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Calculating the $J$ value for atomic terms, having a lot of trouble with this. Already attempted

I am trying to understand this, and want to be very very clear. This is a homework question but I already attempted to answer it, so please don't put this question on hold. The question What ...
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2answers
33 views

Free fall question: Bill shoots his gun [closed]

Bill borrows his dad's gun and when he gets outside he fires it straight up into the air. If the bullet left the gun at 400 m/s: How long does it take the bullet to reach its highest point. I know ...
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1answer
96 views

Is there a systematic way to derive constraint equations?

There's this problem in Goldstein's (Classical Mechanics) derivations section: 5. Two wheels of radius $a$ are mounted on the ends of a common axle of length $b$ such that the wheels rotate ...
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0answers
32 views

How can we show that a map is a completely positive map? [migrated]

I am doing a homework problem where I have to find whether the map $$ \rho ~\rightarrow~ {\rm tr}(\rho) I - \rho $$ is completely positive. If the map is not completely positive, a counter-example ...
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3answers
64 views

Evaluating position vector between 2 hydrogen states

I am trying to find the quantity: $$\langle1,0,0|\vec r|2,0,0\rangle$$ Where $|n,l,m\rangle$ are the hydrogen states. For this, can I just integrate r from? 0 to infinity? Or do I have to break it ...
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1answer
26 views

A question about Hamiltonian phase flow

Show that if a one-parameter group of difeomorphisms of a symplectic manifold preserves the symplectic structure then it is a locally hamiltonian phase flow. Note that A locally hamiltonian ...
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1answer
29 views

A block falling from a height on a block suspended by spring [closed]

The block suspended by the spring is hanging freely and its mass is M. The small block of mass m is dropped on the bigger block from height h. After the small block is dropped 》》》 I want help in ...
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1answer
61 views

Integrating for speed [closed]

Trying to determine the speed of a falling body with respect to traveled distance and initial speed. I've been provided with the following equation for acceleration as a function of distance and the ...
2
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1answer
55 views

Null Geodesics in Einstein Universe

I am currently taking a course in General Relativity, and I've hit a bit of a roadblock with a homework assignment. We are given the metric for Einstein's universe to be (forgive me, this is meant to ...
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1answer
39 views

Hydrogen ionization energy

Proton and electron have a distance equal to the Bohr radius apart in the hydrogen atom. Knowing this, what's the ionization energy of the atom? So we know $U = -kq^2/a_B$, but this is potential ...
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1answer
30 views

Finding release angle and final velocity of projectile when the target has a different coordinations [closed]

I am trying to write some codes for auto-snowball mechanism which seems like a regular projectile but instead of hitting the targets on the ground it is going to be able to hit the target in the air ...
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0answers
18 views

Angular Momentum Expectation in Magnetic Field

I am trying to find the time dependent expectation value for J ($\langle J(t) \rangle$) for a spin 3/2 particle in a uniform magnetic field (in the z direction). My method is as follows: ...
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1answer
72 views

Kirchoff's rules and RC circuits [closed]

You can view the image bigger: http://i.stack.imgur.com/4moUP.png I'm studying RC circuits and I can't understand the part when we use Kirchoff's rule. When working with batteries, when we're ...
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1answer
47 views

Eigenstates of coupled Angular Momentum

SO I have a hamiltonian: $$H=\alpha J_1\cdot J_2$$ And I am asked to find the eigenstates and eigenvalues of this Hamiltonian in terms of products of the eigenstates of the z components of the ...
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4answers
260 views

Blocks stacked on an incline connected by rope around pulley

Two objects A and B, of masses 5 kg and 20 kg respectively, are connected by a massless string passing over a frictionless pulley at the top of an inclined plane, as shown in the figure. The ...
2
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0answers
70 views

How to calculate mass from compound lever? [closed]

A class 1 lever and a class 2 lever are connected in series, on the resistance end of the class one lever is a 500g weight. On the 2nd class lever sits a weight of an unknown mass. From the end of the ...
1
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1answer
48 views

The value of one atomic mass unit

In my textbook, it is given: 1 atomic mass unit equals $1/12$th mass of one carbon 12-atom. Since mass of $6.02 * 10^{26}$ atoms of carbon-12 is $12\space\text{kg}$. Thus, $$1 \text{ a.m.u ...
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1answer
41 views

If you have $N$ 1ohm resistors, how many distinct equivalent resistances can you create?

If you have $N$ 1ohm resistors, how many distinct equivalent resistances can you create? Assume that only parallel and series and mixture of them is allowed and no bridging between two parallel ...
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0answers
26 views

Ratio of position error of orbiter to the size of the orbit

This is an assignment question for online AP physics. As if it isn't already tough. This question is killing me. I even asked my physics teacher from last year and my calculus teacher. It stumped ...
3
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1answer
80 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 ...
2
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1answer
91 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 ...
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2answers
66 views

How much force is required to compress air?

How much force (Newtons) is required to compress normal air in a chamber to 2 atm? For example, if I had a sealed piston pump, how much force would need to be exerted in order for the air to be ...
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2answers
60 views

Ice throw from industrial wind turbine

I was watching a documentary where the residents didn't want to have a wind turbine erected nearby. One of the comments from the company was that an ice throw would have very little importance since ...
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1answer
45 views

Confused with how to approach this pulley problem (solved) [closed]

Question: In the following figure block A has mass m and block B has mass 6.00. The coefficient of kinetic friction between block A and the tabletop is 0.40 The mass of the rope connecting the blocks ...
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0answers
32 views

Fourier series and diffraction gratings [closed]

I'm having trouble with this question and I don't know where to start. A plane wave illuminates a periodic grating which consists of a large number of narrow apertures of width b spaced equally a ...
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1answer
56 views

Lagrangian for a moving spring device

How can I write the proper Lagrangian for such as system as the one shown in picture? Am confused about what is the suitable way to designate the coordinate.
2
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1answer
90 views

Diagonal Hamiltonian of 3 Spin 1/2 Particles

I have three Spin 1/2 Particles and a Hamiltonian given by $$H=A(S_1\cdot S_2)+B(S_2\cdot S_3+S_1\cdot S_3)$$ In order to find the energy spectrum, I want to diagonalize H in terms of ...
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1answer
25 views

Do I need to take both particles' momentum into account in photoelectric emission? [closed]

An aluminum dust particle of mass $m=2.2*10^{-18}$ grams is floating in space ( initial velocity is zero). The particle emits electron under influence of a photon whose frequency is $8*10^{17}$ ...
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0answers
38 views

Showing that the maximum possible uncertainty for any observable is half the difference between its maximum and minimum eigenvalues

Show that the maximum possible uncertainty for any observable is $\frac{1}{2}|x_2 - x_1|$ where $x_1$ and $x_2$ are the extreme eigenvalues of X (Maximize $\Sigma_i p_ix_i^2 - (\Sigma_i p_ix_i)^2$) ...
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1answer
41 views

Equation for magnetic field due to a current in straight wire [closed]

How can I derive the expression for the magnetic field due to a long straight current carrying wire using the Biot-Savart law? The final expression should be: ...
1
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0answers
26 views

charged oil drop in electric field [closed]

I am currently doing coursework for my A2 physics course. I am dropping a charged oil drop in a horizontal electric field and I was wondering how to calculate how much the droplet would deviate given ...
1
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1answer
51 views

Max altitude of rocket [closed]

A rocket is launched perpendicularly with an initial acceleration of 10 m/s2, if the fuel runs out after 1 minute, what will be the maximum height reached by the rocket?
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1answer
31 views

Acceleration Power [closed]

Suppose we have a trolley currently at rest at point A, but the motor switches on, so that it accelerates and reaches point B, at point B, the velocity is 5m/s, Distance of A-B is 10m, mass of the ...
2
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2answers
119 views

Angular Momentum Operator in Quantum Field Theory

I'm following along with David Tong's QFT course and am trying to derive the result shown in question 6 on his 2nd problem sheet, but am running into problems when applying it to the free real scalar ...
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1answer
91 views

Free particle propagator - Evaluating Integral

In path integral formalism, when evaluating the free particle propagator, we obtain the functional integral of the form, $$ K_0 = \lim_{n\rightarrow\infty} \bigg( \frac{m}{2\pi ...
1
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1answer
57 views

How quickly does air return to a vacuum chamber?

I know there are a lot of variables that affect how quickly this would occur. Any information on the topic would be highly appreciated. For sake of argument, lets say 1 square foot chamber, lets say ...
1
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1answer
80 views

How do I recover the 1D wave equation from the Lagrangian?

Consider small displacements, $y(x,t)$, of an element of a string (circled in red and shown below) from equilibrium. The force balance in the vertical direction yields: $$+\uparrow \Sigma F: ...
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2answers
68 views

Tensor of inertia of a hollow cube

I have found the tensor of inertia of a rectangle of sides $a$ and $b$ and mass $m$, around its center, to be $$I_{11}=ma^2/12,$$ $$I_{22}=mb^2/12,$$ $$I_{33}=(ma^2 + mb^2)/12.$$ All other elements of ...
1
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1answer
43 views

Gauss's law problem. ( Need someone to point me in the right direction) [closed]

What force per square meter pushes 2 infinite planes charged positively when their charge density is $0.3 \, \mu C/\mathrm{m}^2$ Second part is - using Gauss's theorem derive the equation ...
0
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1answer
26 views

Kinematics with non constant acceleration II [closed]

I'm getting crazy with this problem and I think that it's pretty simple. An helicopter's helix is spinning at initial speed $w_0=200\ rpm$, all of a sudden the motor stops and it decreases its ...
0
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0answers
21 views

Question about two masses connected by a spring [duplicate]

I have two masses connected by a spring. They are horizontal and are not affected by friction or gravity. The spring's stiffness constant is $k$, and $x_1$ and $x_2$ are the displacements of the ...
0
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1answer
53 views

Why are 3 different road tests enough to say the suspension system of a car can handle any random road?

In an assignment I am given a random car with a random suspension system, and told that it is sufficient to test the safety of the car with regards to the suspension on three different sinusoidal ...
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0answers
63 views

More on the closed-form for a simple pendulum

I've learnt about the simple pendulum, and while the regular curriculum only uses the linear approximation of $\sin\theta$ to obtain $\ddot\theta+\omega_0^{2}\theta=0$. I tried to find out about a ...
2
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2answers
45 views

Acceleration of chairlift [closed]

So I'm struggling with this question, and am wondering if anyone can give me the right direction to go. For the sake of not cheating, I've changed the figures etc. I just need help on the approach. I ...
1
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1answer
60 views

Is radioactive decay spontaneous or random?

When the count rate of a radioactive isotope is measured, the readings fluctuate. Do the fluctuations demonstrate the random nature of the decay or the spontaneous nature? (This question was asked in ...
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1answer
40 views

What are the the characteristics of a standing wave? [closed]

May someone explain #24 from this picture? B is apparently the correct answer. Can any of the other answers be correct here? Isn't D also correct?
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0answers
61 views

How to calculate these integrals about propagator of QFT analytically?

How to get these three analytical solutions? Thanks very much! $$ G_{ret}(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p \, \frac{e^{-ip(x-y)}}{(p_0+i\epsilon)^2 - \vec{p}^2 - m^2} = ...
3
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1answer
158 views

Three integrals in Peskin's Textbook

Peskin's QFT textbook 1.page 14 $$\int_0 ^\infty \mathrm{d}p\ p \sin px \ e^{-it\sqrt{p^2 +m^2}}$$ when $x^2\gg t^2$, how do I apply the method of stationary phase to get the book's answer. ...
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0answers
54 views

Why $A\sin(2\pi ft) =\frac{A}{2j}(e^{j2\pi ft}-e^{-j2\pi ft})$ but not $\frac{A}{2}(e^{j2\pi ft}-e^{-j2\pi ft})$? [migrated]

$$v_{\mathrm{in}}(t)=A\sin(2\pi ft) =\frac{A}{2j}\left(e^{j2\pi ft}-e^{-j2\pi ft}\right) \\ |H(f)|=|H(-f)|;\angle H(f) = -\angle H(f) \\ v_{\mathrm{out}}=H(f)v_{\mathrm{in}}=\frac{A}{2j}H(f)e^{j2\pi ...
1
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1answer
36 views

When is the speed specified for an object experiencing an exponential force?

So this is the question given in my text book: A particle of mass m is at rest at the origin at time $t = 0$. It is subjected to a force $F (t) = F_0e^{–bt}$ in the $x$ direction. Its speed ...