Unit Definition and 1000 Threads

Homework Statement Calculate the integral ∫dθ/(1+acos(θ)) from 0 to 2∏ using residues. Homework Equations Res\underline{zo}(z)=lim\underline{z->zo} (z-z0)f(zo)*2∏i The Attempt at a Solution To start I sub cos(θ)=1/2(e^(iθ)+e^(-iθ)) so that de^(iθ)=ie^(iθ)dθ Re-writing in...

Hey guys, I don't post here often but I like to come here when I have a problem that really rattles my brain. I am an 'overclocker' by hobby (I tune computers), a big part of the overclocking scene is cooling the processor of the computer as far as possible. For years now the 'best' way of...

Early next year I will be beginning an Electromagnetism unit. However, I think I should refresh my maths over the summer break first. Here is the Unit Description from the uni website: A detailed treatment of electric and magnetic fields and theory sources leading to the formulation of...

hi, why electric current is a SI base unit - why not couloumb?

Homework Statement y''-4y'-32y={1 when 0<=t<1 and 0 when 1<=t y(0)=y'(0)=0 Homework Equations The Attempt at a Solution s2L(y) -4sL(y)-32 L(y)=u1(t) I am just struggling to figure out if my unit step function is correct. Solving for L(y) I get: (e-s) / (s(s2 -4s-32))...

Homework Statement a) Find the unit impulse response h(t) of an audio system that causes two echoes, one occurring at 0.5 seconds and the other one at 1.5 seconds. Please sketch H(w). (Magnitude and phase) b) Design a system that can eliminate noise coming from the 60Hz power signal (thus...

1) Show that (R,*,+) is a ring, where (x*y)=x+y+2 and (x+y)=2xy+4x+4y+6. Find the set of unit elements for the second operation. I understand that the Ring Axioms is 1. (R,+) is an albein group. 2. Multiplication is associative and 3. Multiplication distributes. I just don't understand how to...

Hi all; an easy question for you. In the following picture, what is the ventilation box in the corner near the floor? Is there a particular name for these things? I see them everywhere. http://upload.wikimedia.org/wikipedia/commons/7/76/Duracraft_pedestal_fan.jpg Thanks!

I have a worksheet that due to missing the lecture I'm now stuck on. You are given a cartesian vector and told find the polar unit vecors and hence express the original vector as a linear combination of the polar unit vectors just found. I've searched resources online but feel that there is...

A "unit magnitude" EM Wave? Homework Statement Write down the solution of Maxwell's equations corresponding to a plane polarised EM wave of unit amplitude and wavelength λ=2∏m, polarised in the zy plane and traveling in vacuo in the minus y direction.Homework Equations ∇.E = 0 ∇.B = 0 ∇xE =...

Homework Statement OK first, I didn't know where to post this since it is and is not homework,anyways, posting here would be safest. Now, the attached scan is a proof from my (not so trustworthy) textbook and I have some doubts in it. The first doubt is in statement S1 : Every element...

This is the question The flow of a fluid between two large flat parallel plates normal to the y direction is fully developed and steady. The plates are a distance 2h apart in the y direction and the velocity profile, assuming y=0 is at the midpoint between the plate is V(y) = V_0(1-(y/h)^2)...

Let \vec{A} represent any nonzero vector. Why is \frac{\vec{A}}{A} a unit vector and what is its direction? If θ is the angle that \vec{A} makes with the positive x-axis, explain why \frac{\vec{A}}{A}\cdot\hat{i} is called the direction cosine for that axis. I am self-studying and this...

calculate the number of DU assuming that the entire atmospheric O3 column is at a uniform concentration of 3*10^12 molecules/cm^3 between 15 km and 30 km and zero elsewhere. I have no idea how to solve it. I don't know how to convert the 3*10^12 molecules/cm^3 to units of molecules/cm^2 that I...

Homework Statement A wire is fixed at both ends vibrating fundamentally. For what value of x (x position on the wire, with 0 being one edge and L being the other) is the potential energy per unit length has the maximum value? Known: Length of wire (L), Tension in wire (T), Mass of wire (m)...

what is a "scrumple" unit? (pressure) "what size of circular pipe is needed to produce a flowrate of 250 firkins per fortnight when there is a pressure drop of 3x10^5 scrumples per square barleycorn? the pipe is horizontal." I couldn't find what a scrumple was on google, does anyone know...

Homework Statement Consider energy generation in the Sun. Fusion through the pp cycle takes place within its core which has r = 0.2 Rs T = 1.3 x 10 ^ 7 K rho (density) = 1.1 x 10 ^ 5 kg m^-3 X (total mass fraction of hydrogen) = 0.34 The nuclear energy generation rate for the pp...

How this unit comes R = specific volume X (pressure / Temperature ) 0.9m^3/kg (1.3X10^5 N/m^2 / 408 K ) R = 286 KJ/KgK please can anyone explain to me how the unit ( KJ/KgK ) comes ??

I am reading Aschroft and Mermin and I came across the probability per unit time I have trouble understanding the concept as it is. But they do try to explain. They say that the probability that an electron will experience a collision in an ifinetismal time, dt, is just dt/τ. From this i...

I am currently working on a project to determine how much weight a mild steel shelving units can support. This is a project for a friend and for my own interest. I am having trouble deciding exactly what is necessary to determine the weight the shelving units will hold. Each shelf on the unit...

Homework Statement Calculate the Radius of Rubidium ion (which adopts sodium chloride structure.), if the density of Rubidium chloride is 2.76g*cm^(-3) and if we assume that the ions touch each other along the sides of the edge of the unit cell. I'm a bit lost here. I assume the...

Hi , if we have a rotating centrifuge at rpm "a" and we have the radius "b" of the centrifuge and then at the side i have a metal ball that weight's "c" I take the formula which you suggested me here F=ma where a=v2/r and out of that I get Newtons, how do i convert them to like pascals? Because...

Hi all! I must compute a derivative with respect to the components of a unit vector \hat{p}^{i}. In spherical coordinates, \hat{p}^{1}=\hat{p}^{1}(\theta,\phi)=\cos\theta \sin\phi I want to express the derivative \frac{\partial}{\partial\hat{p}^1} as a combination of...

Average Cost. A manufacturer has determined that the total cost $C$ of operating a factory is $C=0.5x^2+15x+5000$ where $x$ is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is $\frac{C}{x}$) taking C' and...

Homework Statement Homework Equations 1 Liter is 1000cm^3 1 foot is .3048m centi is 10^-2 The Attempt at a Solution convert ft to m 400ft * .3048m/1ft = 121.92m convert m to cm 121.92m is 12192 cm 12192 cm is 12.192 Liter 1 gal = 3.78541 L I look at the appendix but there is no equation...

Are the SI units for pressure N m^2 or is it N m^-2?

I'm not sure where to put this thread, so I just placed it in here. One thing I know is that a Newton is the net force required to accelerate an object with a mass of 1kg at a rate of 1m/s2. Now here's one of my questions: if 1N = what I stated earlier, does 2N = the net force required to...

In statistical mechanics, nearly all the textbooks say that the volume of the smallest cell in the phase space of a N-particle system is h^{rN} where h is the Planck Constant, r is the degree of freedom. Also these books say that this comes from the uncertainty principle. However, the...

what is the unit step response of a high pass RC filter ? I want to calculate using transfer function approach. My solution : Y(s)/X(s) = RCs/(1+sRC) X(s)=1/s Y(s)=RC/(1+sRC) taking inverse laplace transform we should get y(t)=exp(-t/RC) But if we consider Y(s)=RC/(1+sRC) RCsY(s)...

I was just looking at wikipedia's article on ring homomorphisms (http://en.wikipedia.org/wiki/Ring_homomorphism) and I am a little confused. If you look at the definition they give for ring homomorphism, they require only that addition and multiplication is preserved over the homomorphism...

Homework Statement f(z) is analytic for |z|≥1. Let C be the unit circle. Show that the integral \frac{1}{2i\pi}\int_C\frac{f(w)}{wz-z^2}dw is 0 if |z|<1, is \frac{f(z)}{z} if |z|>1 Homework Equations The Attempt at a Solution For |z|<1 case, I tried to write the integral as \frac{1}{z2\pi...

If we set c=G=1, then c=1 leads to L=1/T , the G=1 means that M=L^3/T^2 and combining the two means that M=L=1/T so far so good. But say if I also want \hbar=1 this seems to imply M=T/L^2 but combining this with c=1 which gave the L=1/T now suggests that M=1/L=T . Which seems...

Homework Statement Homework Equations The Attempt at a Solution See the 2 figures attached below. Am I doing this correctly? Is the result I obtained correct? Is there a easier way I could've solved this problem? Thanks again!

Greetings everyone, I am taking a course on elementary condensed matter physics and our textbook is "Introduction to Solid State Physics" by Charles Kittel. I have read the crystal structure from 4 books; however, I am still confused about the definitions such as unit cell, primitive vector and...

The first thing that we should notice is that the leading coefficient $a_n = 1$. I was thinking about considering the factored form of p. I googled, and there is an algorithm called the "Schur-Cohn Algorithm" that is suppose to answer exactly this, but I can't find any information on it or...

I was looking at this example: http://keep2.sjfc.edu/faculty/kgreen/vector/block3/flux/node10.html and was confused between the difference between \hat{}n and \vec{}r Why is the original vector field not given in terms of a unit vector? And what difference does this make? Thanks :)

Hi, I have a curve defined by following parametric equation \begin{equation} \gamma(\theta) = 1 + 0.5 \times \cos (N \theta) (\cos(\theta),\sin(\theta)), 0 \leq \theta \leq 2 \pi \ \end{equation} where N is an integer. x and y coordinate of any point on the curve are simply...

OK, this looks like a differential geometry problem, which it is, but at the end of the day I am trying to figure out why the unit normal and unit tangent vectors to a curve aren't orthogonal, so even if you don't know about DG, please respond. Obviously the two choices for E_1 and E_2...

Is there a quantum of time? What’s the smallest interval of time in which acceleration can place? – on the earth? – on the sun? – on a black hole? A chronon is the time that light takes to cover classical electron radius. The other is the Planck time. But these won't serve my purpose, when I...

Homework Statement Express the 5.2-kN force F as a vector in terms of the unit vectors i, j, and k. Determine the scalar projections of F onto the x-axis and onto the line OA. I have attached an image of the problem. Homework Equations Fx = Fcos(θ) Fy = Fcos(θ) Fz = Fcos(θ)...

Hi everyone, I'm having a little confusion here: I measured a value which is 0.27 nN/nm and I converted it's value as 0.27 N/m. Is this correct or should it be 0.27 nN/nm = 0.27*10^9 N/m Thanks for your help

First, I know nothing at all about this topic, which is why I'm looking for help. I'm interested in building a radio transmitter/receiver like a child locator at home. The difference would be I'd like the receiver to beep rather than the transmitter, if that's even the correct language to use...

Homework Statement Let r=(x,y,z). Find ∇r(hat). Homework Equations r(hat)= (x,y,z)/sqrt (x^2+y^2+z^2) ∇f=df/dx x + df/dy y... The Attempt at a Solution Okay I'm having a complete brain freeze at the moment. I know the denominator is a magnitude but am I still supposed to use the...

Homework Statement Find all values of a such that w=ai+\frac{a}{8}j is a unit vector. Homework Equations unit vector has length of 1. and for a vector v unit vectors would be v/magv The Attempt at a Solution 1=magw=\sqrt (a2+(a/8)2) 1=a2+(a2/64) 64=2a2 32=a2 a=\sqrt{32} i know...

Homework Statement r1=(0m) r2=(2000i + 1000j)m v1=(200j)m/s v2=(200i-100j)m/s Homework Equations tantheta=vy/vx v2^2=v1^2+2ax v2=v1+at x2=x1+v1t+1/2at^2 The Attempt at a Solution Thank you for any help

"The average wavelength of white light is 5.0 x 10-7m. What would this be in nanometers? The textbook answer key stated the answer as 500n but I have no idea how that is the answer. I know that the value of nanometers is 10-9 so I figured you add -7 and -9 to get -16... Thanks,

Homework Statement This is the question Still think that unit conversion isn't important? Here is a widely publicized, true story about how failing to convert units resulted in a huge loss. In 1998, the Mars Climate Orbiter probe crashed into the surface of Mars, instead of entering orbit...

Homework Statement Let P(z)=1+2z+3z^2+...nz^(n-1). By considering (1-z)P(z) show that all the zeros of P(z) are inside the unit disk Homework Equations None given.. The Attempt at a Solution Well (1-z)P(z) = 1+z+z^2+...+nz^n and to find roots I set it to 0: 1+z+z^2+...+nz^n = 0...

Homework Statement A neutrino must pass within about 10^-18m of a quark to have any chance of interacting with it. Thus, the maximum target area that a quark presents to a neutrino is about 10^-36m^2. However, a neutrino moves so quickly and the weak interaction is so weak that...

For doing modal analysis of suction and discharge side of an air-conditioning unit, is it needed to consider the inside refrigerant?