Questions tagged [homework-and-exercises]

Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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4 answers
62 views

Can I arbitrarily pick which resistors I should calculate the equivalent resistance with?

Let's say I have some random complex circuit of resistors. Maybe something like: Now I wanna calculate the equivalent resistance of this whole circuit. Can I just randomly pick which resistors I ...
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1 answer
29 views

Body free fall calculation of the time durance as a direct derivation by time (non-relativistic)

Let's assume a body in free fall during 16 meters without resistance and I'd like to directly calculate the time of this fall. Sure, one could painfully calculate: $v^2 = 16 m·9.81 \frac{m}{s^2}$ $v = ...
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1 vote
1 answer
33 views

Derivation of path equation, how to derive $$ r''= - \frac{L^2}{m^2}u^2 \frac{d^2u}{d\theta^2 } $$

So specifically I don't know how to go from $r'$ to $r''$. If we start with $r'$, where the substitution $r=u^{-1}$ is used. $$ r'= - \frac{L}{m} \frac{du}{d\theta } $$ $$ (1): r''= - \frac{L^2}{m^2}u^...
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0 votes
2 answers
60 views

Why is the moment of forces "torque" 0 here?

Why is the moment of forces "torque" 0 here? Let's say we have this situation A spool of mass $M$ rests on an inclined plane a distance $D$ from the bottom. The spool has a maximum radius $...
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1 vote
1 answer
63 views

$\pi/2$ rotation of spin $1/2$ [closed]

$\def\ket#1{{\lvert #1 \rangle}}$ In John S. Townsend's A Modern Approach to quantum Mechanics, an operator is introduced in Ch. 2 that rotates the spin by $\pi/2$ in the $x$-$z$ plane. These ...
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2 votes
1 answer
55 views

Rewriting an asymptotic series as a convergent integral [closed]

I am given the function $$ f(x) = \sum_{n=1}^{\infty} \frac{\Gamma(2n)}{\Gamma(n)}(-x)^n $$ and I need to show that it can be rewritten as an integral that is convergent for a range of values of x. I ...
3 votes
2 answers
432 views

Seeming contradiction in inclined plane

According to the above picture,let's an object falls from rest. After any time $t$,we analyze the distance traveled in two ways: Way $1$ Just like we do in projectile motion,we divide the motion of ...
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0 votes
1 answer
54 views

Is it possible to calculate the moment of inertia of a sphere by taking the element as surface area $* dr$ ( change in radius)?

Usually the proof for moment of inertia of a sphere involves taking the element to be a horizontal circular slabs and then integrating it. I want to use another method to arrive at the same conclusion....
4 votes
1 answer
214 views

Is there a quick way to calculate the derivative of a quantity that uses Einstein's summation convention?

Consider $F_{\mu\nu}=\partial_{\mu}A_\nu-\partial_\nu A_\mu$, I am trying to understand how to fast calculate $$\frac{\partial(F_{\mu\nu}F^{\mu\nu})}{\partial (\partial_\alpha A_\beta)}$$ without ...
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0 votes
1 answer
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Position vector of robot arm

This is related to robotics mathematics. I am having a hard time understanding how they get the position vectors and since z2 is movable, z2 should not be a 0 in the z -column(last column) of position ...
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0 answers
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How does this trick work in solving the 2-body central force equation of orbit?

I am working on understanding the derivation of Kepler orbits via section 8.5 of John R. Taylor's classical mechanics textbook, and one small detail has been tripping me up. The equation being solved ...
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0 answers
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Why the symmetric and the antisymmetric tensor components transform differently in the Lorentz transformation?

In Landau and Lifshitz Classical Theory of Fields, problem $\S 6.1$ (page 22), the components of the symmetric second rank tensor transformed as $$A^{01}=\frac{1}{1-\frac{V^2}{c^2}}\left[A^{'01}\left(...
1 vote
1 answer
46 views

Equilibrium and maximum velocity position of a person jumping on pogo stick (spring)?

Consider the following diagram: It is given that: A is the position of maximum compression of spring and the child is at rest(at that instant). At B, the child is having an upward velocity and the ...
1 vote
2 answers
46 views

How to calculate the linear and angular velocity acceleration based an acting force?

In the first example there is an actig force perpendicular to the direction of the center of mass, resulting in an linear velocity acceleration in the direction of the force. in the second example ...
2 votes
1 answer
96 views

Zwiebach String Theory, Quick Calculation 21.19 [closed]

In "A First Course in String Theory" 2nd ed. by Barton Zwiebach, on page 489 there is a problem to be solved. It seems like a simple plug and chug but I can't make it work out. Equation (21....
1 vote
2 answers
58 views

Why is studying individual particles in a rigid body not correct? And questions about momentum

I've just come across an exercise that consists of a rigid, ideal rod that can move around a fixed axis: After letting it move , the rod's angular velocity at time t (when it is vertical) is asked. ...
0 votes
1 answer
54 views

Potential of a Hertzian-esque dipole in Lorenz gauge

Given the current density ${\bf j}({\bf r},t) = \mathbf{v}_{0}\,\omega\, \sin(\omega\,t)\,\delta({\bf r}-{\bf r}_0),$ what is the vector potential? From a previous question I noticed the density is ...
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0 votes
1 answer
52 views

Why do we assume harmonic oscillator to have only one fulled level of energy?

My question is related to this problem. There were considered only one $n_i$ level of energy for i-th oscillator, but I think we should write $\{n\}_i$ sequence of fulled levels for every oscillator.
1 vote
0 answers
40 views

An identity for Grassmann Gaussian integrals

Suppose, for each $i=1,...,N$, $\bar{\psi}_{i}$ and $\psi_{i}$ are Grassmann vectors with $n$ entries $\bar{\psi}_{i,1},...,\bar{\psi}_{i,n}$ and analogously for $\psi_{i}$. Let $d\mu_{C}(\bar{\psi},\...
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2 votes
0 answers
69 views

Fitting a curve to my data [closed]

I got some data of the I-V characteristics of a solar cell (diode) in the dark and I have been trying to fit the data with the standard equation: $$ I = I_0(e^{qv/nkT} - 1) $$ The below table is my ...
0 votes
1 answer
37 views

How do charges arrange themselves at electrostatic equilibrum?

How do charges on conductors re-arrange themselves when they are placed next to other conductors? I understand how charges arrange themselves on the surface of conductors but I can't find an ...
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1 vote
1 answer
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Calculation in the book Path Integrals by Kleinert

I've been reviewing some fundamental calculations for path integral and I came across a passage to which I cannot figure out how it is supposed to be done. On page 92, the author started off, by ...
1 vote
1 answer
52 views

Is there a difference between 10kg weight exerting 98N force vs. a person pulling the string with 98N force? [closed]

My question is related to an AP Physics question (2.k acceleration of systems), which appears simple, but the premise of part 2 of the question is difficult to understand, hence asking the physics ...
0 votes
2 answers
28 views

Magnetic flux due to movement [closed]

How does the magnetic flux decrease in the example shown below if the rectangle moves down due to the gravitational force, and there is no friction. The surface $A$ of the rectangle nor the magnetic ...
2 votes
2 answers
36 views

Work done by ladder on the boy and work done by boy on ladder [closed]

I was stuck in a question: In a children's park there is a slide which has a total length of $10 \,\mathrm m$ and a height of $8 \,\mathrm m$. Vertical ladder is provided to reach the top. A boy ...
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0 votes
2 answers
48 views

How to find the position expectation value from the Fourier transform of a wave function?

Here's my reasoning: $$\langle \hat{x} \rangle=\int_{-\infty}^{\infty}\psi^*(x,t)\hat{x}\psi(x,t)$$ $$=\frac{1}{2\pi}\int_{-\infty}^{\infty}dx(\int_{-\infty}^{\infty}\phi(k,t)e^{ikx}dk)^*\hat{x}\int_{-...
2 votes
2 answers
84 views

What happens to the angular velocity of a man if he drops the mass that he is holding on a platform?

A man holds in his hands two equal masses with outstretched arms, standing on the center of a platform that rotates with a certain angular velocity. If you drop both of the masses without moving your ...
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-2 votes
2 answers
46 views

Separation of Variables; Why are these solutions given? [closed]

Can someone show me a step by step of how you get the solutions in the form of $A \cos$ and $B \sin$ of the equation $y''(x) + k y(x) = 0$?
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0 votes
1 answer
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Finding Tension in a pendulum [closed]

When trying to find the tension in the string, can you find the centripetal force and subtract it from the weight of the bob? i.e. $\frac{mv^2}{r}+mg=T$. Also, can you do $Tcos\theta=mg$ to find T too?...
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0 votes
3 answers
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Mass-spring system linear equations: I don't get the last term, shouldn't it be $V=\frac{1}{2}k_3x_{\text{wall}}^2-2k_3x_{\text{wall}}x_2+k_3x_2^2$?

I don't understand the last term in setting up the linear system of equations for multiple mass-spring systems. It is about the last spring in the next example: Source: https://math24.net/mass-spring-...
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0 votes
1 answer
70 views

Bra-Ket Notation for creation and annihilation operators

I'm reading from Landau's book about second quantization and I confused about the bra-ket notation for the creation and annhilation operators. From the book, annhilation oparator defined as $$ a_i|N_i\...
1 vote
0 answers
29 views

Derivation of Air resistance using Conservation Of Energy [closed]

I have been asked to derive an expression for the air resistance that a car moving with a constant velocity faces. The variables are mass of car, velocity of car, mass of air, density of air, cross ...
2 votes
0 answers
31 views

Propagator for radial force field?

The propagator $K(x,y;t)$ is well known for the (1D) harmonic oscillator: $$H = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + \frac{m}{2}\omega^2 x^2$$ is there a simple closed form solution ...
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1 vote
1 answer
54 views

The maximum air drag force doesn't coincide with the maximum velocity

I'm trying to decode my data from an experiment conducted today. We wanted to calculate the air drag acting on a pendulum. In order do to this, we first created a model for our frictional force F: ...
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1 vote
1 answer
39 views

String action in light-cone coordinates

I am going through textbook Einstein Gravity in a Nutshell by A. Zee and I got mathematically stuck at page 147 where he is talking about the classical string action using light cone coordinates. ...
2 votes
0 answers
56 views

What is wrong with my approach to this BPHO problem

I am a tutor, and one of my students is practicing for the BPHO. One of the problems he wanted to go over is below. I decided to use the fact that $$F_{net}=\frac{dp}{dt}=M\frac{dv}{dt}+\frac{dM}{dt}...
0 votes
1 answer
27 views

Compressed air efficiency if expansion cooling is used [closed]

Compressed air energy storage is looked down upon because of the inefficiencies it brings along. Every article I've found till today, makes use of the stored energy by converting it into mechanical ...
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2 votes
1 answer
40 views

Arbitrary (Non-Radial) Charge Distribution and Gauss's Law in Integral Form [closed]

Say we have an Electric Field, produced by a charge distribution, given as- \begin{equation} \mathbf{E}=c(1-e^{-\alpha r}) \frac{\hat{\mathbf{r}}}{r^2}, \end{equation} $c$ and $\alpha$ being constants....
1 vote
0 answers
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Prove the inverse of $H_\text{cl} =2(L_0+\bar L_0-2)/\alpha'$ is $$\Delta=\frac{\alpha'}{2} \int_0^1 d\rho \rho^{L_0+\bar L_0 -3}$$ [closed]

Quote Clifford Johnson $D$-brane page 153 $\Delta$ is the closed string propagator... the inverse of $H_\text{cl} =2(L_0+\bar L_0-2)/\alpha'$, the closed string Hamiltonian, which we can easily ...
1 vote
1 answer
43 views

Transformation on Squeeze Operator?

Yesterday, my professor briefly glossed over the following computation without details, and I haven't been able to figure it out for myself. How would I compute $$(\cosh (q) \hat{a} + \sinh (q) \hat{a}...
0 votes
1 answer
32 views

How to find the voltage across a resistor in a RCL circuit? [closed]

In the circuit below I am trying to find an expression for the voltage across $R2$. I have found an expression for the voltage across R1 which I have confirmed with a simulation, but I can't get it ...
1 vote
0 answers
39 views

Linearity of partial trace

In Quantum Processes Systems, and Information by Schumacher and Westmoreland we are given this property of the partial trace $$ Tr_R G^{RQ} = Tr_R \left( |\alpha^R,\phi^Q \rangle\langle\beta^R,\psi^Q| ...
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2 votes
2 answers
94 views

Converting Dirac Notation to Coordinate Space

I am trying to find how to explicitly calculate: $\langle x|p\rangle$. Intuitively, this means the momentum operator is acting on a state $\phi$ which is then projected into the coordinate space. ...
0 votes
1 answer
46 views

How much force from the charges in a gram?

In Molecules, Theodore Gray says, But if you could separate all the protons in that piece [1 gram] of iron from all the electrons and put all the protons on one side and all the electrons of the ...
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1 vote
0 answers
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Conservation of momentum of a bob attached to ceiling with string taut [closed]

In this question a bob(mass m) is tied to a string of length 5m and is attached to the ceiling. It is then released and hits the floor at a distance of 4m from the ceiling. What will be the maximum ...
3 votes
2 answers
112 views

How to prove a single-point correlation function equal to zero?

A short question, when I am studying QFT-P&S's book, try to use completeness relation (7.2) to expand the two-point correlation function: $$\langle\Omega|\hat T{\phi(x)\phi(y)}|\Omega\rangle\tag{7....
2 votes
0 answers
29 views

Person is in a lift and the lift is accelerating downwards [closed]

My interpretation of part (ii) is that as $F=ma$, and the lift is going downwards, therefore the weight of the person would be greater than its reaction force. So $W-R=ma$. And $R=W-ma$. So the answer ...
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0 votes
1 answer
32 views

Finding the expectation value given an operator in the form of a matrix and wave vector? [closed]

I was wondering how one would find the expectation value $\langle \hat{S} \rangle$ where $\hat{S}$ is just any operator in the form a matrix, such as the identity matrix $\begin{bmatrix} 1 & 0 \\ ...
0 votes
1 answer
30 views

Is the norm of the acceleration the same as the componentwise calculation of the acceleration? [closed]

I am using the following question as an example to base my conceptual question on: 4.00-kg object has a velocity of 3.00i m/s at one instant. Eight seconds later, its velocity has increased to (8.00i +...
0 votes
1 answer
47 views

Time derivatives in a rotating frame of reference

I am watching a youtube video regarding time derivatives in a rotating reference frame. The stationary reference frame is S and the rotating one is S'. Unfortunately I don't understand why the red ...
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