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5
votes
1answer
215 views

Chain of balls on an inclined plane

Suppose we have some inclined plane, and there is some chain of balls of length $l$ and mass $m$ lying on it. No friction at all in the system. 1) What is $x_0$ (the vertical hanging part of the ...
0
votes
1answer
139 views

Absolute Viscosity of Water at certain temperatures

I just started my class on fluid mechanics. There's a problem that requires absolute viscosity $u$ of water at 25C. I looked up my table in the book and I only have it for water at 20C and 30C. I ...
-3
votes
2answers
120 views

Why is $r'/r^2 = -1/r$? [closed]

If $r=r(t)$, why is $\frac{r'(t)}{(r(t))^2}$ = $\frac{1}{r(t)}$ where $'$ denotes the derivative? I saw it in a lecture. Can you please explain?
0
votes
2answers
236 views

Electron in an infinite potential well

Does this problem have any sense? Suppose an electron in an infinite well of length $0.5nm$. The state of the system is the superposition of the ground state and the first excited state. Find the ...
1
vote
0answers
137 views

Mercury's Orbital Precession in Special Relativity

I am researching Mercury's orbital precession. I have considered most perturbations and general relativity. I am still not satisfied. I need your help. I need a solution to Exercise 13, Chapter 6, in ...
1
vote
1answer
130 views

Measurement uncertainty of the quantity, that is function of two others quantities

I'm trying to compute uncertainty for the density of the ball. I measured its radius 6 times, so I was able to compute the stastistical uncertainty (we call it uncertainty type A, I don't know, if ...
0
votes
2answers
109 views

Constant of gravity in earth fixed coordinate system

I have this problem: If the constant of gravity is measured to be $g_0$ in an earth fixed coordinate system, what is the difference $g-g_0$ where $g$ is the real constant of gravity as ...
0
votes
2answers
421 views

Simple conservation of momentum and frame of reference problem

I'm making a very simple physics engine based on momentum, and I'm solving what response to use for a collision from each involved object's frame of reference. However, something about how I'm ...
1
vote
2answers
299 views

Center of mass problem

According to the definition of potential energy, we use $U= mhg . $ In the figure below , A thin uniform rod of mass m and length h is positioned vertically above an anchored frictionless pivot ...
0
votes
2answers
594 views

Angle between acceleration and velocity

Problem: A particle is constrained to move in a circle with a 10-meter radius. At one instant, the particle's speed is 10 meters per second and is increasing at a rate of 10 meters per second ...
2
votes
1answer
106 views

2nd order pertubation theory for harmonic oscillator

I'm having some trouble calculating the 2nd order energy shift in a problem. I am given the pertubation: $\hat{H}'=\alpha \hat{p}$, where $\alpha$ is a constant, and $\hat{p}$ is given by: ...
1
vote
1answer
673 views

When should angles be expressed in degrees vs. radians?

I am trying to calculate the albedo of a given latitude by following the methods of Brutsaert (1982), I have copied the formula below: 3.6 Shortwave and long-wave radiative fluxes Albedo ...
1
vote
1answer
228 views

Center of mass error - calculating systematic error in change in PE

Suppose we have to calculate systematic error in change in PE. Let's suppose systematic error due to scale is 1%. I'm confused about the center of mass error. \begin{align} \Delta PE = m*g*h_1 - ...
0
votes
2answers
506 views

Time period for spring connected body

Two identical springs with spring constant $k$ are connected to identical masses of mass $M$, as shown in the figures above. The ratio of the period for the springs connected in parallel (Figure 1) ...
1
vote
1answer
96 views

impulse problem [closed]

The figure above shows a plot of the time-dependent force $F_x(t)$ acting on a particle in motion along the x-axis. What is the total impulse delivered to the particle? ...
6
votes
0answers
266 views

Calculating the branching ratio of higgs for decay to two photons? [closed]

I need to use the three lowest order Feynman diagrams to first calculate the squared matrix element to put into Fermi's golden rule formula and then from there get the branching ratio of higgs decays ...
1
vote
1answer
769 views

Energy required for ionizing Helium

The energy required to remove both electrons from the helium atom in its ground state is 79.0 eV. How much energy is required to ionize helium (i.e., to remove one electron)? ...
1
vote
0answers
77 views

tricky electric potential [closed]

I have this question: $q_1$ is a Uniformly Charged long Wire(inf in z axis) with $\lambda$ (charge per unit length). In (0,0,0) I have A very long conducting cylinder of radius a (also inf in z axis). ...
2
votes
1answer
81 views

Statistical sum of physical quantities in a quantum system

Let $C = A + B$ (statistical sum, so $\mathbb{E}[C] = \mathbb{E}[A] + \mathbb{E}[B]$), and let $p(A = a) = 1$. Are the following true? $\mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2]$ ...
6
votes
2answers
238 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 ...
1
vote
2answers
635 views

Relation between the time, velocity and acceleration

This is question from I.E. Iredov's General Physics: $1.22$ : The velocity of a particle moving in the positive direction of the $x-axis$ varies as $v = α \sqrt x$, where $α$ is a positive ...
2
votes
1answer
103 views

Is this 2D structure triclinic?

The only rotation axis obvious to me is rotation by 360 degrees, the identity. Vertical mirror planes I've been dicing and cutting it through several planes and I still see none. Yet, the structure ...
2
votes
1answer
362 views

The gauge-invariance of the probability current

It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\ \phi\to\phi-\frac{\partial \chi}{\partial t}\\ \psi\to \psi ...
5
votes
4answers
470 views

Is there a closed form solution to the Esdale river problem?

This is probably not well known problem but it looks like open problem. What kind of methods there are to find a closed form solution to the physical situation? Can you solve this problem? You're ...
0
votes
1answer
489 views

Calculating the moment inertia for a circle with a point mass on its perimeter

I want to calculate the tensor of the moment of inertia. Consider this situation: The dot represents a points mass, in size equal to $\frac{5}{4}m$. $m$ is the mass of the homogenous circle. I'm ...
1
vote
1answer
134 views

Energy eigenvalues of a Q.H.Oscillator with $[\hat{H},\hat{a}] = -\hbar \omega \hat{a}$ and $[\hat{H},\hat{a}^\dagger] = \hbar \omega \hat{a}^\dagger$

I just finished deriving the commutators: \begin{align} [\hat{H}, \hat{a}] &= -\hbar \omega \hat{a}\\ [\hat{H}, \hat{a}^\dagger] &= \hbar \omega \hat{a}^\dagger\\ \end{align} On the ...
0
votes
2answers
496 views

Paraxial rays and marginal rays question

Paraxial rays are found to focus far away the lens whereas marginal rays focus near to the lens, why? I didn't find satisfactory answer in my academic book..
7
votes
4answers
671 views

Integrating radial free fall in Newtonian gravity

I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
3
votes
1answer
375 views

inductance value of a single turn thin circular coil

the question may seem simple but I haven't found any fitting formula yet. The problem is the following: consider a single-turn, circular coil made of reasonably thin wire (diameter of the wire much ...
5
votes
3answers
280 views

Horizontal $E$-field for a charged conducting disk

For part of a simulation I am writing, I need to know the electric field emitted from a charged conducting disk. If the disk was laid out in the $x$-$y$ plane, I am interested in the field in that ...
4
votes
2answers
155 views

Vector potential

I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
3
votes
2answers
438 views

Coherent State, Unitary Operators, Harmonic Oscillator

Consider the operator: $$O = e^{\theta(a^\dagger b - b^\dagger a)}$$ where $\theta$ is a constant. $O$ is a unitary operator. $a$, $a^\dagger$, $b$, and $b^\dagger$ are ladder operators for two ...
1
vote
1answer
326 views

Eigenfunctions in a harmonic oscillator

This assignment is about the one dimensional harmonic oscillator (HO). The hamiltonian is just as you know from the HO, same goes for the energies, but I get that the wavefunction of the particle, at ...
-2
votes
4answers
838 views

Resistors in Parallel

From my book: "A length of wire is cut into five equal pieces. The five pieces are then connected in parallel, with the resulting resistance being 2.00 Ω. What was the resistance of the ...
1
vote
2answers
456 views

How can I solve for time without knowing the vertical velocity?

A guy posted this problem on a forum: There is a bird sitting on a pole of height h. you throw a rock at it and the moment the rock leaves your hand the bird starts flying horizontally away from ...
-1
votes
1answer
111 views

Lifting house with balloons [closed]

I have an assignment about the movie Up. Here is the question: Critique the brief floating scene. Did the animators use enough balloons during this scene? What important variables, (which affect ...
3
votes
1answer
628 views

Pendulum in an elevator

Suppose we have a pendulum tied to the ceiling of an elevator which is at rest. The pendulum is oscillating with a time period $T$, and it has an angular amplitude, say $\beta$. Now at some time ...
1
vote
1answer
343 views

Apparent and real depth object in water [closed]

Did I get my formula right? Seems like the correct answer is $d_o = 1.33 \times d_i$ but I thought the formula I should use is $d_i = - \frac{n_2}{n_1} d_o$
2
votes
1answer
415 views

Time evolution operator to find expectation value

I have a state $\Psi (x,0) = \sum_{n=0}^{\infty} c_{n}u_n(x)$ and want to find the expectation value of any observable A at time t, $\langle \Psi(t)|\hat{A}|\Psi(t)\rangle$. I know that I should ...
1
vote
4answers
2k views

Capacitor Charging and Discharging when connected to the ground

When we charge a capacitor using a battery and then remove the battery, the plates of capacitor becomes charged. One holds positive charge and the other one gets equal negative charge. o. k. ? Now ...
2
votes
1answer
164 views

Liquid benzene magnetic susceptibility

In a solid state physics problem, I'm asked to make a rough estimate of the contribution to the diamagnetic susceptibility of the outer electron of each carbon atom. The wavefunction of these ...
4
votes
2answers
354 views

Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$

I know how to derive below equations found on wikipedia and have done it myselt too: \begin{align} \hat{H} &= \hbar \omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)\\ \hat{H} &= ...
4
votes
2answers
100 views

What's the physical difference between the quantities $\langle v_{i}v_{j}\rangle$ and $\langle v_{i}\rangle\langle v_{j}\rangle$?

What's the physical difference between the quantities $\left\langle v_{i}v_{j}\right\rangle $ and $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle $? Where $\left\langle ...
2
votes
3answers
372 views

How to determine the direction of medium's displacement vectors of a standing wave?

Consider the following problem taken from a problem booklet. My questions are: What is displacement vector? And how to determine the direction of displacement vector at a certain point? Where is the ...
1
vote
2answers
219 views

Calculating the change in entropy in a melting process

I have a homework question that I'm completely stumped on and need help solving it. I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
0
votes
1answer
151 views

Reachable area of cannonball given fixed initial speed [closed]

The trajectory of a cannonball fired from the origin with initial speed $v_0$ at an angle $\theta$ is given by $$y = x\tan\theta - \frac{g}{2v_0^2 \cos^2\theta}x^2.$$ For fixed $v_0$, at what angle ...
0
votes
1answer
433 views

Spacetime and Timelike Intervals

The difference between a “timelike” spacetime interval and a “spacelike” spacetime interval can be understood in the following way: If the spacetime interval between two events is timelike, there ...
2
votes
1answer
198 views

Induced Current, Dipole Falling Under Gravity Towards Circular Loop [closed]

Suppose a magnetic dipole $\mathbf{m} = m \hat{z}$ is falling towards a circular loop of radius $b$ under gravity. Assuming the dipole always stays along the $z$-axis of the loop, determine the ...
2
votes
2answers
457 views

Hamiltonian of Harmonic Oscillator with Spin Term

We have the usual Hamiltonian for the 1D Harmonic Oscillator: $\hat{H_{0}}=\frac{\hat{P^2}}{2m} + \frac{1}{2}m \omega \hat{X^2}$ Now a new term has been added to the Hamiltonian, $\hat{H} = ...
0
votes
2answers
142 views

Escape velocity to intersection of two gravitational fields

Find the minimal velocity needed for a meteorite of mass $m$ to get to earth from the moon. Hint: the distance between the center of earth and the center of moon is $\approx 60 R_E$, and the ...