Unit Definition and 1000 Threads

Here's my story: I bought a license plate frame for my motorcycle. It has 4 banks of LED lights. I want to wire it to my brake lights. That's the easy part. But, I want them to flash. Can I get them to flash in sequence? at 12v, it takes 0.1 to 0.2 amps to get full intensity. What parts...

Homework Statement Define a relation on R as follows. For a,b ∈ R, a ∼ b if a−b ∈ Z. Prove that this is an equivalence relation. Can you identify the set of equivalence classes with the unit circle in a natural way? Homework Equations The Attempt at a Solution I have already proven that this...

Homework Statement Two vectors are given by the relations a = 2i-3j-3k b = 6i+2j+k Find unit vectors corresponding to a 3- dimensional orthogonal right handed coordinate system where one of the axes is parallel to _{}a and another of the axes is perpendicular to _{}b Homework...

1) Analogy in F = ma From experiment, we find that F = k m a and we deliberately choose k = 1 (dimensionaless) and thus we define the unit Newton, a derived unit. 2) In the definition of ampere, it is in terms of the force per unit length between two straight parallel conductors...

Homework Statement Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. Homework Equations r(t) = (-3tcost)i + (3tsint)j + (2\sqrt{2})t(3/2)k 0 ≤ t ≤ ∏ The Attempt at a Solution So I found dr/dt (I think), which is v(t) =...

Is there a singular, smallest unit of gravity between 2 objects? For example, is it possible that a speck of dust on Earth, and a speck of dust on the opposite side of the universe, in the farthest away galaxy will have no gravitational attraction to each other? Or does the gravity will always...

Homework Statement Determine the behavior of convergence on the unit circle, ie |z| = 1 of: Ʃ \frac{z^{n}}{n^{2}(1 - z^{n})} Homework Equations Obviously this is divergent then z is a root of unity. The question is what happens when z is not a root of unity. The Attempt at a...

Consider the sequence (n) n=1 to infinity. Plot the sequence on the unit circle: n modulo 2*pi for n≥1. What do you see? Attempt: I really honestly have no idea what to do. We are learning in class about limit laws and how to prove them, so this question seems to be coming out of nowhere. :(

Physically/conceptually, I understand why the unit normal vector will always point toward the side of concavity on a curve. It's because the unit normal's direction is the derivative of the unit tangent, and the unit tangent's change in direction is always toward the concave side. But how is...

Knowing the atomic weights of Na+ and Cl- are 23 and 35.5, respectively, calculate the density (g/cm^3) of NaCl crystal. Hint: Avogadro’s number N = 6.02 x 10^23 is the number of atoms in one mole (weight of 1 mole = atomic weight in grams) unit cell is Face centered unit cell contains a...

I know how to obtain the unit tangent, it is very easy. But for the case of unit normal, I am confused. Usually we need to know \vec{T'}(t) and |\vec{T'}(t)| in order the find \vec{N}(t). However are there any quicker method to do it? Since I saw the textbook do it without step, it seems...

Hi, I am building control panel for automation testing unit. - Ambient Temperature to measure:- - pulley speed and temperature to measure. So far... for Ambient Temp I have used T-Type and for pulley speed I have used magnetic pick up 10V. And for interfacing used USB6009. Can...

Is there any quantity in physics that has the unit kg^2 in it?

As the usual argument goes, as I understand it, everything can be expressed in units of G, h and c. (though this argument exclude the particle masses from consideration.) The permittivity of the vacuum seems to be independent of G,h,c. Am I wrong?

Homework Statement Currently, I'm expected to find the side length of a square garden whose area is 25cm2. Of course, we're talking about a square here, and since the area of a rectangle is l * w, and, when talking about a square, l = w, the area of a square is S2. Of course, I know each side...

So I usually use VESTA to make my figures, and though the new version is able to do many mad things with calculated electron density isostructures and whatnot, I can't seem to just be able to throw in some clover-leaf d or p orbitals like what was done in the image below (from this paper on...

Homework Statement use unit vectors to express the vector C where C=3.00A-4.00B the answer is apparently C=12.0i + 14.9j Homework Equations cross product The Attempt at a Solution i have no idea where to even start how is it possible to find the i orj because i don't even know...

Homework Statement Compute the maximum amount of water vapor per unit volume that air can hold at the surface, where Ts = 288 K, and at a height of 10 km where T = 220 K. Express your answers in kg m-3. Homework Equations e_{s}=Ae^{\beta T} e=\rho _{v}R_{v}T The Attempt at a...

Hello. :smile: I understand most of the work involved with these types of questions, but there is one point in an example I'm following that I don't understand. Homework Statement Evaluate: I = \int{(z^2)}dS over the positive quadrant of a sphere, where (x,y > 0). Homework...

Homework Statement Impulse is defined as: force x time a) Find its unit expressed in term of the base units. b) What quantity has the same unit? What could it mean? (Impulse = change in momentum) Homework Equations I = F x T P = mv The Attempt at a Solution a) First, we...

Vitamin E (alpha-d-tocopherol) has been shown to prevent creeping arterial occlusion*, increasing cerebral circulation and decreasing the risk of ischemic strokes at a minimum effective dose of 100IU/day**. As a blood thinner (anti-coagulant) it has been shown to increase the risk of hemorrhagic...

In rectangular corr. 3i+j mean leght in x-direction =3 in y-3direction =1 However, how about in polar coorindate? 3r+1\theta (r and \theta are the unit verctor in polar coor., I don't know how to type it out, I hope you understand.) Dose it mean a line with length 3 from origin and angle...

Homework Statement Draw the following vector. Label the angle that specifies the vector's direction, then find its magnitude and direction. Homework Equations vector a = 2.0i - 6.0j The Attempt at a Solution I get stuck here: I don't know which angle to use.

Homework Statement Given: P=(1,-2,3), Q=(-4,2,5) and S=(2,1-4) Find a unit vector that is perpendicular to triangle PQS Homework Equations Cross and Dot Product The Attempt at a Solution Correct me if I'm doing wrong. I have two solutions that I've thought: 1)What I...

Homework Statement Let A be an arbitrary vector and let n be a unit vector in some fixed direction. Show that A=(A.n).n+(A*n)*n Homework Equations The Attempt at a Solution I know that (A.n).n gives component of arbitrary vector, assume that it equals to Ax

Hello, am having an understanding problem, about an exercice on LTI systems with unit sample response. i've been given the graphical depicted output y[n], and the following output x[n]= u[n]-u[n-2] the system is as follow x[n]----> h1[n]----->h2[n]------>y[n] with h2[n]= s[n] - s[n-1]...

I'd like to know how to do it without solving via Hermite polynomials, so that I can check by both methods when I solve other problems. I have tried to figure out myself but I need some help. Let's say H:=x^2+p^2 , and a:= x-ip . So that [a,a^+]=2\hbar , H a \varphi_i = (E_i -...

Homework Statement okay i don't have the exact problem in front of me right now but it went something like this: they gave the force, F, which equaled 500 N. for part a they said to express in terms of a magnitude times a unit vector. for part b they wanted the force expressed in orthogonal...

Why is the kilogram the base unit of mass, instead of the gram? http://en.wikipedia.org/wiki/Cgs_system_of_units" explains the replacement of the cgs- (centimeter-gram-second) by the mks-system (meter-kilogram-second) by: "The values (by order of magnitude) of many cgs units turned out to be...

Some help with Si Unit conversions :) Homework Statement 762 Mg/m to ng/µm Homework Equations Si unit conversions The Attempt at a Solution How do I know where to place the variables? Can someone give me a tut or written explantion on how to do this?

Hi all, I'm trying to build a transformerless converter unit, that will take an input of 240v a.c, and will output 12v d.c. I used a voltage divider to get a 16v from the a.c supply of 240v and connected my rectifying circuit across the 16v. I got an output of 14.59v. But on connecting the...

Homework Statement Consider the following vectors: a = (5.0m) i + (2.0m) j b = (-14m) i + (6.0m)j Sum of a+b in unit vector notation? Homework Equations The Attempt at a Solution I'm not sure about this notation, all I know about adding vectors is graphically. Does (5.0m)...

[SOLVED] Ideal gas unit conversions Homework Statement The ideal gas constants used in this text are typically mass-based: kJ / (kg*K). It is more useful to have them in units of kJ / (kmol*K). How to convert them using data from this text? Homework Equations The Attempt at a...

Hello everybody Normally you say that the unit of torque is Nm but could also be (Nm)/°.? I'm claiming this because of the fact that you normally do not give radians any unit, and that is why you just write Nm and not (Nm)/rad. SI claims that: "torque may be thought of as the cross...

Homework Statement there is a surface xy3z2=4. What is the unit normal to this surface at a pt in the surface (-1,-1,2)?? Homework Equations what is a unit normal to a scalar region? how can it be calculated? The Attempt at a Solution i calculated the gradient (del operator) of...

Let's say I have 4163 kJ/mol of energy coming from a substance with molar mass 86.14g/mol. How would I convert the 4163 kJ/mol of energy to kJ/litre? Thanks.

In group representation theory, identity element's representation matrix is unit matrix. But why? Could you give me an exact explanation? Thany you.

So I've been reading about orientated surfaces lately, and I always see the definition that a surface S is orientable if it is possible to choose a unit normal vector n, at every point of the surface so that n varies continuously over S. However, what does "varies continuously" mean? I never...

Homework Statement Let z1; z2; z3; z4 be four complex numbers on the unit circle (i.e., |z1|=|z2|=|z3|=|z4|=1). It is known that z1+z2+z3+z4=1+i . Find the value of 1/z1 + 1/z2 + 1/z3 + 1/z4 Homework Equations 1/z = barZ/|z|^2 The Attempt at a Solution I've been trying for about a day now...

Hi to all experts! I know individually about primitive cell("It has lattice point at corners only") and unit cell("It has lattice point at corners as well as at center if bcc or at faces if fcc or at bases if it is base centered") Are these right? But I don't know what is Wigner-Seitz cell...

Homework Statement Find the maximum and minimum value of the function, defined over x2 + y2 + z2 \leq 1. x \geq 0, y \geq 0, y \geq 0. Homework Equations f(x,y,z) = xy(z+1) The Attempt at a Solution \nablaf = (y(z+1), x(z+1), xy) = 0 Gets me (0, y, -1), (x, 0, -1), (0, 0, z) and...

Hello everyone, I represent an iron & steel manufacturing industry which runs on electricity. Currently our electricity consumption is 1,000,000 units/month @ 5.5 INR/Unit consumed along with maximum kVA reached during the time of manufacturing of product which is affecting the costing of...

Homework Statement Solvinf the unit time step equation mathematically. Homework Equations x(t) = u(t+1) - 2u(t) + u(t-1) The Attempt at a Solution How can i solve this signal mathemtically :( and using plotted signals , i couldn't understand, here is my approach and I'm...

I am using an equation that states that critical sonic velocity is: a_{cr}=\sqrt{\frac{2\gamma}{\gamma+1}gR_{gas}T'} The units should result in velocity (\frac{m}{s}) Yet, when I do the unit reduction I do not get that answer. Here is what I get: Lets ignore the square root for now. Also...

Homework Statement "The gravitational constant G is 6.67*10^-11 m^3*s^-2*kg^-1. What is G in units of cm^3*s^2*g^-1 Homework Equations 1kg = 1000g 1m = 100cm The Attempt at a Solution I don't understand how the dimension can change from [L^3,T^-2,M^-1] to [L^3,T^2,M^-1]...

Homework Statement That is what I learnt, and that it is expressed in Newton*meter. Then I learned that G is equal to 6.47 x 10^ -11 joules and that h is equal to 6.6262 x 10^ -34 joules x sec (N*m*s)and that one photon of light (say red) is equal to 4x 10^ 14 Hz(frequency) and its...

I have one differential equation like dN/dt=c*(other terms with no unit) unit of c is 1/ns. Now if I solve this equation, I will get value of N corresponding to t. (1) Then what will be the unit of t? (2) and if I calculate dN/dt1=(other terms with no unit). where t1=t/c. Then what...

I have always been critical of the idea of Planck units. They seem to be something conjured from numerology - particularly in view of the fact that it is possible to arrive at diffeent values of the so called fundamental dimension(s) by combiing different constants. But I recently had reason...

Homework Statement The graph shows the vector-valued function r(t). It is given that r(1) = <-1,1> and r'(1) = <1,2>. Find the unit tangent vector T(1) and unit normal vector N(1). (the graph given is that of y = x^2 shifted 2 units left.) Homework Equations (1) T(t) =...

Largest Unit of Heat Energy? Which of the following is the largest unit of heat energy: (a) calorie, (b) Btu, (c) joule, or (d) kilojoule. I narrowed it down to kilojoule or btu. I think it is btu.