Unit Definition and 1000 Threads

Homework Statement If lightning strikes a tree such that there is the same current through it as there was through the lightning conductor, then a much larger potential difference exists between top and bottom of the tree. Explain why this is so. The Attempt at a Solution Is this...

How do you calculate cost per unit of electricity over a certain time that a generator produces?

Help please...Transmission line parameters in per unit hello there I'm trying to work on a program that converts electrical quantities of transmission line ( R , L , and C ) into per unit system using Matlab the thing is that I'm finding difficulties with the formulas , how I can obtain...

How was a unit of energy first defined? I know we measure energy in units of Joules as named after James Prescott Joule and a Joule is defined as 1kg*(m/s)^2 But I can't find any information on the history of the unit itself, how and when was it first defined, by whom? How was it decided or...

Why unit of torque is not m.N 1.Torque=rFSinθ =>m.N 2. 1 N.m = 1 Joule but 1 N.m in torque ≠ 1 Joule For the above 2 reasons i reckon it should have unit of m.N.

Hello, I have two datasets containing power spectral density data to be compared. One of these datasets is presented in units mm/sqrt (Hz)/degree, and I would like to do some transformation so that data is comparable with the other set, which has units m^2/Hz/rad. Any help on how to do...

Hi guys, what does it mean to observe a filter response to a unit step? The book gives a transfer function and I've recreated it in Proteus ISIS. Now it asks me to simulate a square wave as an input (i used a pulse generator), and then observe a filter response to a unit step, describing the...

I keep reading that a random vector (X, Y) uniformly distributed over the unit circle has probability density \frac{1}{\pi}. The only proof I've seen is that f_{X,Y}(x,y) = \begin{cases} c, &\text{if }x^2 + y^2 \leq 1 \\ 0 &\text{otherwise}\end{cases} And then you solve for c by integrating...

If we have a unit circle within a square s.t. the square touches the circle in 4 places then the biggest gap we can find is just √2 - 1. Doing a similar thing with a sphere in a cube we get √3 - 1 I've heard the n-dimensional analogue is √n - 1. Which is crazy as it means the gap is bigger...

hello, I can't seem to make sense out of amper/meter...one amp flowing throw a wire with a length of 0.5m would be 2A/m ? how does relate to the magnetic field?

For a unit mass sliding down the stationary curve y = f(x) at the point (x, y), we can consider our mass to be sliding down a stationary inclined plane which is tangential to the curve at the point (x, y). The slope of this inclined plane is thus \frac{dy}{dx}(x). For the remainder of this...

The start of a new school year in Ap physics C, and our favorite engineering professors causing students distress! Maybe the champions of the textbook can help me out... = ) Homework Statement 1. Two vectors are given by a = 4i hat - 3j hat + k hat b = -i hat +j hat + 4k hat. Find a) a + b...

Ok, so I'm trying to plot the unit circle using the chebyvhev metric, which should give me a square. I am trying this in MATLAB, using the 'pdist' and 'cmdscale' functions. My uber-complex code is the following: clc;clf;clear all; boundaryPlot=1.5; % Euclidean unit circle for i=1:360...

Homework Statement At a high point in the Earth’s atmosphere, He2+ ions in a concentration of 2.8 x 10^12 m^-3 are moving due north at a speed of 2.0x10^6 m/s. Also, a 7.0 x 10^11m^-3 concentration of (O2)- (dioxygen -)ions is moving due south at a speed of 7.2 x 10^6m/s. Determine the...

I want to show that if the complex variables ζ and z and related via the relation z = (2/ζ) + ζ then the unit circle mod(ζ) = 1 in the ζ plane maps to an ellipse in the z-plane. Then if I write z as x + iy, what is the equation for this ellipse in terms of x and y? Any help would be...

how a step function has frequency content in it? thanks

Hello again. First off, I wasn't sure how to say this in the title but I'm not taking the inverse Laplace transform of a unit step function. I'm taking the Laplace transform of something that comes out to the unit step function. I have this question, which is a similar version of the...

I was reading a link i found here on physicsforums called "The relativistic rocket". There was lots of calculations of the required fuel for certain distances and such. However, I understand that time→0 when our velocity v→c. And that will mean we travel a larger distance for a shorter...

I would like to inquire whether there has been any recent work on representing matrices in unit vector notation? Thanks in advance!

Say for example v = <3,4> I was taught to divide each component by the magnitude in order to get the unit vector, i.e. 3^2 + 4^2 = ||v||^2 5 = ||v|| So the unit vector of that vector is <3/5,4/5> or 1/5<3,4> But if I forgot that I had to divide the components by the magnitude, I would not...

Suppose you look at all of the equilateral (non-self-intersecting) polygons** with an odd number of sides, and each side length is equal to 1 unit. For examples, the polygon with the fewest number of sides in this group is the equilateral triangle, and then the next one is an equilateral...

I have grammar S → ABaC | BaC | AaC | ABa | aC | Aa | Ba | a A → B | C | BC B → b C → D D → d Can someone please help me to eliminate all the rules of grammar production unit. Thanks for help! :biggrin:

Question: Carbon-14 has a half-life of 5730 years. A bone is found in which \frac{7}{8} of the original [16g of] carbon-14 has decayed. How old is the bone? Formula: C(t)=Co(\frac{1}{2})\frac{t}{H} (it's hard to see but it says \frac{1}{2} to the power of \frac{t}{H}) C(t) - the number at...

Homework Statement Starting with: G = \frac{I}{V}= \frac{-\int_{s}\sigma\mathbf{E}\cdot d\boldsymbol{s}}{-\int_{l}\boldsymbol{E}\cdot d\boldsymbol{l}} Derive the conductance per unit length, G', of a coaxial cable by assuming a line charge of \rho_{l} on the center conductor...

What does the unit "hp" means? I admit that my physics sucks because it has been a long time since I heard the word "physics" but putting that aside, what does the unit "hp" represent/means? I don't remember learning that unit in school. Eg. An engine develops 85hp I'm guessing it's a Power...

Now that other solar systems have been discovered, as well as binary and trinary star systems, is the helio-geocentric Astronomical Unit still useful? Wouldn't it be clearer to use the terms light second, light minute. light day, light year, etc., instead? Obviously, these terms are still...

It seems to me that luminous intensity should really be put in terms of energy, not a special unit (which itself is based on some arbitrary specification of energy.) The other 5 units and Avogadro's number should be the only fundamental units.

1. The problem I need to know what unit I would use for my calculated velocity? 2. Relevant Information T (Relative Time) = 9 years To (Stationary Time) = 2 years U (Velocity) = ? Solution? What unit would I use for the velocity received?

1) I'm not sure how to solve this question A 20MVA induction motor connected at 13.8kV draws a load current of 1.0 p.u, 0.85 power factor lag. Calculate the rated load current in Amps and the real power and reactive power drawn by the motor. Express these quantities in per unit form using...

Homework Statement This question comes out of "Introduction to Topology" by Mendelson, from the section on Identification Topologies. Let D be the closed unit disc in R^2, so that the boundary, S, is the unit circle. Let C=S\times [0,1], and A=S \times \{1\} \subset C. Prove that...

I'm on the last chapter of a 1200 page calc book, I'm really psyched. Homework Statement The Attempt at a Solution The method I learned for finding the unit normal of a vector field, n, is take the derivative of the equation and divide that by the magnitude of the...

Hello. Let's say we have the quantity f=1/(1+x) where x has no unit of measure. What is the unit of measure of f, once we take f^t, where t can be in years? Thanks

Homework Statement Two parallel whires, separated by a distance D (midpoint distance), are charged with a current density L (each whire has a radius R). If the whires have the potential +/- X Volts, what is the force per unit length between them? Homework Equations B = μ0*I /(2πr) is...

Homework Statement Show that the function f(z) = z/(1-z) maps the unit circle to an infinite line. Homework Equations Polar form z = rexp(iθ) The Attempt at a Solution I've tried to see what happens, when we let f(z) = f(eiθ) and then get: f(eiθ) = eiθ/(1-eiθ) But I need some...

What are Chords? What is the smallest "unit" in physics? Someone told me they read a Yahoo AP article stating the most basic "building block" of the universe was a sound wave, and upon discovery this had been named a chord(or perhaps cord/kord/etc). Again, this was an AP article, but I...

When you write vector quantities with unit vectors, do you still have to draw an arrow on top to indicate that it's a vector? e.g. velocity and acceleration. My textbook doesn't have it bolded so does that mean they're just taking the magnitude and then multiplying by the unit vector to make it...

Our teacher taught us a way to represent a force as a unit vector. Suppose a force of 12 N acts along the line 2i+j-2k. The force is written as: F = 12 N (2i+j-2k/√1^2+2^2+2^2) Therefore, F = 8i+4j-8k But, I can't understand why is it so. Please explain.

Hi everyone, It's been years since I solved a physics problem for school. Now that I'm back at it I could use some help on this problem: Question "The astonomical unit (AU) is defined as the mean centre to centre distance from Earth to the Sun, namely 1.496 x 10^11 m. The parsec is...

Homework Statement Please can someone look at the attached question (I have extracted MS and relevant previous pieces of information) Where do they get the idea that 100 W is produced over 24 hours ?? Homework Equations The Attempt at a SolutionI know power = work done / time but if power...

We're given x^2+2*y^2=1. so x^2=1-2y^2 now using distance formula d^2=x^2+y^2 since x^2=1-2y^2, substituting it in the distance formula we get: d^2=1-2y^2+y^2=1-y^2; differentiating and then setting the eq to 0 we get; 0=-4y or y=0. now x^2=1-2y^2=1 so x=+-1 so point having...

Homework Statement The uranium isotope 235U captures a neutron and undergoes fission to produce 93Rb and 141Cs. Calculate the energy released in this process. The nuclear masses of the relevant isotopes are 235U 235.0439u, 93Rb 92.9217u, 141Cs 140.9195u Homework Equations...

Homework Statement Given vector OP = 2i+3j, OQ = qi+2qj. How can i find the possible value for q? note that PQ is a unit vector. Homework Equations Given (p-1)i + (2p-6)j having magnitude 10, find p The Attempt at a Solution From the formula, i was told that the unit vector...

Let $f$ be a nonconstant entire function that maps the unit circle, $\{z: |z| = 1\}$, into itself. Prove that $f$ maps the open unit disc, $\{z: |z| < 1\}$, into itself. I am having a little trouble starting this one. z in C

Does there exist a holomorphic function f(z) on the unit disc and satisfies f(1/n) = f(-1/n) = 1/n^3 for every n in N?

Why doesn't $1+z^{2^n}$ have zeros on the unit disc?

For better understanding of it's principles, electrotechnics is often compared to hydronics (and, probably, vice versa). But, why having the electrical resistance to a flow of charged particles - with it's basic unit "Ohm", there in general Physics is no unit of measurement of the hydronic...

Let f(z) = \prod\limits_{n = 1}^{\infty}(1 - nz^n) Prove that each point on the unit circle is an accumulation point of zeros of f So we have that z = \sqrt[n]{1/n} . Now where do I go from here? Probably should note that this is a Weierstrass Product.

Homework Statement The diagram provided shows a man pulling a box across the floor. Assume that the force of the friction can be ignored and that the acceleration of the box is 1.27 m/s. Find the angle to the horizontal that the man must pull. 65N figure located on the rope the person is...

Homework Statement I don't know if this is a physics problem per se but its from physics class. So we were supposed to pick out a solar panel and figure out what is the cost per unit of energy for this form of solar energy? I know where supposed to use the data sheet for the panel that we...

So I'm kinda new to Physics Forums but I've been using threads as guides for about a year now. Basically, I'm hardcore studying for my Calc III exam (the final is in a few weeks) and I came across an interesting lapse in my understanding (well many in fact, but one in particular). First of...