Unit Definition and 1000 Threads

Please help -- Efficiency of car engine question... Unit test tomorrow Homework Statement A car's engine is only 12% efficient at converting chemical energy in gasoline into mechanical energy. If it takes 18000 N of force to keep the car moving at a constant speed of 21 m/s, how much chemical...

Homework Statement Consider the following circuit which uses ideal components. Prior to t=0 switch S is open. Then suddenly at t=0 switch S is closed. Find the impedance Z_{2} such that the system output is a unit step function of voltage. Be certain to show all components used to construct...

Is it possible to create a portable steam unit similar to this but without the use of the a heating element from a stove. http://vimeo.com/42042554 If so?, briefly how would one go about this? I would like to create something identical but with it's own heating unit and be hand...

Hi, I was given 1Btu/(h.ft^2.°F) to W/m^2.K with these conversion ratios 1m^3=1000L 1Btu=1.055*103 1m=3.2808ft and Δ1K=Δ1.8°F I can convert most of the units but I'm stumped by the temperature conversion here. Because I'm not converting a change in temperature but the discreet value of...

Hey everyone, the question I am faced with is this: Which of the following expressions involving δ[n] is incorrect? where "m" is a non zero integer and u[n] is the unit step function. A. u[n-m] = δ[n] + u[n-m+1] B. x[n]δ[n-m] = x[n-m] C. δ[n] = u[n] - u[n-1] D. δ[n]δ[n-m] = 0...

EDIT: Nevermind I see what I did wrong near the end. Homework Statement x'' + 4x = f(t) Where f(t) is 1 if t is between 0 and π, 0 if t > π. Initial conditions are x(0) = x'(0) = 0. Homework Equations Transform of a derivative: L(f^{(n)}(t)) = s^nF(s) - s^{n-1}f(0) -...-f^{n-1}(0)...

Homework Statement \rho(\lambda)d\lambda=\frac{8(\pi)hc}{\lambda^{5}}\frac{d\lambda}{e^{hc/(\lambda)KT}-1} What does this represent? Calculate the number of photons per unit volume in a blackbody from \lambda to d\lambda Homework Equations N/A The Attempt at a Solution I...

When my textbook talks about energy it starts with kinetic and potential. The derivation goes like this. F=ma=m(dv/dt)=-mg then they split the derivative using chain rule (dv/dt)=(dv/dy)(dy/dt) therefore since (dy/dt)=v we get F=mv(dv/dy)=-mg then they write mv dv= -mg dy...

Homework Statement Find the La Place transform of cos(x)*(u(x-\pi)) Homework Equations L{u(t-a)}(s)=(e^(-as))/s The Attempt at a Solution I don't think I can just multiply this by the La Place transform of cos (x), which is s/(s^2) ?

Homework Statement I need to find the mass of a disk with a hole, given inner and outer diameters of 0.10m and 0.30m, respectively. The disk has a mass per unit of 20 \frac{kg}{m^2}. The Attempt at a Solution Since I needed mass units, I thought that I could multiply the mass per unit...

Homework Statement Let ##100!=N\cdot 10^n##. If N is relatively prime with 10 and unit digit of N is d, then n+d is equal to A)26 B)28 C)30 D)32 Homework Equations The Attempt at a Solution I don't think it would be a good idea to expand the factorial and separately write out...

Homework Statement How much energy per unit mass (E/m) must you give a rocket to put it into a geosynchronous orbit three Earth radii above the surface of the Earth? Radius of Earth : 6380 km GM/r = 6.25 x 10^7 m^2/ s^2 Homework Equations U(r) = - GMm/r The Attempt at a...

Homework Statement A 45 kg object is lifted vertically at a constant speed to a height of 9.0m by a 750 W electric motor. If this motor is 25% efficient in converting electric energy to mechanical energy, how long does the motor take to lift the object? Homework Equations The...

Homework Statement The research notes from an x-ray diffraction experiment were damaged and information was lost. The wavelength of the x-rays used in the experiment, and measurements of the three smallest Bragg angles (θ) from the sample were all that remained: they were 0.71Å, 10.1°, 14.4°...

So I'm trying to find the DTFT of the following; where u(n) is the unit step function. u \left( n \right) =\cases{0&$n<0$\cr 1&$0\leq n$\cr} I want to find the DTFT of u \left( n \right) -2\,u \left( n-8 \right) +u \left( n-16 \right) Which ends up being a piecewise defined function...

I want to find the unit vector of ## \vec E= \hat x A\;+\;\hat y Be^{j\phi}## ##\hat E=\frac {\vec E}{|\vec E|}## From my work: ##|\vec E|=\sqrt{A^2+(Be^{j\phi})^2}## My question is what is ##(Be^{j\phi})^2##? Do I substitude ##e^{j\phi}=\cos \phi +j\sin \phi##? So...

Homework Statement I would like to use the Weierstrass M-test to show that this family of functions/kernels is uniformly convergent for a seminar I must give tomorrow. H_{t} (x) = \sum ^{-\infty}_{\infty} e^{-4 \pi ^{2} n^{2} t} e^{2 \pi i n x} . Homework Equations The Attempt at a...

Hello, In my lab report, I am trying to discuss what the units of resistivity mean. For instance, the unit of speed m/s second can be described as the time it takes to travel 1 m; specifically, 50 m/s would say that it would take 1 s to travel 50 m, or, we travel 50 m every second. Could...

So I'm busy struggling with some worked examples in my signals class. I understand the theory from the notes and textbook but I cannot seem to apply them to proper examples. We are asked to find the derivative of g(t) = (1-e^(-t))*u(t) where u(t) is a unit step function. I know the...

I'm completely stuck here, can anyone help me?

Homework Statement Is (x^2-1) a unit in F[x]? where F is a field. 2. The attempt at a solution I might say yes, cause we can find the taylor expansion of 1/(x^2-1), is my idea right?

Homework Statement The problem states to find a unit vector that is orthogonal to \left\langle1, 1, -2\right\rangle, forms an angle of \frac{\pi}{4} with \left\langle1, 1, 1\right\rangle and has v1 > 0. Homework Equations cos\theta = \frac{\vec{u}\bullet\vec{v}}{|\vec{u}||\vec{v}|}...

"find a unit tangent vector and the equation of the tangent line to the curve r(t) = (t, t^2, cost), t>=0 at the point r(pi/2)." NOW, what I don't get is, how is that a curve? This is not like the example I have studied and I don't really get the question. So I don't know where to start. Once I...

Homework Statement Not sure if this belongs in homework or general discussion - I found this in reading In studying the divergence and curl of the magnetic field (B), I found a statement that I need some help with. In the derivation of the divergence of B using the Biot-Savart, I have...

Hello, now I'm reading Peskin Shroeder. I have a question about the Casimir operator on page 500 in Chapter 15. From the following eq, ## \ \ \ [T^b , T^a T^a ] = 0 \ \ \ \ \ \ \ (15.91) ## ## T^2(=T^a T^a) ## is an invariant of the algebra. Thus the author concludes that ##T^2## is...

Homework Statement Calculate the three-phase short-circuit fault currents flowing into all five busbars. Homework Equations MVA base = 150MVA All base voltages were set to the local busbar voltages. Formulas I have used can be seen in the attached photos. The Attempt at a...

I seem to recall when taking college Trigonometry my professor saying that the unit circle and sinusoidal curves were basically a mathematical represention of a slinky in that the unit circle was the view of a slinky head on, so that what you saw in the two dimensional sense was a circle, and...

OK, I'm really rusty on this. I need to convert a unit vector to right ascension and declination. I believe I recall the formulae correctly, as I seem to have gotten 1 as my radius. So, that's good. In the pic I have my unit vector (P2), my actual answer below, my expected answer in...

Hi all, How do I compute the Fourier series coefficients for unit periods for cos(pi)x, the interval is from -1/2 to 1/2. I know the formula but I am getting a wrong answer ?

Homework Statement Find all the unit vectors orthogonal on the line L. Homework Equations L passes through the vectors u = [9; 7] and v = [1; -5] The Attempt at a Solution I found the slope of L from the two vectors: 3/2. I know that to be orthogonal, the vector will have a...

hi... we know the unit of velocity is m/s2 and while calculating the mean square velocity we find the average(or mean) of the 'squares' of the given velocities. then the unit of MEAN SQUARE VELOCITY should be 'm2/s4' then how come its unit is also m/s2 and not m2/s4 ?

Today I came across a statistical report of world energy consumption. There was a tab named energy generated and the values were given in TWh. There was a tab named Primary energy consumed and the values were given in Mtoe. I saw that the energy generated by the world is around 20000 TWh and the...

I have been wondering what type of measurement is used to measure the space inside of a four dimensional (space, not time) object. For example, a one dimensional line's distance gets measured, a two dimensional object's area gets measured, and a three dimensional object's volume gets measured...

Homework Statement Hi,can someone explain to me through real world examples what the unit step and unit impulse means in systems control?How are they related to the system's input? Thank you.Homework Equations δ(t) = unit umpulse u(t) = unit stepThe Attempt at a Solution

Homework Statement f(t) = cos (pi*t) if 1\leq t <4 and 0 elsewhere using unit step functions to find Laplace TransformHomework Equations The Attempt at a Solution I came up with the unit step function f(t) = cos(pi*t) u(t-1) - cos(pi*t) u(t-4) in order to use the second shifting theorem f(t)...

Homework Statement So I have this laplace transformation chart and was a bit unsure about the laplace and inverse laplace of this. The unit step function, where u(t) = 0 where t < 0, u(t) = 1 where t > 0. The laplace transformation chart that I have has two columns, the column on the...

Hi guys, I've run across a problem. In finding the potential energy between two electrical quadrupoles, I've come across the expression for the energy as follows: U_{Q}=\frac{3Q_{0}}{4r^{4}}\left[(\hat{k}\cdot \nabla)(5(\hat{k}\cdot \hat{r})^3-2(\hat{k}\cdot \hat{r})^2-(\hat{k}\cdot...

I'm not sure that I understand the vectors \hat{r}, \hat{\theta}, and \hat{\phi} in spherical coordinates correctly. I was looking through this link earlier. I understand that \hat{r} always points radially outward from the origin. That seems to imply to me that any position in space could be...

Hi all, I need help with something basic but I'm not sure how to handle it. The doubt is about how to consider the topology of the unit interval I=[0,1] inherited of the real line with its usual topology (intervals of the type (a,b)). I think that is just to pay attention to the definition...

Homework Statement Solve for the unit vectors x-hat and y-hat in terms of r-hat and phi-hat. Homework Equations r-hat=cos(phi)x-hat+sin(phi)y-hat phi-hat=cos(phi)y-hat-sin(phi)x-hat, The Attempt at a Solution I have been working on this for a really long time, and I keep getting a...

Homework Statement http://i.imgur.com/B1hFY6E.png Homework Equations -Basic geometry -Similar triangles (?) -Pythagorean Theorem The Attempt at a Solution -I need to find the angle the bar AB makes with the horizontal, correct? And with that, I will be able to figure out the...

Homework Statement When an object falls through air, there is a drag force that depends on the product of the surface area, A (m2), and the square of the velocity, in (m/s). The equation is Fdrag = CAv2. The metric unit of force is the Newton, or (N). 1 N = 1 kg*m/s2. What are the units...

Homework Statement http://prntscr.com/p7dxt Here's a screenshot of the revision question. Homework Equations The Attempt at a Solution Co-ordinates of each point A, (0, 60, 0) B, (40, 0, 0) C, (-40, 0, 40) D, (-60, 0, -60) Position Vectors rAB, 40i + -60j + 0k rAC, -40i + -60j + 40k rAD...

hello i got to ask if the center of symmetry is specific to a unit cell or a pattern or system of specific unit cell? I mean is Cubic (Bravis Lattice) is Centro symmetric or the structures formed by it. As an example, Tetragonal unit cell appears centro-symmetric but forming structures like...

Homework Statement If one truck runs on 6000 barrels of oil per year, how many trucks could run on the oil produced in the US in one year (1.9*10^10 barrels)?Homework Equations (6000 barrels/year) used by one truck (1.9*10^10 barrels/year) for US productionThe Attempt at a Solution I simply...

If Rn = 1/2(a^n + b^n) where a= 3+ 2root2 b= 3 - 2root2 and n= 0,1,2,3,4,5,... then R12345 is an integer. Its units digit is.. I didn't have any ideas so I started to plug in numbers looking for a pattern. I am sure this is not the right approach. R0 = 1 R1 = 3 R2= 7 R3= 9 Could I get...

Hello, I'm reading a textbook and in the textbook we are discussing the fundamental group of the unit circle and having some difficulty making out what a degree of a map is and why when there is a homotopy between two continuous maps f,g from S^{1} to S^{1} why the deg(f)=deg(g) We have...

And what are some good examples besides humans? I'm guessing that years don't matter as much as generational cycles. edit: for example, how many evolutionary cycles for humans would be contained in 100 years? Or dogs? Do you count by total age or reproductive age?

Hi I'm trying to study over break, this isn't an exact quote but its the part of the problem I need help with. Thanks. Homework Statement Draw the unit circle and plot the point P=(3,2). Observe there are TWO lines tangent to the circle passing through the point P. Lines L1 and L2 are...

Hi How do you get a photon flux per unit wavelength curve for solar radiation? My understanding of "per unit wavelength" is that the wavelengths within a very short range are fired at a detector. The range is then gradually changed to cover higher wavelengths. The values of flux measured by...