Unit Definition and 1000 Threads

Homework Statement I have a problem that is the curl of jln(rsinθ) Since this is in spherical, why is there a bold j in the problem? Doesn't that indicate it's a unit vector in cartesian coordinates? Can I do the curl in spherical coordinates when I have a cartesian unit vector in the...

If a and b are unit vectors and |a + b| = sqrt(2). What is the value (dot product) of (2a-b).(a+3b)? Is the answer -1 by any chance? If not... I know how to find the dot product and find the magnitude and add vectors, etc. but I have never came across this a question before. I am very unclear...

I was looking over my notes today, and I realized that there was a point that isn't pretty clear. If we have the image under T (being T a matrix transformation induced by a matrix A) of the unit square, then its area should be abs(det(A)). Why is this though? I was looking at the proof and I...

Ok, so I start out with the basics and find k. F=ma=kx (1.5 kg)(9.8 m/s^2) = k (4.9 m) k = 3 N/m I also know from the problem that c=0 (no damping) and x(0) = 2m and x'(0) = 0. ƩF = ma ma = -cx' - kx, a = x'' mx'' + cx' + kx = 0 and since c=0 mx'' + kx = 0 Nothing out of the...

Homework Statement A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force f = (30N)i - (40N)j to the cart as it undergoes a displacement s = (-9.0m)i - (3.0m)j How much work does the force you apply do on the grocery cart? Homework Equations...

I remember in my first year physics classes, when dealing with a force F we would find the vector's x- and y-components using F_x=r cos(θ) and F_y=r sin(θ) I also remember learning in my mathematics classes about unit vectors, but cannot seem to remember using them to break vectors down into...

A trivial question. I know that current is the amount of charge passing per unit time across a area. And Potential difference is change in potential or change in potential energy per unit charge or work done per unit charge. And also from Ohms law, V is directly proportional to I. So...

Homework Statement Consider the bivariate density of X and Y, f(x, y) = pi/2 for x^2 + y^2 ≤1 and y > x and = 0 otherwise. (a) Verify that this is a bivariate density (that is, the total volume ∫∫ f(x,y)dxdy = 1) Homework Equations The Attempt at a Solution The problem I'm having is...

Hey, everyone. I am going to post a question—but it's not the question I need help with. It's something deeper (and way more troubling). Consider a particle of mass m subject to an isotropic two-dimensional harmonic central force F= −k\vec{r}, where k is a positive constant. At t=0, we...

I have seen different equations for computing the unit normal vector to a surface. What is the difference between the normal vector ##N## of a curve and ##n##. I have seen this formula for a unit normal vector: ##n = \frac{x_1 \times x_2}{|x_1 \times x_2|}##. Which is different from ##N##. For...

Please see attached for problem and schematic I know from the question i should expect a decaying exponential funtion. Input: a unit impulse denoted in the laplace transform is 1 outputs: -Kx0 - Cdx/dt -Kx0 - Cdx/dt +1 = 0 factorise X0 ( -K - C*S) + 1 = 0 -1 / ( -K - C*S ) =...

I have a real simple question. I'm doing a problem that involves Coulomb's law. My charge separation is 5 nanomeers, and the charges are each elementary. So, for the equation, I have: (9E9 (N*m^2/C^2) *(1.6E-19)^2 (C^2) ) / (5 nm)^2 Units are bolded. The denominator has to be converted...

Homework Statement The Attempt at a Solution I already know how to do a), but what I am wondering is what the question means by expressing position in the terms of those unit vectors.

Given a trapezium ABCD with AB parallel to CD. Show that the line joining the midpoints of the diagonals is parallel to AB & CD (done). Show also that its length is the difference of AB and CD. working: I called the midpoint of AC, E and the midpoint of BD, F Then found that ##...

Homework Statement Let ##\alpha(s)## and ##\beta(s)## be two unit speed curves and assume that ##\kappa_{\alpha}(s)=\kappa_{\beta}(s)## and ##\tau_{\alpha}(s)=\tau_{\beta}(s)##, where ##\kappa## and ##\tau## are respectively the curvature and torsion. Let ##J(s) = T_{\alpha}(s)\dot\...

Homework Statement At what wavelength does a cavity at 6000 degrees Kelvin radiate most per unit wavelength? Homework Equations $$\rho_T(\lambda)d\lambda=\frac{8\pi{hc}}{\lambda^5}\frac{d\lambda}{e^{{hc}/{\lambda{kT}}}-1}$$ The Attempt at a Solution I'm pretty new to this whole...

Homework Statement A steel ball is fired from a ballistic launcher at different angles. The launched ball has been found to travel from the edge of a table to land 30.0 cm from the far end of the table when starting from the height of the table and launched at an angle of 30.0◦ above the...

Homework Statement given r(t) = <t, 1/t,0> find T(t) N(t) aT and aN at t = 1 Homework Equations T(t) = r'/||r'|| N(t) = T'/||T'|| aT = a . T = (v . a)/||T|| aN = a . N = ||v x a||/||v|| = sqrt(||a||2 - aT2) The Attempt at a Solution for my T(t) I get <t2, -1 , 0>/(sqrt(1+t4) (I...

Homework Statement We are to assume an infinite transmission line with the following parameters: capacitance: 296 ρF/ft Zc=52Ω inductance: 8.0 × 10-7 H/ft We are told that a 100MHz signal is attenuated 31 dB per 100 feet and asked based on the information, assuming no leakage through...

Homework Statement http://imgur.com/VzZjSEH I took a screen shot so I did not leave anything out. Homework Equations Surface area, and volume of a sphere. The Attempt at a Solution I am trying to find the linear charge density from the charge volume density. I got it explained...

Hello, I am reading Planck's Unit. What I understand is that what is the need for Planck's unit. Kilogram, meter and second are measurement, rather arbitrary measurement, which humans have done in the past. The question is what do we know that is constant throught the universe? We know (1)...

Homework Statement Let ##S = \{ (x,y) \space | \space x=\frac{1}{n}, n = 1, 2, 3,... \}## be a subset of the unit square. Prove ##S## has outer content zero. Homework Equations ##C(S) = inf\{ \sum A_i \} = inf\{Area(P)\}## The Attempt at a Solution There are no answers I can check my work...

Find a two unit vectors that make the angle \pi/3 with the vector \vec{v} = \vec{i} + 2\vec{j} + 3\vec{k}. "That isn't asking much since there are apparently infinite such vectors" - Prof. I get as far as to say that \pi/3 = arccos( 1/2 ) and that \frac{v \bullet w}{|v||w|} = 1/2 but from...

Hi; How to raising a square matrix to the power of a complex number? for example: [1 2;3 4]^(1+i) or mathematics software such as Scilab how solve such problems? -->[1 2;3 4]^(1+%i) ans = - 0.1482039 - 0.2030943 - 0.3046414 - 0.4528453 Thanks in advance...

What is the Unit Normal Vector in Acceleration.\vec{u}_n How would I go about calculating the normal. Wiki and Wolfram Alpha were very vague about calculating the normal of an orbit. I would like to know the normal to the orbit of a mass orbiting a much larger mass not counting any other...

what will happen if static pressure in supply duct is higher than the fan compartment in AHU?? or vice-versa thanks

I have two questions 1) How the radial and traversal unit vectors are vector funcitons of scalar variable θ (angle between the position vector and polar axis. 2) To find velocity and accleration in polar co ordinates why it is need to write the traversal and radial unit vectors by...

Homework Statement The Attempt at a Solution I know that u(t) is a unit step function and holds a value of either 0 or 1. In laplace transform, when we integrate f(t) from 0 to infinity, we take u(t) to be 1. In this case, since u(t) is u(-t), does this mean it holds a value of 0? Does not...

Homework Statement The vector -i+j+k bisects the angle between the vector c and 3i+4j. Determine a unit vector along c. Homework Equations The Attempt at a Solution Taking the dot product of the two vectors (other than c) gives me the cosine of the angle = 1/5√3. This is also equal...

Hello, I'm studying The Theory of Polymer Dynamics by Doi and Edwards and on page 98 there is a tensor, defined as a composition of two identical unit vectors pointing from the monomer n to the monomer m: \hat{\textbf{r}}_{nm}\hat{\textbf{r}}_{nm} As far as I understood, the unit vectors...

Homework Statement Given that the stretched length of a string is Δx(1+1/2(dy/dx)^2) show that the potential energy per unit length is equal to 1/2F(dy(x,t)/dx)^2 Homework Equations potential energy = kx^2 cos(kx-wt) idk really... The Attempt at a Solution The fact that the...

Is there a smallest possible amount of energy? Like, one where all energy quantities in the universe are a multiple of it and the only way to have less energy is to have none at all? If a photon had that energy, it would be the longest possible EMR wavelength. Or can energy be divided...

i have a problem : A small loop antenna in free space and centered about the origin on the xy-plane is producing a (far-field) radiation electric field (in phasor notation) : http://postimg.org/image/63tm76h5l/ and their solution : http://postimg.org/image/6mdm6roh9/ i don't understand how...

The unit consists of a single, long rectangular chamber. On the inside is a moving wall. On one side of the wall is a vacuum, and the other side is room-temperature air. The moving wall starts much closer to the side with the air and moves slowly in the vacuum direction. As this happens, air...

I have some difficulty understanding how the volume per unit cell for the diamond structure is calculated. I've seen in various websites that this volume is: ##v=a^3 = \left( \frac{8r}{\sqrt{3}} \right)^3## Here ##r## is the radius of an atom. But how did they work out ##a## (the edge of the...

I keep reading about polar unit vectors, and I am a bit confused by what they mean. In the way I like to think about it, the n-tuple representation of a vector space is just a "list" of elements from the field that I have to combine (a.k.a. perform multiplication) with the n vectors in some...

1. Homework Statement Let S be the set of complex numbers z such that |z|=1. Is S a cyclic group? 3. The Attempt at a Solution I think this group isn't cyclic but I don't know how to prove it. My only idea is: If G is a cyclic group, then there is an element x in G such that...

Is there atopological space X such that XxX (the product space) is homeomorphic to the unit circle in the plane

0. The app does not have the template built in so ill do my best, sorry i don't have a computer right now. 1. This is a personal project, and there is a lot to it but I'm cutting out down to where i need help. Imagine a 2x2 grid of squares (2d for now). The center vector is at (0,0), and the...

Hi Guys, I'm tired of waiting for my tenants to finish their midnight laundry loads. I have a hydraulic sliding door assembly ready but I am having trouble getting parts to create the digital system to tie it all together. I want: 120-240VAC Power Relays (for the washing/dryer machines...

Homework Statement This isn't really homework, but I've been reviewing calc & trig and realized that the area of one period of sin(x) = 4. Since sin(θ) can be understood as the y-value of points along a unit circle, I noticed that the area of a unit square that bounds the unit circle is...

Homework Statement In fact it is problem 8.5 in Griffiths 3rd ed p357 Consider an infinite parallel plate capacitor with the lower plate carrying the charger density - \sigma , and the upper plate carrying the charge density + \sigma . (a) Determine all nine elements of the stress...

Fist a little bit of background on why I am doing physics 12, I am currently a first year electrician and recently found out in order to get a job with BCHydro physics 12 is a pre req. Unfortunately this is the only science I didn't take in highscool. The job posting for apprentice ships will be...

Let x be a real number and let M=\frac{3x-1}{1+x}-\frac{\sqrt{\mid x\mid-2}+\sqrt{2-\mid x \mid}}{\mid 2-x \mid}. Find M and also the unit digit of M^{2003}.

Homework Statement What is the integral of e-1/z around a unit circle centered at z = 0? Homework Equations - The Attempt at a Solution The Laurent expansion of this function gives : 1 - 1/z + 1/(2 z^2) - 1/(3! z^3) + . . . . . The residue of the pole inside is -1. So the integral...

How would I go about algebraically (not graphically) performing operations on two or more Heaviside function.H(x) = {0, if x<0 ...{1, if x>=0 ex. define the function piecewise and graph. a.) (x+1)*H(x+1)-x*H(x) b.) (x+1)*H(x+1) i'm having a hard time solving this please help me!

Homework Statement a proton moves with a velocity <6*105,3*105> m/s through a magnetic field given by <.2,.2> T a. Find the magnetic force per unit charge on the proton b. Find the work done by this forceHomework Equations Fm=qv x BThe Attempt at a Solution For part a, I used a property of...

Would either or both of these work as a lattice on the closed unit circle in the plane? (1) Using a linear order: Expressing points in polar coordinates (with angles 0≤θ<2π), define: (r,α) < (s,β) iff r<s or (r=s & α<β) (r,α) ≤ (s,β) iff (r,α) < (s,β) or (r=s & α=β) The meet and join...

Homework Statement Given ε > 0, show that there is a collection of disjoint dyadic squares in the unit disk that has a total area which exceeds π - ε. Homework Equations Define a dyadic interval as an interval of the form [a, b] such that a = p/2k and b = (p + 1)/2k, p and k are integers. A...

If force includes strength/magnitude and direction, then why do we say a Newton or Pound is a unit of force? Isn't it more a unit of the magnitude of force? Please help. Now that i have been thinking about forces always having direction, this is all confusing me. Thanks