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3
votes
2answers
74 views

Prove identity of partial derivatives

I can not do the following problem: Prove the identity: $$\left( \frac{\partial x}{\partial y} \right)_{z}\left( \frac{\partial y}{\partial z} \right)_{x}\left( \frac{\partial z}{\partial x} ...
4
votes
3answers
705 views

Capacitor with different charges on each plate

I am confused as to whether/how capacitance changes when each plate has a different charge. For example, consider a coaxial cable and put $20Q$ on the outer cable, and $-Q$ on the inner. Or how about ...
0
votes
2answers
315 views

Schrödinger's Equation and the depth of a finite potential well

Before I ask my question, I have to stress: I have absolutely no idea what the math is going on. I've read my textbook, several Wikipedia articles, scoured the internet, and don't feel anymore ...
0
votes
3answers
957 views

Deriving the Poynting Theorem

I am trying to derive the Poynting theorem. So far, I've only been able to narrow down which equations I think I'll need to do so. These are the equations: Maxwell's Equations: $$ \nabla\times{\bf E} ...
0
votes
3answers
1k views

Tension on a string between two objects on a friction less surface [closed]

I just need my work checked here. Please let me know if I am correct. I had this problem in one of my test in which I did not get full credits. I am re-doing this(hopefully correctly this time) just ...
2
votes
0answers
208 views

Equation of motion for a falling rod (with one end touching a frictionless surface)

I have a quick question about the equation of motion for a falling rod (with one end touching a frictionless surface). The end touching the surface is not fixed. I am given the moment of inertia about ...
1
vote
1answer
64 views

Deriving commutation relations in second quantisation

I am trying to start from: \begin{align*} [\phi(x),\pi(x')] = i\hbar\delta(x-x') \\ [\phi(x),\phi(x')] = [\pi(x),\pi(x')]=0 \end{align*} to derive: \begin{align*} [a(k),a(k')^\dagger]=\delta_{kk'}\\ ...
0
votes
0answers
50 views

Kirchoff Loop and current

The pic of the circuit/problem: I got the problem right, but i want to make sure my reasoning is correct for the current left of the 2.1 V battery. Its the same current as $I_1$ because the ...
2
votes
1answer
86 views

Rotation of angular momentum eigenfunctions?

I am struggling to understand this apparently obvious example in my group theory notes: Where do the $e^{i\phi} $ and $e^{-i\phi} $ factors come from? I know that the $m_l$ = -1,0 and +1 angular ...
2
votes
2answers
68 views

Solving actual weight lifted

I was wondering if anyone knew the formula to calculate how much force is required to lift a tire or any object by the edge. For example if a tire weighs 500 lbs (or has a mass of 226.8 kg). I would ...
1
vote
2answers
86 views

The best way to cool the teapot

My professor today in the class made us a question: "Lets say we have a teapot with water in it.The water is hot.Now we want to cool the water. Will it cool faster if we put an ice cube above the ...
0
votes
2answers
320 views

Colors in the secondary rainbow reverse of that in the primary rainbow

Why the colors of Secondary rainbow is reverse of that in the color in the Primary rainbow? What can be the possible reason among the following options Because it is formed by one internal ...
0
votes
1answer
41 views

Determining the horizontal position of an object [closed]

In my calc-physics class we were given the following question: A movie stuntwoman drops from a helicopter that is $30.0 m$ above the ground and moving with a constant velocity whose components are ...
0
votes
3answers
155 views

In what situations do water levels not reach equilibrium?

I have been taught that water levels will always equal out. However, now I find that sumps and some other setups allow for water not to become equal. What other arrangements allow for the water levels ...
2
votes
1answer
101 views

prove: $[p^2,f] = 2 \frac{\hbar}{i}\frac{df}{dx}p - \hbar^2 \frac{d^2f}{dx^2}$

I need to prove the commutation relation, $$[p^2,f] = 2 \frac{\hbar}{i}\frac{\partial f}{\partial x} p - \hbar^2 \frac{\partial^2 f}{\partial x^2}$$ where $f \equiv f(\vec{r})$ and $\vec{p} = p_x ...
1
vote
2answers
409 views

Derivation of relativistic uniformly accelerated motion

I'm trying to understand solution of the following problem from Landau, Lifshitz, Classical Theory Of Fields: (ending skipped). What I see when I "write out the expression for $w^iw_i$", using ...
2
votes
0answers
64 views

The proof that Dirac's hamiltonian commutes with inversion operator

I tried to check the statement that Dirac free Hamiltonian commutes with inversion operator. For $$ \hat {P}\Psi(\mathbf r , t) = i\hat {\gamma}_{0}\Psi (-\mathbf r , t), \quad \hat {H} = (\hat ...
1
vote
0answers
44 views

Coherent State in 2 dimensions

I am looking at a 2D harmonic oscillator $$H=\frac{1}{2m}(p_x^2+p_y^2)+\frac 12m(\omega_x^2x^2+\omega_y^2y^2)$$ Where $\omega_x=5\omega_y$. I am told that the oscillator is prepared in a coherent ...
0
votes
1answer
83 views

How to obtain the distance traversed by a free falling body equation?

I know that the distance that a free falling body has traverse through time is given by $d=0.5*g*t^2$. I would like to know how to get to this equation to study a bit more how it was obtained. I have ...
1
vote
4answers
71 views

Wrong positioned Ampere-meter and Voltmeter [closed]

I'm dealing with a problem here and even that I'm trying to solve it i can't It says: In what figures the voltmeter and ampere-meter are wrong positioned? I think that all the the others are ...
1
vote
1answer
78 views

Vertical Circular Motion

I know that I can use conservation of energy to find the velocity of a particle at a point when it's travelling in a vertical circle by saying $$mgr(1-\cos{\theta})=\frac{1}{2}mv^2$$ then ...
1
vote
0answers
47 views

Derivation of cylindrical line heat source problem?

I have a line heat source embedded inside a cylinder and I am trying to find the temperature distribution T(r,t). By using the similarity variable, the solution to the differential equation is ...
0
votes
2answers
69 views

Determining if a particle is bounded or unbounded with motion in polar coordinates

Firstly, I determined the equation for the particles path for $k <-mV^2a^2$ as $u = {Ae^{\sqrt{\alpha}\theta}+Be^{-\sqrt{\alpha}\theta}}$ where $ \alpha = 1 + \dfrac{k}{mV^2a^2},$ $u = 1/r$ I ...
0
votes
1answer
46 views

Force on a line

Say you have a rigid line of mass $m$ and length $\ell$ along the $x$ axis and you apply a constant force $f$ at one end in a direction that is always perpendicular to the line, starting in the $y$ ...
4
votes
1answer
218 views

What are the generators of spherical symmetry?

The title says it all. I think this should be a pretty simple question but I just couldn't find the answer. Ok -- I'll give a bit more context to my question. I'm encountering this in the context of ...
2
votes
2answers
105 views

Infinite well particle subject to additional time dep. potential

I am asked to find the wavefunction of the particle in a well subject to an additional potential $$V(x,t)=\frac{\pi x \hbar}{L}\delta(t).$$ I have already solved that ...
0
votes
1answer
111 views

Calculate gravitational force between a sphere and a uniform rod

I want to calculate the gravitational force between a uniform rod of mass 2 kg, length 1 meter and a uniform sphere of mass 0.2 kg. Distance between the sphere and the rod is 0.1 meter ( The sphere is ...
0
votes
2answers
97 views

Circular motion, deciding what the tangential speed must be to maintain theta [closed]

A bob of mass m = 0.250kg is suspended from a fixed point with a massless string of length L = 25.0cm . You will investigate the motion in which the string traces a conical surface with half-angle θ = ...
-2
votes
1answer
152 views

Calculating the velocity needed to make a distance in the horizontal with a given height and no upward motion [closed]

In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running over the edge of the cliff above Ohio's Cuyahoga ...
0
votes
1answer
90 views

Finding an equation to solve for the velocity of a swimmer crossing a river [closed]

Where $\theta=45^\circ$, $d_1=200\:\mathrm{m}$, and $d_2=150\:\mathrm{m}$. I do not know how to combine the following equations: $$\begin{align} t&=\frac{d_1}{v_s\cos(45^\circ)}\\ ...
0
votes
1answer
241 views

Relative motion and how to calculate magnitude and velocity of objects relative to different given objects [closed]

A canoe has a velocity of 0.550m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.540m/s east relative to the earth. Alright so I attempted many different things an ...
1
vote
0answers
59 views

Different phase in capacitively coupled RLC circuits

I was trying to work with some data for a lab report I'm writing about capacitively coupled RLC circuits. The setup is pretty simple and looks like that: Where $C^{'}$ is the coupling capacitance. ...
0
votes
1answer
36 views

Two masses collide on a ramp [closed]

M1 slides down a frictionless ramp and collides with M2 They both compress the spring. How far is the spring compressed? What is the final velocity of M1 on the rebound up the ramp? I was thinking ...
3
votes
1answer
207 views

Fermi-Dirac distribution derivation?

I am trying to derive the Fermi-Dirac statistics using density matrix formalism. I know that $$<A>= Tr \rho A.$$ So I started from $$<n(\epsilon_i)>= Tr \rho n(\epsilon_i)=\frac {1}{Z} ...
-5
votes
1answer
78 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?
0
votes
2answers
70 views

Sign of Potential Energy

The mass is released at height $h$ above the spring, how far will the spring move? $E_i=mgh, E_f= kx^2/2+mgx$...why the second equation isn't $ E_f= kx^2/2-mgx$? Since it is below the "zero".
1
vote
0answers
37 views

Loaded die problem

A loaded die has an uneven mass density distribution. A given die is constructed from a square pyramid of material with mass density $\rho_1$ whose bsase lays on the face marked "1",with the rest of ...
1
vote
3answers
858 views

charge density in a wire

If we have a infinitely thin and infinitely long straight wire on the $z$-Axis with given current $I(t)$, how can I compute the charge density? I figured out that the current-density is given by ...
-2
votes
2answers
65 views

Is R1 R2 and R3 parallel? [closed]

or R2 and R3 are parallel then they are in series with R1?
0
votes
2answers
74 views

How can I calculate the initial velocities of a set of objects with a consistent force?

I'm trying to figure out which object would have the largest time of flight when launched from a slingshot. To do this, I need the initial velocity. How can I calculate this if I know the mass and ...
1
vote
1answer
252 views

Modeling a 2-dimensional mass spring system

First of all, I am unfortunately not an expert in physics, so please be indulge with me. I am trying to model a $2$-dimensional mass-spring system with $1$ mass and $3$ springs to solve a dynamics ...
0
votes
1answer
71 views

Density Matrix Characterization

I am working a two dimensional Hilbert space with basis {$|0\rangle, |1\rangle$} and I am trying to show that the density matrix is characterized by 3 real numbers and show that these three numbers ...
0
votes
0answers
23 views

Density operators in a Hilbert Space [duplicate]

let $|\psi\rangle = a_0|0\rangle + a_1|1\rangle \in H$. Show that there are 3 real $r_x,r_y,r_z$ s.t. $$|\psi\rangle \langle\psi|= \frac{1}{2}(I + r_x\sigma_x + r_y\sigma_y + r_z\sigma_z.)$$ Any ...
2
votes
2answers
116 views

Harmonic Oscillator driven by a Dirac delta-like force

Consider that there is no damping for simplicity. As we know, a driving force of the form $\sin(\omega t)$ will make the oscillator at steady state vibrates at the external frequency $\omega$. What ...
3
votes
4answers
2k views

Divergence of $\frac{\hat{r}}{r^2}$

In David J. Griffiths's Introduction to Electrodynamics, the author gave the following problem in an exercise. Sketch the vector function $$ \vec{v} ~=~ \frac{\hat{r}}{r^2}, $$ and compute ...
0
votes
1answer
59 views

How to find the tension [closed]

A massless rod of length L attached to mass m and with axle to cart of mass M. The cart has a shape of equilateral triangle (edge L). the cart is at rest and its center of mass is above x=0 and a rod ...
3
votes
1answer
144 views

A tensor product of two spin-1 particles

I'm rather confused, and I was hoping if someone could help me figure out this (probably rather elementary) issue. I have two particles with spin 1, whose state I describe by $m_S$ and $m_I$ ...
-3
votes
2answers
103 views

Force applied to two blocks [closed]

Due to application of force tow blocks of mass 1Kg and 0.5Kg move together. Each block exerts a force of 6N on each other. What is the acceleration by which both the blocks move?
0
votes
2answers
83 views

Angle rotated by a rod when it's hit by a pendulum

Consider a pendulum of length $h$ with a bob of mass $m$ it is held horizontally at and angle of $90^{\circ}$ with the vertical. A rod of mass $M$ and length $h$ is pivoted at its upper end and this ...
0
votes
3answers
67 views

Confused about Impulse

Encountered a problem that involves impulse while studying for my exam and I'm not sure how to even approach it. I know that momentum is conserved, but I'm not sure how to relate that to avg force. ...