Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

0
votes
0answers
28 views

Block in the rain [closed]

The water is falling horizontally on the masses with speed u, and a constant rate of k kg/sec. When the rain hits the block it drips to the sides. My question is how to deal with the rain dripping to ...
0
votes
0answers
44 views

Constant density in Sommerfeld model

In chapter 2 of Ashcroft and Mermin's Solid state physics we reach this expression of the electron energy density: $$ n=\int_{0}^{\varepsilon_{F}} g(\varepsilon) d \varepsilon+\left\{\left(\mu-\...
0
votes
1answer
35 views

Calculating the kinetic energy of an electron in a given potential [closed]

Let $\Phi(x,y,z)$ with $U_0$ be a potential. $$\Phi(x,y,z)=\begin{cases}-U_0, & y<-d \\ \frac{U_0}{d}\cdot y, & -d\leq y \leq d \\ U_0, & y>d\end{cases} \tag{1}$$ Further assume ...
0
votes
1answer
24 views

How do you calculate the capacitance of a parallel plate capacitor with multiple dielectrics? [closed]

My question is how would you go about calculating the capacitance of a parallel plate capacitor which has two mediums in between the parallel plates. I am aware that for a regular parallel plate ...
1
vote
1answer
35 views

How is the area vector larger by a factor of $\frac{1}{cos \theta}$ for proving the gauss law?

So I was reading Electricity and magnetism by Purcell and I came across the Gauss law. Now in here its said I quote "The area of the patch $A$ is larger than that of the patch $a$ by two factors: ...
-1
votes
2answers
38 views

Question regarding a wave problem [closed]

An example problem from my openstax physics textbook: A student takes a 30.00-m-long string and attaches one end to the wall in the physics lab. The student then holds the free end of the rope, ...
3
votes
1answer
49 views

Kinetic theory of gas. Pressure in a container derivation feels wrong

NOTE: Please Imagine A cube with 2 parllel faces I and II lying along the x axis. In the derivation what we are thought Change in the momentum of the molecule = Final momentum - Initial momentum =...
0
votes
1answer
41 views

Airplane executing horizontal loop

The Problem: An aircraft executes a horizontal loop at a speed of $720$ kmph (or $200$ m/s) with its wings banked at an angle of $15^{\circ}$. What is the radius of the loop. My Confusion: Unlike ...
0
votes
1answer
28 views

Help with deriving simple heat equation [closed]

$$j^{q}=\frac{1}{2} n v[\varepsilon(T[x-v \tau])-\varepsilon(T[x+v \tau])]$$ To this: $$j^{q}=n v^{2} \tau \frac{d \varepsilon}{d T}\left(-\frac{d T}{d x}\right)$$ At first I was thinking of using ...
0
votes
1answer
45 views

Relation between voltage and EMF of a battery [closed]

In the image :- R is resistance in the circuit r is the internal resistance of the battery E is the EMF of the battery V is the voltage across the resistor R Arrows show the direction of current. ...
1
vote
1answer
57 views

Symmetry of the Batalin-Vilkovisky (BV) antibracket operation

Batalin and Vilkovisky define $^1$ an operation they call antibracket which is $$(F,H) = \Big(\frac{\partial_r F}{\partial \Phi^A}\Big) \Big(\frac{\partial_l H}{\partial \Phi^* _A} \Big) - \Big(\frac{...
-2
votes
0answers
10 views

Functions… I’m not able to solve after (x+t)sin(x+t)=xsinx [migrated]

Period of xsinx? I’m not able to solve after (x+t)sin(x+t)=xsinx
1
vote
0answers
27 views

Relation between surfaces of an infinitesimal tetrahedron [migrated]

Let $d\sigma_1,d\sigma_2, d\sigma_3$ denote the areas of the faces perpendicular to the axes $x_1,x_2,x_3$ and let $d\sigma_n$ denote the area of the inclined face with unit exterior normal n. My book ...
-1
votes
1answer
26 views

Relation between Temperature and heat current

This problem: I was able to solve it doing this: But I think i have nowhere " exploited " the equivalence given above. How can this be used in this problem?
1
vote
0answers
46 views

Green's function for infinite square well

The Green's function can be given in terms of left and right solutions. $G(x,x';k) = \frac{1}{W}\left(\Psi_{L}(x_{<})\Psi_{R}(x_{>})\right)$ But I don't understand how to determine these left ...
-1
votes
0answers
14 views

How to find amplitude of oscillation of SHM in a non inertial frame of reference? [closed]

I'm trying to solve this problem which asks to find the amplitude of oscillation of a spring block system, which was initially hung in a stationary lift and was at rest, when the lift begins to ...
0
votes
0answers
43 views

How to solve this particular problem of Wick's theorem?

So I know the basics of Wick's theorem, but unsure about how to solve this time ordered product of a term that involves normal ordering. Is it just simply the sum of all possible contractions, but no ...
0
votes
2answers
54 views

Euler-Lagrange Equation, Shortest Path On Sphere

The equations for spherical polar coordinates are $$x = r \sin(\theta) \cos(\phi) \\ y = r \sin(\theta) \sin(\phi) \\ z = r \cos(\theta)$$ Now, consider a path expressed as $\phi = \phi(\theta)$...
4
votes
0answers
85 views

Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
0
votes
2answers
60 views

If I immerse a coin in a cup of water, help me define the forces acting on it

So the coin is hanging in an equilibrium position midway in the water filled cup, concerning the force acting on the upper face of the coin, I define it as F=mg where m is the weight of the water ...
0
votes
1answer
43 views

Probability of measuring Energy [closed]

I have done the first part of the question, but in (b) and (c) are struggling me . I second part : My tutor wrote : $$ P(req.) = \frac{|\int \phi_E^*(x)*\psi(x,t) dx |^2}{|\int\: \psi^*(x,t)*\...
-1
votes
1answer
39 views

Gauss's Law and Superposition Principle [closed]

Hi I am doing the homework in MIT 8.02 by Dr.Lewin, I doubt that the answer provided online for Problem set is wrong, here is the problem. For question(a)(b)(c) it answers For me, I think the ...
1
vote
3answers
98 views

Show the following equation satisfies the wave equation [closed]

So I am trying to do a problem from my book that says show the following equation satisfies the 3 dimensional wave equation. $$E(r,t)\space = \frac{A}{r}\ e^{i(kr-\omega t))} ~ $$ I am rather ...
0
votes
1answer
41 views

Three bulbs of 40W, 60W and 100W are arranged in series with 220V. Which bulb has minimum resistance? [closed]

My approach: As they are arranged in series, the current through each of the resistors is the same, and so $P=I^2 R$ should be the most feasible relation to use. So $P$ is directly proportional to $R$...
1
vote
2answers
26 views

The image charge inside the conducting sphere without producing any electric field [closed]

In the method of images for a grounded conducting sphere, we calculate the position of image charge at $$\frac{R^2}{r}$$, due to which there should be an electric field inside the conducting sphere ...
1
vote
2answers
48 views

Acceleration downhill, fastest trajectory for a ball

Given 3 ways of going downhill, like in this image: Would a ball behave like that in real life? Intuitively, it makes no sense. The shortest path here is not the fastest. Any hints to the math ...
0
votes
1answer
26 views

Applying one of the Kinematic formulas to a 2D projectile question failed [closed]

I started learning Kinematics for fun at Khan Academy, and so far it's quite interesting. Anyway, I was reading about 2D Projectile Motion, and was trying to solve the second example myself. You can ...
2
votes
1answer
46 views

How to calculate the inertia tensor of a spherical cap?

In this question, an attempt is made at calculating the diagonal elements of the inertia tensor of a homogeneous spherical cap, where the $z$-axis is the symmetry axis. The mass moment of inertia ...
0
votes
1answer
37 views

Stress tensor of a rope in equilibrium [closed]

First of all, let me say that I'm not a student of physics but of mathematics, so please be comprehensive. I'm currently studying continuum mechanics. As an example of applications of Cauchy stress ...
1
vote
2answers
41 views

Calculation of Gravitational Potential at the centre of the cube [closed]

I came across this problem in a test and have been able to come up with a solution however I am unsure if it is correct. I started by building a cube of twice the initial dimensions to bring point P ...
0
votes
2answers
88 views

How is solving Proca equation equivalent to scalar field equation?

My prof. told me that using differential forms proca equation reduces to solving for scalar field equation. How is that? I can’t see how does one relate to Scalar equation using differential forms. ...
1
vote
1answer
57 views

Equilibrium between Steam and Ice

Problem Statement: $15 \ g$ of steam at $373 \ K$ ($100^{\circ} \ C$) is mixed with $25 \ g$ of ice at $273 \ K$ ($0^{\circ} \ C$). What is the final temperature of the mixture. My Question: The ...
1
vote
1answer
26 views

Confusion of measuring two quantities on a quantum system

Let's say there are two observables corresponding to two operators A and B, and let's say my system is in a state Phi where with probability 1 if I measure A I get 3 (let's say 3 Joules), If I ...
0
votes
0answers
23 views

Approximation of electric dipole with discs of radius R

I've been recently assigned a problem whereby I have to numerically solve the 2D Poisson equation for an electric dipole approximated by two charged discs of some radius $R$, a distance $d$ away from ...
0
votes
2answers
71 views

Approximating ground-state energy without using variational principle

Given the Hamiltonian for one dimension harmonic oscillator: $$H=-\frac{\hbar^2}{2\mu}\frac{d^2}{dx^2}+\frac{\mu\omega}{2}x^2 ,$$ I need to calculate the approximate ground state energy using the ...
-1
votes
0answers
21 views

Gravity assist, space probe

How do I calculate how close a space probe is to the sun after passing by Venus. It is travelling with velocity $v_1 = 30 km/s$ and $\Delta v = 3 km/s$ after flying by Venus.
1
vote
2answers
59 views

Slope of $x$-$t²$ curve (displacement vs time squared)

I know that slope of $x$ vs $t^2$ curve gives $\frac{a}{2}$. How do I prove it? This is what I did : $x = ut + \frac{at^2}{2}$ $x = \frac{at^2}{2}$ (for $u=0$) $\frac{dx}{dt^2} = \frac{a}{2}...
0
votes
4answers
93 views

Why is $\exp \left ( \frac{\pi}{2\hbar}(L_x^2 + L_y^2) \right )$ not a unitary operator? [closed]

I should prove that $$\exp \left ( \frac{\pi}{2\hbar^2}(L_x^2 + L_y^2) \right )$$ is not a unitary operator. Where $L$ is the total angular momentum of a 2-particle system ($L = L_A + L_B$ for the ...
2
votes
1answer
61 views

How does one deal with derivative operator in quantum field theory properly?

Given creation and annihilation operators, ${a^{\dagger}(x,t)}$ and $a(x,t)$ in non-relativistic quantum field theory, respectively, which satisfy the following properties: Now, I want to prove $$[...
0
votes
2answers
39 views

Magnitude of an electric field on a long rod [closed]

You place $2.7 \: \rm \mu C$ of charge along a long nonconducting rod. The rod extends from $x=0$ farther than you can see along the positive $x$ axis. The charge distribution has the form of a ...
-1
votes
1answer
17 views

Doppler effect when two bodies are not moving in straight line [closed]

What is a Doppler line? Why are the velocity components taken along Doppler line as shown here? And what is the derivation of formula $$f_0=f \frac{v+v_1 \cos\theta_1}{v-v_2 \cos\theta_2}$$ where $...
0
votes
1answer
37 views

How forces act on the two masses on a rotating table [closed]

Consider a system on the figure: two masses on a rotating turntable are connected by a string over a frictionless pulley. The masses of the bodies are related as $m_A<m_B$. They are at distance $R$...
1
vote
0answers
25 views

Notation in a question on probabilities and particle counting

I'm working through Stephen Barnett's book on quantum information and have come across the following question (1.5, for anyone keeping track at home) A particle counter records counts with an ...
-2
votes
1answer
53 views

Probability of WaveFunction [closed]

A particle is confined in a one dimensional box of length $a$. What is the probability of finding the particle at $x = a/4$? I know that the wave function is written as $$y= A\sin([(\pi x)/a]$$...
0
votes
0answers
41 views

Find the Christoffel symbols from an expression

I have a problem of General Relativity (introduction) and know how to solve it, but i don't know how to solve it with the expression. This problem is from here (the first) in spanish, so I translated ...
3
votes
1answer
85 views

Symmetry group of two complex scalar fields with different masses

Which is the symmetry group of the following Lagrangian: $$ \mathcal{L} = (\partial^\mu \phi_1^\dagger)(\partial_\mu \phi_1) + (\partial^\mu \phi_2^\dagger)(\partial_\mu \phi_2) - m_1^2\phi_1^\dagger\...
2
votes
1answer
51 views

Volume per $k$-state

We're talking about Fermi-energies for the first time, for $N$ spin $\frac{1}{2}$ particles in a 3D box, and she writes down that $$2 \times \frac{1}{8} \times \frac{4}{3} \pi k_f^3 = Nq \times \frac{\...
0
votes
4answers
62 views

Friction acting as an internal force

I was solving this problem in my assignment: Assuming a frictional force F acts on the block of mass m, a force -F will act on plank of mass M. Hence, the net work done by frictional force should be ...
0
votes
1answer
45 views

Does $x$-component $\hat{L}_x$ of angular momentum commute with $\hat{x}$? [closed]

Question from lecture notes: What of the following operators does not commute with $\hat x$? A. $ \hat L_x $ B. $ \hat L_y $ C. $ \hat L_z $ D. None of the above. The answer ...
0
votes
2answers
64 views

Engine speed and flywheel [closed]

My doubt is about the third part of the question. I want to understand that if an engine is running at a constant speed, say 210 rpm, then can there be an acceleration in the flywheel? Because if the ...