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0
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1answer
464 views

Calculating torque in a structure

I posted this on math stack exchange but realize it is more a physics question. I have a structure which is set up as shown in the image. A weight hangs from point A with mass $m$. Joint B is free ...
0
votes
1answer
622 views

Time taken for object in space to fall to earth

The Problem For a small mass a distance $R_i$ away from the center of the Earth, how long would it take for the object to fall to the surface of the Earth, assuming that the only force acting upon the ...
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3answers
3k views

Why does salty water heat up quicker than pure water? [duplicate]

Possible Duplicate: Why does adding solutes to pure water lower the the specific heat? Why do higher concentration salt solutions heat up more quickly?
0
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1answer
194 views

Question about interaction between three objects

I have been thinking of Newton (insert bad words because of frustration) laws for hours and hours today, and I'm not going anywhere. I'm going insane! So, I made up this question. Object A | ...
0
votes
2answers
2k views

Vertical component of moving weight at a 45 degree angle

Here's an easier one. I use the leg press machine at the gym so I don't have to worrying about hurting myself while lifting heavier weight. The weight glides on a track that looks to be 45 degrees. ...
0
votes
2answers
629 views

Understanding weight on an inclined plane

I'm trying to solve a problem where I have an object resting on an inclined plane, with the angle of the plan being alpha, and the weight being w. I'm having trouble figuring out how I can calculate ...
-1
votes
2answers
118 views

Harmonic Motion [closed]

A light elastic string is stretched between two points, one lying vertically below the other. A particle is attached to the midpoint of the string, causing it to sink a distance h. Assuming that the ...
-1
votes
1answer
3k views

What affects the damping of a spring?

What variables affect the damping of a spring executing simple harmonic motion? What are the independent variables, and what variables would need to be controlled in an experiment? I'm attempting to ...
-5
votes
1answer
79 views

Ascertain the height an object has fallen from given force exerted and mass [closed]

An object of a given mass falls from an unknown height. If the force exerted by the object on contact with the ground is known, how would you ascertain the height from which the object fell?
6
votes
3answers
602 views

Gauge invariant Chern-Simons Lagrangian

I have to prove the (non abelian) gauge invariance of the following lagrangian (for a certain value of $\lambda$): $$\mathcal L= -\frac14 F^{\mu\nu}_aF_{\mu\nu}^a + ...
4
votes
1answer
2k views

Solving a statically indeterminate truss

I'm trying to solve the statically indeterminate truss shown below and I'm having a little trouble. $H$, $P$ and $\beta$ are given. The material is aluminum (density is 2700 ${kg/m^3}$) and has a ...
2
votes
0answers
104 views

Showing that the Ricci scalar equals a product of commutators

I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor ...
7
votes
2answers
367 views

Quantization of a particle on a spherical surface

Suppose we have a particle of mass $m$ confined to the surface of a sphere of radius $R$. The classical Lagrangian of the system is $$L = \frac{1}{2}mR^2 \dot{\theta}^2 + \frac{1}{2}m R^2 \sin^2 ...
7
votes
4answers
341 views

Distribution of point charges on a line of finite length

How will $N$ freely moving charges confined to a line with length $L$ be distributed? What are their equilibrium positions?
6
votes
1answer
182 views

Free Particle Path Integral Matsubara Frequency

I am trying to calculate $$Z = \int\limits_{\phi(\beta) = \phi(0) =0} D \phi\ e^{-\frac{1}{2} \int_0^{\beta} d\tau \dot{\phi}^2}$$ without transforming it to the Matsubara frequency space, I can ...
6
votes
3answers
848 views

Force between two charged rods?

Suppose that we have two rods of length $l_1, l_2$ connected at one end but free to rotate. These rods have charge density $\lambda$ uniformly distributed, so the total charge of rod $i$ is $\lambda ...
6
votes
3answers
4k views

Why can't a single photon produce an electron-positron pair?

In reading through old course material, I found the assignment (my translation): Show that a single photon cannot produce an electron-positron pair, but needs additional matter or light quanta. ...
3
votes
4answers
325 views

How are we able to view an object in a room with bulb..?

This is a very basic question on optics. How are we able to view an object kept in a room with a bulb? From what I understand, light rays from bulb will hit the object and some colour will be ...
7
votes
1answer
261 views

Virial theorem and variational method: a question

I have an hydrogenic atom, knowing that its ground-state wavefunction has the standard form $$ \psi = A e^{-\beta r} $$ with $A = \frac{\beta^3}{\pi}$, I have to find the best value for $\beta$ ...
7
votes
2answers
219 views

The geodesic line on Poincare half plane

I was calculating the geodesic lines on Poincare half plane but I found I somehow missed a parameter. It would be really helpful if someone could help me find out where my mistake is. My calculation ...
5
votes
2answers
797 views

Quantum Mechanics Notation for BRA KET

I've been given this homework problem, but I do not understand its notation. Please perform the following where the wavefunctions are the normalized eigenfunctions of the harmonic oscillator ...
5
votes
3answers
4k views

Convert acceleration as a function of position to acceleration as a function of time?

Suppose I have acceleration defined as a function of position, $a(x)$. How to convert it into a function of time $a(t)$? Please give an example for the case $a(x)= \frac{x}{s^2}$.
4
votes
1answer
415 views

Lie derivative of Riemann tensor along killing vector ( = 0 )

I'm currently learning the mathematical framework for General Relativity, and I'm trying to prove that the Lie derivative of the Riemann curvature tensor is zero along a killing vector. With the ...
4
votes
3answers
191 views

Finding the equation of motion of anharmonic potential [closed]

If I have a potential given by: $$U=U_0\left[2\left(\frac xa\right)^2-\left(\frac xa\right)^4\right]$$ It says that at $t=0$, the particle is at the origin ($x=0$) and the velocity is positive and ...
4
votes
2answers
160 views

Is there a general form for heat capacity?

Can you derive a general form (not keeping either volume or pressure constant) for heat capacity from the first law of thermodynamics? Do you have to make any assumptions to do so? It sounds trival, ...
4
votes
1answer
437 views

QED BRST Symmetry

This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim: "Consider QED ...
3
votes
1answer
135 views

Directional derivatives in the multivariable Taylor expansion of the translation operator

Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$. Where $P=-i\hbar \nabla$. Here's what I've gotten: ...
3
votes
2answers
302 views

Unitary spacetime translation operator

Srednicki writes: We can make this a little fancier by defining the unitary spacetime translation operator $$ T(a) \equiv \exp(-iP^\mu a_\mu/ \hbar) $$ Then we have $$ T(a)^{-1} \phi(x) T(a) = ...
3
votes
1answer
89 views

Why doesn't this equation for orbital motion change with position in the orbit?

The question and answer are on pg.8-10 of this PDF: At first, I went through it, thinking nothing of it. But then, I wondered: "What if we picked a final state in which the space junk was NOT at ...
3
votes
0answers
797 views

Effective mass in Spring-with-mass/mass system

Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the ...
3
votes
1answer
527 views

What is non-thermal plasma?

I read about non-thermal plasma, but I still have some questions: The ions and neutral particles are not in thermal equilibrium with the electron, does that mean that the overall temperature is low ...
3
votes
2answers
763 views

The Energy-Momentum Tensor and the Ward Identity

I have a question regarding a homework problem for my quantum field theory assignment. For the purposes of the question, we can just assume the Lagrangian is that of a real scalar field: ...
2
votes
1answer
229 views

Variation of modified Einstein Hilbert Action

In general relativity one can derive the Einstein Field Equations by the principle of least action through variations with respect to the inverse of the metric tensor. In some modified theories of ...
2
votes
3answers
213 views

How to show that probability and statistics are very important in Quantum Mechanics?

I'm doing a research for my stats class in high school and I chose quantum mechanics as my subject. I narrowed down to electron localization in an atom and radial probability distribution. However, I ...
2
votes
3answers
3k views

Proving angular momentum is conserved for a particle moving in a central force field $\vec F =\phi(r) \vec r$

A problem I am trying to work out is as follows: A particle moves in a force field given by $\vec F =\phi(r) \vec r$. Prove that the angular momentum of the particle about the origin is constant. ...
2
votes
3answers
4k views

Finding Lagrangian of a Spring Pendulum

I'm trying to understand Morin's example of a spring pendulum. What I don't get is his expression for $T$. I can understand the $\dot x^2$ term in the brackets. But I don't understand the $(l + ...
1
vote
1answer
531 views

How to apply the WKB approximation in this case?

I'm trying to learn how to apply the WKB approximation. Given the following problem: An electron, say, in the nuclear potential $$U(r)=\begin{cases} & -U_{0} \;\;\;\;\;\;\text{ if } r < ...
1
vote
3answers
975 views

Energy Spectrum of pair of spin-1/2 particles with general Hamiltonian

I found this problem, and so far I am stumped. I was wondering if anyone wanted to solve it with me, or help me calculate eigenvectors, or just give insight on my questions. Consider a system of ...
0
votes
3answers
215 views

Navier-Stokes system

I have to study this system which name is Navier-Stokes. Can you explain please what means that $p$, $u$ and $(u \cdot \nabla)u$. What represents in reality? Tell me please, how should I read the ...
0
votes
3answers
7k views

Finding Angular Acceleration of rod given radius and angle

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular ...
8
votes
4answers
20k views

What is the relationship between kinetic energy and momentum?

I can't seem to figure out the relationship between $E_k$ and $p$ or $F$. I understand that the units are pretty different. But for example: A bullet with a mass of 10.0g is moving at the speed of ...
7
votes
2answers
409 views

Equivalence principle and radiation from falling particle

I am currently having a hard time solving a problem of GR from Lasenby's book. I can't make it more clear than by quoting the exercise: 7.2 A charged object held stationary in a laboratory on the ...
6
votes
2answers
326 views

How to show that every Killing vector field is a matter collineation?

Various texts make this claim, but no proof is given. Explicitly, let $L$ denote the Lie derivative. Suppose $L_X g_{ab} = 0$ for some vector field $X$, called a Killing vector field. Suppose that ...
6
votes
2answers
598 views

Infinitesimal Lorentz transformation is antisymmetric

The Minkowski metric transforms under Lorentz transformations as \begin{align*}\eta_{\rho\sigma} = \eta_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*} I want to show that ...
6
votes
2answers
241 views

Radioactive Decay

Problem:Nuclei of a radioactive element $\Bbb X$ having decay constant $\lambda$ , ( decays into another stable nuclei $\Bbb Y$ ) is being produced by some external process at a constant rate ...
5
votes
2answers
569 views

relativistic acceleration equation

A Starship is going to accelerate from 0 to some final four-velocity, but it cannot accelerate faster than $g_M$, otherwise it will crush the astronauts. what is the appropiate equation to constraint ...
4
votes
1answer
251 views

What the heck is negative effective mass?

I am reading this book:Solid State Electronic Devices by Ben G Streetman and Sanjay Kumar Banerjee. I have some doubts in the article 3.2.2 Effective mass. In this the aythors say that ...
4
votes
2answers
101 views

Top angular speed of electric motor

I recently came across a question asking the following: If a motor is switched on, it quickly reaches a top speed. Why does it not just go faster and faster and faster? I thought it might be ...
4
votes
3answers
233 views

Non-SHM oscillatory motion

How to solve these kind of questions , where $|F| \propto x^2$? How to find time period and velocity type related things to the oscillatory motion? ...
4
votes
4answers
4k views

Infinitely charged wire and Differential form of Gauss' Law

I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get $$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty ...