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9
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1answer
227 views

“Redshifting” of forces in stationary space - times

Here's the problem statement: Let $(M,g_{ab})$ be a stationary spacetime with timelike killing field $\xi ^{a}$. Let $V^{2} = -\xi _{a}\xi ^{a}$ ($V$ is called the redshift factor). (a) Show that the ...
8
votes
1answer
220 views

Gamma Matrices in Dimensional Regularization

Prove that $tr\left(\gamma_\mu\gamma_\nu\gamma_\rho\gamma_\sigma\gamma_5\right)=0$ when the spacetime dimension is not 4. What I have tried: We know that $\gamma_\alpha\gamma^\alpha=d\mathbb{1}$, so ...
7
votes
1answer
129 views

The problem in Sredniki's textbook: How do I calculate loop corrections for $\phi\phi\to\phi\phi$ with this Lagrangian?

The problem in Sredniki's textbook 10.5 : For a free scalar field $\psi$, the Lagrangian is $$\cal{L}= -\frac{1}{2}\partial^\mu\psi\partial_\mu\psi-\frac{1}{2}m^2\psi^2$$ Here we use the metric ...
6
votes
1answer
209 views

Is it possible to determine particles' velocities from their crossings on a ring?

2 particles are constrained to move in a ring. Both particles begin moving at $t=0$ from $p=0$, each particle moving in the opposite direction of the other. It is known that they are moving at ...
5
votes
1answer
644 views

Adiabatic expansion in van der Waals gas

Given a Van der Waals gas with state equation: $$\left( P+\frac{N^2 a}{V^2}\right)\left( V-Nb \right)=NkT,$$ show that the equation of an adiabatic process is: $$\left( ...
5
votes
1answer
125 views

Force problem related to adhesive and bonding

I have two PCBs (printed circuit board), and they are glued by adhesives, as show in the pictures. And the location of the adhesives are indicated on the picture (please notice that NO adhesive is ...
4
votes
1answer
84 views

Pressure and Density Using a General Lagrangian

Given a lagrangian of a form: \begin{equation}\mathcal{L}=f(\phi,\partial_{\mu}\phi\partial^{\mu}\phi)\end{equation} where $f$ is a function, I need to derive pressure and density in a FLRW universe ...
4
votes
1answer
156 views

Pipe in a flowing river problem

I'm working on a certain problem in fluid mechanics, which isn't really my strongest area. The problem is as follows: Curved pipe is partially submerged in a flowing river so that one end is pointing ...
4
votes
1answer
195 views

Thermodynamic relations from Gibbs-Duhem

Given the Gibbs-Duhem relation $V dp = S dT - N d \mu$, I am having trouble deriving the following identity: $\ (\frac{\partial N}{\partial \mu})_{V,T} = N (\frac{\partial \rho}{\partial p})_T$ ...
4
votes
1answer
935 views

Infinite-range 1D Ising model + Hubbard-Stratonovich-Transformation

I have a probably quite simple question RE the HST. After some work, I obtain as the partition function for the infinite range 1D Ising model $$Z = \int_{-\infty}^\infty \frac{dy}{\sqrt{2\pi / ...
3
votes
1answer
83 views

Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
3
votes
1answer
136 views

Is there a graphical representation of the Lorentz transformation equations?

I always loved theoretical physics as a kid and when I came upon this site while seeking computer advice via superuser I had to stick my silly little head into an oasis of intelligence. I have often ...
3
votes
1answer
125 views

An Electric Potential Glued to a Cubic Insulator to Replicate a Point Charge: Charge Distribution

I have been going back over this problem with a friend for the better part of a day: A potential is glued to a cube insulator so that outside of the insulator the field is the same as a point ...
3
votes
1answer
262 views

Homopolar motor and Lorentz force

My second grader thought making a homopolar motor for her science experiment would be fun. And, it was. Now I am trying to explain how it works and the Lorentz force. Please help me by giving me a ...
3
votes
1answer
763 views

Simple thermodynamics basics - can internal energy be calculated?

Well this got me stumbled, because I've been wondering what the "question" is. One of the example examns got the following question (strangely there are no supplied solution books): A $0.2 {\rm ...
3
votes
1answer
258 views

Semiconductor problem: how much Boron is required to establish a certain amount of charge carrier density

The problem description is as follows: Boron is used to dope 1 kg of germanium (Ge). How much boron (B) is required to establish a charge carrier density of 3.091 x 10^17 / cm^3. One mole of ...
2
votes
1answer
28 views

Looking for a simple proof of symmetry of linear susceptibility tensor

Getting a diagonal susceptibility tensor: Define the linear susceptibility tensor as $\chi_{ij}$: $P_i = \epsilon_0\chi_{ij}E_j$, using standard notation for the electric field and the polarization. ...
2
votes
1answer
136 views

Sum of forces with liquid in rotation

It's not homework (I'm teacher). I would like to compute sum of forces on this study : The shape is symmetrical like that I'm sure the center of gravity is in the center of the shape. I compute ...
2
votes
1answer
232 views

Line of action force

The task is to reduce the two forces into a single net force and then find the equation of its line of action. I chose to find the net force and momentum with respect to the origin. The magnitude of ...
2
votes
1answer
308 views

Spring system - 3 DoF system and its properties while changing stiffness

I was given the attached 3 degree of freedom spring system with the purpose of analyzing it. I came up with the following equation of motion and then I ran Matlab to calculate the corresponding ...
2
votes
1answer
176 views

Dog running after sephard

Assume there is a dog A on a field and a sephard B. B moves on straight line with constant ...
2
votes
1answer
338 views

What defines the adiabatic flame temperature?

What defines the adiabatic flame temperature? In a case I have to solve, I need to describe the combustion of natural gas (Groningen natural gas, to be specific). However, I am having some problems ...
0
votes
0answers
289 views

Maximum Shear on a Beam - beam with fixed support on one end and hinge on other end

A beam $\displaystyle 3m$ long with fixed support on one end and hinge on the other end is subjected to a uniform load of $10\ kN/m$. What is the maximum shear of this beam? The solution is this one: ...
0
votes
0answers
284 views

What is the current induced in a straight wire when a magnetic field is turned from on to off?

Consider a straight wire which runs along the y-axis. A B-field exists which is uniform and only in the x-direction: $$\vec{B}=(B(t),0,0)$$ The B-field at time $t_0$ is 'switched off' in ...
0
votes
0answers
399 views

Nuclear reaction: creation of deuterium

A proton p collides with a neutron(at rest) n at relatively low-energies and creates a 'deuterium-core' d: $$p+n->d+\gamma$$ Find the wavelength for the photon as a function of the proton's ...
0
votes
0answers
120 views

Finding final charge distribution on capacitors on grounding

I am trying to solve the following problem on capacitors: Here's the circuit I have to find the total energy loss when all three switches are closed, and subsequent equilibrium attained. I had ...
0
votes
0answers
41 views

How do I minimize the the stress created by fore-aft forces?

My friends and I are designing a bench press spotter. Essentially, when the user needs help lifting the barbell due to muscle fatigue, an arm on each side of the user raises to provide assistance. ...
0
votes
0answers
372 views

Whats the contact area for elastic contact between a cylinder and a plane surface?

I am trying to determine the contact area between a cylinder and a plane surface of two different materials so that the plane lies tangent to the cylinder. There is elastic contact between the two ...
0
votes
0answers
122 views

Number of microstates of discretized paths

Let us consider a square grid, which has been rotated by 45deg. On this grid we define a path, the directed polymer, which starts at the origin ($t = 0$) and extends in the positive $t$-direction ...
0
votes
0answers
304 views

How to solve fixed-fixed beam with finite difference method?

What equations to use on this system to form a matrix $A$ with dimensions $[n,n]$ and load vector $q$ with dimension $[n]$ ? I am trying to get vertical displacement $w$. $$w = A^{-1}\times q$$ ...
0
votes
0answers
318 views

How to find angular velocity of a point inner a circumference

Let's consider a cicumference that have the center in the origin of axes and rotates around x-axes. Let's stick a bar in a point $A$ of this circumference and at the end of the bar let's stick a mass ...
0
votes
0answers
351 views

How do you determine the torque caused by the mass of a lever?

Suppose we have two objects sitting on two side of a lever, and the lever also has a mass, and those objects have masses. Then how we can balance $\sum τ$? This is what I have done: ...
0
votes
0answers
93 views

Using thermodynamics and Kinematics together to solve a parachuter problem?

I need to find a parachutist's displacement after a given height (nearly 37000m) and at a given latitude. I have his mass, area, parachute area, drop height, parachute deployment height, data about ...
0
votes
0answers
358 views

What is the pressure in a vertical pipe that has moving fluid through it?

I have a system like this When the valve is closed, pressure along any point along the thin tube may be found thru pgh. 1. What about when the valve is opened? 2. Does the top of the jar need to be ...
0
votes
0answers
529 views

Question about the refraction of light in a swimming pool

Here is a homework question that I'm having a hard time understanding: Out of pure intellectual curiosity you have donned a snorkeling face mask and allowed yourself to sink to the bottom of the ...
0
votes
0answers
267 views

Reflectance and phase shift vs incident angle and wavelength

Plot the refectance and phase shift on reflection $\varphi$ for p and s polarized light versus incident angle $\theta$ for various wavelength $\lambda_1=.., \lambda_2=..,..$ in the simple case of ...
0
votes
0answers
146 views

I'm having trouble understanding the dimensions of this falling body problem

I'm working with this: A 50 kg mass is shot from a cannon straight up with an initial velocity of 10m/s off a bridge that is 100 meters above the ground. If air resistance is given by 5v ...
0
votes
0answers
152 views

Describing the movement of the object in a particular situation in Lagrangian way

Suppose there is a object M, (sliding motion) moving by the initial speed $v$ and the initial location $x_0$. Otherwise noted, friction is assumed to be nonexistent. It then meets a circular mold ...
0
votes
0answers
86 views

deriving differential equation of a cart moved by a motor

This is homework and I'm having some trouble getting started. How do I go from whats given to the form that they ask for? Normally in something like this I would try to balance torque, but I'm not ...
0
votes
0answers
100 views

Mass loss rate of planetary nebulae

The “interacting wind” model of planetary nebulae is based on the idea that the white dwarf phase of stellar evolution is preceded by a red giant phase. A fast wind from the hot white dwarf overtakes ...
0
votes
0answers
185 views

Reduction in velocity in pipe

I have two pipes divided from main pipe. If I add one more pipe, what would be the amount of velocity in each pipes. I know the velocity of main pipe, then diameter and radius of each pipe. Edit: 1) ...
0
votes
0answers
508 views

Error Analysis, Change in momentum, Kinetic Energy

If momentum of an object is increased by 10%,then its kinetic energy will be increased by? Well, I don't need the solution logically by calculating the change in Kinetic Energy etc, but my question ...
0
votes
0answers
81 views

Is it necessary to use all solutions when calculating an expectation value in a spin state?

I'm given an spinor $\Psi$ which is solution of the Free Dirac equation, such that is an eigenfunction of $\hat{\vec{p}}$ and has positive energy. Then I'm asked to calculate the expectation value of ...
0
votes
0answers
79 views

How do I write the energy of a constant, uniform 2D charge distribution?

Let's consider a 2D electromagnetic field defined in a square domain $[0,\Lambda]^2$, with periodic boundary conditions, with a constant charge distribution, uniform all over the aforementioned ...
0
votes
0answers
85 views

Can a wave propagate in an elastic fluid in the absence of volume forces?

A motion (wave) $\mathbf{x}: \mathcal{B}_0 \times [t_0,t_1] \to \mathcal{E}:$ such that $q-o = \mathbf{x}(p,t)=(p-o)+\mathbf{a}_0 cos(\mathbf{k}_0\cdot(p-o) - \omega_0 t)$ can propagate in an elastic ...
0
votes
0answers
171 views

How do I tackle this problem WITHOUT focusing the whole system as a “single mass”?

Problem/Solution ! ! In the third FBD, they made the whole system as one object. What happens if I don't want to do that? What if I jsut apply Newton's second Law to the mass M? I tried it out but ...
0
votes
0answers
135 views

2 streams going into an engine and 2 come out. Find the enthalpy?

Problem: Steam supply to an engine is made of two streams that mix before entering the engine. Stream 1 flows at a $.01\frac{kg}{s}$ with an enthalpy of $2952\frac{kJ}{kg}$ and a velocity of ...
0
votes
0answers
462 views

Ground state energies with fermions of same spin?

Consider two non-interacting Fermions (half-integer spin) confined in a 'box'. Construct the anti-symmetric wavefunctions and compare the corresponding ground-state energies of the two systems; ...
-1
votes
0answers
13 views

Spherical charge distribution along a wire of length $L$ in which its center coincides with the origin of the system

I've already tried to find the expression but I don't find the expected result for the quantity of charge when I use the expression I found. For example, I checked it by integrating the expression ...
-1
votes
0answers
44 views

Relative acceleration pulley

Considering If we have pulley with strings on both sides giving different velocities to them, we know velocities of points between them, on diameter, as velocity vector is tangent to it, just ...