeter detector. As far as I know this would detect airborne radiation. And presumably at far lower levels than the source. "A spokesman stressed there was no risk to the public or...

The problem is in the paint doc.. My question is why is the base vector aR have a negative sign attached to it?

Is my professor v. fast, or is it normal in colleges?? My 2nd semester of my college degree has just started. My maths course has ODE PDE Linear Algebra Eigenvalues and Eigen-vectors Fourier Series Laplace Transforms Complex Variables So far I bought, GF Simmons(textbook) for...

Homework Statement A machine fills cereal boxes, normally distributed, with standard deviation of .1 oz. What amount setting should the machine be set to if only 1% of the boxes can have less than 16oz of cereal? Homework Equations The Attempt at a Solution I am thinking that I...

I have a final exam in probability and I faced a question that made me think of the logic and the concept of the normal distribution. Here is the question: A food industry company imports oil in big tanks and refills bottles of different sizes with it. One of the main filling sizes is the...

Hi everyone, :) Here's a question I encountered recently and did partway. I need your advice on how to proceed. Question: What can be said about the Jordan normal form of a linear transformation \(f:V\rightarrow V\) where \(V\) is a vector space over \(\mathbb{C}\), if we know that...

Homework Statement If a simple pendulum has a metal bob having negative charge and is allowed to oscillate above a positively charged metallic plate will the time period increase, decrease, become zero or remain the same. Could you guys please give me an insight into what happens in the...

Greetings folks, I'm new to this forum and to physics in general so apologies if I come off like a greenhorn or if I am posting these questions in the wrong place. I have an Arts background and have never really "gotten" science, but my interest in post-Enlightenment philosophy has led me to a...

I've been working on Multivariable Calculus with a few books. In Vector Analysis, I've had some parts which made some questions come up in my mind. I have two questions about them. 1)Can we think of surface normal vector (\vec{n}) as a vector field (\vec{F}) or just a position vector...

A particle moves along the curved path sown. if the particle has a speed of 40ft/sec at A at time ta and a speed of 44ft/sec at B at time tb, determine the average values of he acceleration of hte particle between A and B, bath normal and tangent to the path. I found the average tangent...

If the distribution of a sum of N iid random variables tends to the normal distribution as n tends to infinity, shouldn't the MGF of all random variables raised to the Nth power tend to the MGF of the normal distribution? I tried to do this with the sum of bernouli variables and...

Homework Statement I am self-studying this note and I am stuck in the derivation of the normal shear stress. I can't see how the relations (23) and (24) come about, i.e. I don't understand \tau'_{xx} = \frac{\tau_{xx}+\tau_{yy}}{2}+\tau_{yx} and \tau'_{yy} =...

I was just brushing up on some Algebra for the past couple of days. I realize that the lattice isomorphism theorem deals with the collection of subgroups of a group containing a normal subgroup of G. Now, in general, if N is a normal subgroup of G, all of the subgroups of larger order than N do...

I just wanted to clarify a concept that I'm confused about. When a problem states that a scale reads a value, is that value the normal force? If it is, is that value the normal force, let's say, on an accelerating elevator too? Or is it actually the weight on the accelerating elevator?

Hi When we talk about shear stresses in a fluid, we find that the shear stress is given by \tau_{xy} = \mu(\partial_y u + \partial_x v) = \tau_{yx} This relation we get when only looking at one side of our fluid-"cube". Now, in order to take into account the opposite side we assume that the...

In mathematics, a normal number is a real number whose infinite sequence of digits is distributed uniformly in the sense that each of the digit values has the same frequency, also all digits are equally likely. Wikipedia says that it is widely believed that pi is normal, but a proof remains...

Homework Statement So I'm given two horizontal masses coupled by two springs; on the left there is a wall, then a spring with k_{1}, then a mass, then a spring with k_{2}, and finally another mass, not attached to anything on the right. The masses are equal and move to the right with x_{1}...

I am going through Friedberg and came up with a rather difficult problem I can't seem to resolve. If ## F = ℝ ## and A is a normal matrix with real eigenvalues, then does it follow that A is diagonalizable? If not, can I find a counterexample? I'm trying to find a counterexample, by...

Homework Statement 1) A 0.25kg book rest on a table. A downward force of 9.5 N is exerted on the top of the book by a hand pushing down on the book. 2)what is the size of the normal force exerted by the table on the book Homework Equations F=ma The Attempt at a Solution 1)...

Hi everyone, :) Recently I encountered the following problem. Hope you can confirm whether my method is correct. My answer seems so trivial and I have doubts whether it is correct. Problem: Find the Jordan normal form of a unitary linear transformation. My Solution: Now if we take the...

Tangent and normal parabola Homework Statement P is a point 't' on the parabola y^2=4ax and PQ is a focal chord. PT is a tangent at P and QN is a normal at Q. The minimum distance between PT and QN is equal to Homework Equations The Attempt at a Solution I think minimum distance will...

I'm having trouble seeing how this equality is possible which is seen in proofs of properties of normal operators. ||Tv||^2 = <T*Tv, v> = <TT*v, v> = ||T*v||^2 As far as I can get is ||Tv||^2 = <Tv, Tv>

Homework Statement A vertical spring is fixed on a table. A book is put on the spring. The book compresses the spring until static equilibrium is reached. Question: Is there a normal force exerted by the spring on the book? Why or why not? Homework Equations The Attempt at a...

Obviously it makes sense when considering the force of weight and the fact that the object is not moving up or down, but what is it composed of? What I mean is, the ground you are standing on is made of molecules bonded through the electromagnetic force, right? But those bonds are parallel to...

Homework Statement Find Normal Contact force between the sphere and wedge A and wall B. All surfaces are frictionless and in rest. Diagram :- 2. The attempt at a solution Let normal force on A be N and on B be R. My Diagram :- By The Diagram, N = mgcosθ ...eq(1) R = Nsinθ ...eq(2) =...

Homework Statement Three points, ABC and a downward force exerted at O. C is pinned to a vertical wall. C to B extends horizontally for 15m. At B, a bend occurs downwards to point A on the ground. The downward force is applied between points B and A at point O. The horizontal distance...

What do all possible combinations of the pochhammer contour over the normal Riemann surface for the function ##w=z^{1/2}(1-z)^{1/3}## look like? I imagine like a pumpkin with six ridges longitudinally from north pole to south, one for each joining along the cut between zero and one, the contour...

Here is the question: I have posted a link there to this thread so the OP can see my work.

Problem: I need to use the Monte Carlo method to generate the mean, variance and kurtosis of the standard normal distribution. It has to be coded in Matlab, so there are two parts to this question: 1) The theory 2) The code Any help on either is appreciated. My attempt: To find $E[X]$ for a...

~~Conceptual Normal Force Question~~ Hello! Suppose there is a meter stick suspended from and parallel to a table. On one end, the meter stick is held up by a piece of string at an angle. On the other end, the meter stick is held up by a metal thing about 10cm tall, simply allowing the stick...

Hi everyone, :) Take a look at the following question. Problem: Determine which of the following quadratic functions \(q_1,\,q_2:\,V\rightarrow\Re\) is positive definite and find a basis of \(V\) where one of \(q_1,\,q_2\) has normal form and the other canonical...

Homework Statement A molecule consists of three identical atoms located at the vertices of a 45 degree right triangle. Each pair of atoms interacts by an effective spring potential, with all spring constants equal to k. Consider only planar motion of this molecule. What are 6 normal modes and...

When normal force isn't "normal"l Homework Statement A box with a certain mass is pulled across a horizontal surface by a rope at an angle. Figure out the components, the friction, the acceleration of the box, when the tension in the rope, its angle, the mass of the box, and mu are given...

What is the expectation, E(log(x-a)), when x is log normally distributed? Also x-a>0. I am looking for analytical solution or good numerical approximation. Thanks

Homework Statement Homework Equations The Attempt at a Solution Solution: Graph: For part a, I understand mathematically why the value of c matters. What I don't understand is how it can possibly matter intuitively. I get that ##\overrightarrow { \nabla }...

Hi everyone, :) Here's a question I found on a Wiki book. Question: The matrix \(T\) is \(5\times 5\) with the single eigenvalue 3. The nullities of the powers are: \((T-3I)\) has nullity two, \((T-3I)^2\) has nullity three, \((T-3I)^3\) has nullity four, and \((T-3I)^4\) has nullity five...

Hi everyone, :) Here's a question that I encountered recently. I would appreciate if you could go through my solution and let me know if you see any mistakes or have any comments. Question: Given a linear transformation \(f:\,\mathbb{C}\rightarrow \mathbb{C}\) with matrix...

Homework Statement Find the equation of the normal line of function f(x,y) = x^2+y^2-1 through points (2,1,4) Homework Equations (x-xo)/f_x = (y-yo)/f_y = (z-zo)/f_z The Attempt at a Solution so... f_x = 2x = 4 f_y = 2y = 2 f_z = ? I don't know how to solve for f_z... here...

What does one mean by normal mode of an object? Why is it 3n-5 for linear particles, 3n-6 for non linear particle where n is the number of particle.

Homework Statement In Fig. 8-28, a small block of mass m = 3.0 kg can slide along the frictionless loop-the-loop. The loop has radius R = 0.80 m. The block is released from rest at point P, at height h = 2.9R above the bottom of the loop. I attatched a picture (a) Find the speed of the...

Hi. I'd like to find the normal modes / harmonics, displayed in a dB - Hz graph, of a given 3D object, namely a wind instrument shaped like a hyperbolic con with holes. I'm trying to perform simulations on Comsol Multyphysics, but I don't know how to do it. Is Comsol the best suited software...

Homework Statement I am studying the solution used for the following question: http://answers.yahoo.com/question/index?qid=20131014213456AA4eCNl And I am unable to understand why normal force Fn = mgcosΘ + PsinΘ Should it not be just Fn = mgcosΘ, When drawing the FBD, the only...

Homework Statement A photo of this problem is available at: http://imgur.com/l5lnI56 (the visual is needed to understand the question) Problem text: A ski jump training hill can be thought of as featuring a near vertical plunge followed by a gradually decreasing (in magnitude) slope...