Components Definition and 911 Threads

I wonder if it is possible to write the components of the metric tensor (or any other tensor) as a summ of functions of the coordinates? Like this: g^{\mu\nu} = \sum_{\mu}^{D}\sum_{\nu}^{D} g_{_1}(x^{\mu}) g_{_2}(x^{\nu}) where g1 and g2 are functions of one variable alone and D is the...

I am not looking for a solution, just a "starting point"/guidance for calculating the expression: [M^{\mu \nu} , \phi_a] with M^{\mu \nu} being the angular-momentum operators and \phi_a being the field's component, which happens to transform under Lorentz Transformations: x'^\mu = x^\mu + \delta...

By the form of electricity, would it be possible to change brain chemistry without using the procedures of ECT? For instance, I would think in this day and age we could make a device that one would touch (like a doorknob) that could create a similar form of electroshock, only difference being...

I appreciate the link to the field strength calculator. http://www.calctool.org/CALC/phys/electromagnetism/solenoid I'm also looking for recommendations on sources for magnets. What I'm trying to do is put together a Faraday Rotation Effect Lab. This is my Faraday Rotator, a 12 cm x 2.0 cm...

Consider a Carnot's cycle diagram for an ideal gas. It will resemble a square. How do we know which side represents isothermal expansion/compression, which side shows work done by the gas or on the gas, adiabatic expansion/compression and which side represents the heat was added/exhausted?

Dear All, how to know whether electronic components such as spectroscopy amplifier (canberra 1413 or 2010), single channel analyzer (from ortec) and NaI Scintillator counter with its basis are working good. Are there any testing methods using a oscilloscope. I have a Mössbauer radioactive...

Homework Statement I just can't seem to find anything that I can relate to for solving this problem and it's giving me a headache. I don't even know how to start solving this question. Please help: A man drags a package across the floor with a force of 40 N. The mass of the package is 10 kg...

Homework Statement A(n) 8.5-kg object is sliding across the ice at 2.34 m/s in the positive x direction. An internal explosion occurs, splitting the object into two equal chunks and adding 12 J of kinetic energy to system. The explosive separation takes place over a 0.16-s time interval. Assume...

Homework Statement Replace the force system by an equivalent resultant force and couple moment at point P. Suppose thatF1 = 455 N and F2 = 700 N . (Figure 1) Homework EquationsThe Attempt at a Solution I found the solution to the problem. My question is how do I know which direction the...

Could a 3D printer print its own ink, plastic filament, motors or anything / everything else that it uses to operate and print?

Here is an example of a problem I am having trouble with. I need to find the i, j, k of A. I have no issues with finding the components for B, but A I just can't wrap my head around when to use cos or sin. Especially here with double projection. I know that A is : (-10 cos70 sin30, 10 cos70...

Homework Statement ##\overrightarrow{a} = (58m/s^2, 40°## below positive ##x## - axis) Find the ##x##- and ##y##-components of the vector. Express your answers using two significant figures. Enter your answers numerically separated by a comma (##a_x,a_y##). Homework Equations None I can think...

I have some conceptual issues with functions in vectors spaces. I don't really get what are really the components of the vector / function. When we look at the inner product, it's very similar to dot product, as if each value of a function was a component : So I tend to think to f(t) as the...

Homework Statement Grounded conducting sphere in uniform electric field has potential V(r,θ) = -Vo(1 - (R/r)3)*cosθ Find Er and Eθ. Homework EquationsThe Attempt at a Solution In the textbook I found Er = -∂V/∂r Eθ = -1/r ∂V/∂θ Those are in the chapter we're working with but those two...

Homework Statement there is a frictinless slope. And there is a box sliding down the slope. let's say that the slope slides from right, towards the down and left. object's mass is unknown value m. angle of the slope is 35deg. calculate the absolute value of the acceleration that the box has...

Homework Statement Write down the component form of the differential equations of motion of a projectile if the air resistance is proportional to the square of the speed. Are the equations seperated? Show that the x component of the velocity is given by \dot{x}=\dot{x}_0e^{^-\gamma s} where s...

In an earlier thread, Science Vulnerability to Bugs, I mentioned the case Here is a similar case. In another recent case (can't find the link), an author decided to un-license his public domain contribution and withdrew it from publicly shared libraries, which broke very many products...

Homework Statement why the strain of εxy , εxz , εyx , εzx , εyz , εzy is γ_xy / 2 , γ_xz / 2, γ_yx / 2, γ_zx / 2 , γ_yz / 2 , and γ_zy / 2 ? how to get that ?. Homework EquationsThe Attempt at a Solution Taking an example of εxy , what does γ_xy / 2 mean ? [/B]

I have been having some problem resolving the velocity component along the rope. My question will be clear if you read an illustration that I encountered which is very helpful in showing my doubt very clearly. In the Fig. given below the block ##'A'## and ##'B'## are connected with an...

I have a vector that represents the electric field at a specific point. How to find the vertical and horizontal polarization components of this vector?

So I am constructing an analogy between the self replicating fracturing effect on thin films and the path of a charged particle. (Qualitatively, several cracks have similar shapes to charged particle motion) I won't go into the details of the fracture mechanics, so I will only use E+M...

Say you have a circuit component with impedence Z(\omega). Is it possible combine it in some way to resistors, capacitors, and inductors, so as to shift the phase of the impedance by a constant?

Homework Statement Givens: - Each of the 2 cylindrical posts are 0.5 inches thick. - The posts and chain links are made of galvanized steel of identical material composition. - The posts and chain links are solid. - Each post is permanently fixed to unbreakable surfaces. The surfaces will move...

Dear all, I am trying to understand how they get they get the following components: $$c_\textbf{p} = \langle \textbf{p} | \psi\rangle = \int \frac{d\textbf{r}}{\sqrt{V}}e^{-\frac{i}{\hbar}\textbf{p}\cdot\textbf{r}}\psi(\textbf{r})$$ Where ##|\textbf{p}\rangle## are the plane waves $$...

This question really pertains to motivating why vectors have components whereas scalar functions do not, and why the components of a given vector transform under a coordinate transformation/ change of basis, while scalar functions transform trivially (i.e. ##\phi'(x')=\phi(x)##). In my more...

What 20 index combinations yield Riemann tensor components (that are not identically zero) from which the rest of the tensor components can be determined?

hi, Initially I would like to ask a little and basic question: I know that $$v=\sum_{i=0} e_i v^i$$ where $$v^i=e^i v$$ But sometimes I think we can write the first equation like $$v=\sum_{i=0} e_i e^i v$$, and I am aware that $$e_i e^i=1$$ , then our equation becomes $$v=\sum_{i=0} v$$, ın...

The problem I want to calculate the following sum $$ \sum^{5}_{k=2} \frac{k(-1)^k}{2^k} $$ The attempt I wrote ## \frac{(-1)^k}{2^k} ## as ##\frac{1}{(-2)^k}##. I was hoping that I could calculate the sum ## \sum^{5}_{k=2} \frac{k(-1)^k}{2^k} ## by multiplying the sums ##\sum^{5}_{k=2} k##...

Homework Statement The Resultant of the system of forces shown is R = 425 j lbs. Determine the possible values of P and Θ. Homework Equations R = F1 +F2+P The Attempt at a Solution I ended up with two equations, one in the "i" direction and one in the "j" direction. I think you have to use...

An upward force of magnitude 30N is combined with a second force F which makes an angle of 10degree with the horizontal. The resultant makes an anglre of 40degree with the horizontal. a. Determine the magnitude of the second force b. Determine the magnitude of the resultant

I recently salvaged a Melles-Griot HeNe laser from an FTIR system. I neglected to save any of the electronics except for what I think is the step-up transformer attached to the laser tube. The laser is "05-LSC-708-540" and the transformer is "05-LPM-850-045". I have a 12V power supply, but was...

Homework Statement A plane flies 600km/h south. The plane encounters a southwestern wind of 100km/h. Homework Equations What is the velocity (magnitude and direction) of the plane The Attempt at a Solution What I did was break the 100km southwestern vector into its components. 100*cos45 =...

Homework Statement A particle with charge ##e## and position vector ##\vec{r}## (relative to some frame, S) moves with constant velocity ##\vec{v}##. A second charge ##e'## is moving with the same velocity ##\vec{v}## through the field generated by ##e##. If ##\vec{d}## is a vector from ##e##...

Homework Statement Imagine we have a tensor ##X^{\mu\nu}## and a vector ##V^{\mu}##, with components ## X^{\mu\nu}=\left( \begin{array}{cccc} 2 & 0 & 1 & -1 \\ -1 & 0 & 3 & 2 \\ -1 & 1 & 0 & 0 \\ -2 & 1 & 1 & -2 \end{array} \right), \qquad V^{\mu} = (-1,2,0,-2). ## Find the components of...

Homework Statement This is a real world problem, which I have been thinking about for some time now. The problem is this: I have a weighted sled which requires a pulling force to move it, and I have a team of dogs generating that pulling force. I am trying to figure out the differences between...

for a electron in a cubic box ( dimension of the box is L) problem how to show the components of the wave vector k are quantized...

I understand that in an electrical circuit, a positive test charge will gain electrical potential energy when moving from the negative to positive terminal of a battery (as it's moving against the electric field); it will then naturally flow around the circuit back to the negative terminal as it...

In the transformation of tensor components when changing the co-ordinate system, can someone explain the following: Firstly, what is the point in re-writing the indicial form (on the left) as aikTklajl? Since we're representing the components in a matrix, and the transformation matrix is also...

Although mass-less, a photon, like any other quantum particle, has a frequency/wavelength associated with its energy/momentum. If we have a group of photons all with the same specific energy, then each photon can be represented by a little, complex-valued plane wave. Photons are also EM waves...

Homework Statement A circle-formed circuit with an area A lies in the (xy)-plane. An electric current I runs clockwise through the circuit (figure 1). An external magnetic field B exerts a torque t = D(3i - 4j) on the circuit, where D is a positive constant, i is the x-axis unit vector and j is...

Something said in my physics textbook really confused me. The following was written : "Applied Force is our label for a contact force that a person exerts. When an applied force acts at an angle, it is actually a combination of two forces : normal and friction. The component of the applied...

What happens to a mechanical force's real original direction i.e. when we divide it into components of basis vectors, which in turn change as per problem at hand (like gravity components at inclined plane ), how we arrive at correct physics by taking two/three arbitrary directions of our choice...

I used the expression Rabcd=-Rbacd=-Rabdc=Rcdab to reduce the number of components. I also used if a=b=0 the R=0 and if and c=d=0 then R=0. This reduced the number of components to 64. How do I get them down to 21? I know I need another equality to reduce it to 20. <<Mentor note: Fixed...

Homework Statement In the diagram below, each division on the horizontal axis (the displacement s) is 0.10 m while each division on the vertical axis (the electric potential V) is 1.0 V. What is the electric field component along the displacement axis s in each of the regions specified below...

Homework Statement Finn is lost in the woods, trying to find his way back home which he knows is 7.00 km at a 120.0° angle from his current location. He decides to travel 2.00 km at a 40.0° angle followed by another 5.00 km at a 100° angle. 1) What is his current location using a km coordinate...

Dear friends I need the names of these components show in attached pictures of Switchyards. So that I will get information form google and there manufacturer. Picture 1 Picture 2 Picture 3

Homework Statement [/B] Given the following vector components of vectors C and D: Cx = 8.10, Cy = -5.40, Cz = -7.90, Dx = 4.40, Dy = -2.50, Dz = 4.50, find the x, y, z components of their sum. Homework Equations No relevant equations that I know of...[/B] The Attempt at a Solution I am...

HI everyone, Imagine we are sampling of a gaussian signal along time and need to know the power/variance associated with the first N spectral components. So we take our favorite fft algorithm to get the PSD. The error associated with a given estimated spectral component f(w) (w is the...

I usually come across expressions for the Stress energy tensor showing them as three densities (normally over a space-like slice. In wikipedia's article on the spin tensor, they clearly (it does not appear to be an error) both write about and express the components of the stress energy tensor as...

Homework Statement Calculate the net torque about the axle of the wheel shown in https://jigsaw.vitalsource.com/books/9781269392464/content/id/ch08fig39 . Assume that a friction torque of 0.40 m · N opposes the motion. Where F=18N (in photo). The picture is here...