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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4answers
310 views

Potential difference across a capacitor

Look at the above circuit, I didn't get anything of it. Firstly i tried it using Kirchoff's voltage rule, I failed. I'm confused with those batteries. Can someone please explain me the role of those ...
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0answers
34 views

Why is the electric field negative?

I have a doubt in an exercice of a Thomson's apparatus deflecting an electron beam. The problem is: Electrons pass undeflected through the plates of Thomson's apparatus when the electric field is ...
3
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2answers
66 views

Why can't I choose blocks attached with pulley B as a system?

Three blocks of masses m1, m2 and m3 are connected as shown in the figure. All the surfaces are frictionless and the string and pulleys are light. Find the acceleration of the block of mass m1. ...
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1answer
514 views

Internal energy changes for a van der Waals gas

A mole of a van der Waals gas is expanded isothermally from $V_1$ to $V_2$. Derive the expressions for the changes in the Helmholtz energy and internal energy. I have already calculated the change in ...
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0answers
21 views

Efficiency of kettle

I have the following table of results for an experiment in which water is boiled in a kettle. For the final column to calculate efficiently it says divide the internal energy change by the work ...
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1answer
713 views

What is the effect of volume on liquid temperature during evaporative cooling?

Imagine two evaporative cooling experiments: In the first, a beaker contains a known volume of liquid. The liquid starts at ambient temperature. The temperatue of the body of liquid remaining in the ...
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0answers
28 views

Estimate the force on your legs if you jump off a 2m high wall and land on your feet [on hold]

My final answer was 686.7N. I used F = ma, so let the mass be 70 because the average weight of a 15-year-old is near that. (the question was purposed for A-level students). 70kg x -9.81 m/s^-2 = 686....
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0answers
37 views

Pseudorapidity: Derive conversion to Cartesian momenta

I am working on the ATLAS opendata as part of a lab course at my uni at the moment and stumbled upon the identity $p_{z} = p_{T}*\sinh(\eta)$ with the pseudorapidity $\eta = -\ln(\tan(\frac{\Theta}{...
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2answers
58 views

Show $\langle \alpha| (\cos \mu)^{-a^{\dagger} a} | \alpha \rangle =e^{|\alpha|^2(\frac{1}{\cos \mu} -1)}$ for coherent states $|\alpha \rangle$

I am reading"Quantum continuous variables, A primer of Theoretical Methods" by A.Serafini, page 120. Let $ a $ be the annihilation operator for the Fock basis. I want to show $$\langle \alpha| (\...
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1answer
40 views

How to find the possible measurements of a quantum system?

A wave function of an infinite square well is given as $$ \psi(x) = \frac{1}{\sqrt{5a}}\sin\left(\frac{\pi x}{a}\right) +\frac{2}{\sqrt{5a}}\sin\left(\frac{3\pi x}{a}\right),\quad x\in[0,a] $$ How do ...
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1answer
482 views

Electric field from metal rod with surface charge

I'm not sure if I'm thinking about this problem right. If you have a metal solid rod of length $L$, radius $a$ and charge density $\sigma$ and want to know the electric field outside and inside ...
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0answers
32 views

Doppler effect with two moving resonators [on hold]

Sound source with frequency $\mathcal{V}_0$ is located between two moving resonators set to wavelengths of $ \lambda_1$ and $\lambda_2$, respectively. Determine speed ratio of the two resonators $\...
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2answers
385 views

Usage of momentum conservation during collision of 2 blocks 1 connected to a spring (at rest) and other hitting with a velocity

suppose I have 2 blocks say A and B which are connected by spring and at rest, and there is a third block C which is colliding with A, will it be correct to use momentum conservation equation on this ...
9
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1answer
574 views

Deriving the Poisson bracket relation of the Ashtekar variables

I'm trying to figure out how to calculate the orthogonality of Ashtekar variables with respect to the ADM hypersurface metric and conjugate momentum. $$\{{A_a}^i(x), {E^b}_j(y)\} = 8 \pi \beta \delta^...
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0answers
17 views

Evaluating the Heisenberg Hamiltonian for a spin chain in the z basis

The problem I need to evaluate the expectation value of energy for a spin-1/2 chain governed by the Heisenberg Hamiltonian (Wikipedia link). Specifically, $$ H = \sum\limits_{\langle i j \rangle} \...
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0answers
28 views

Exhaustion of a gas Pressure Tank [on hold]

Gas tank of the volume $V$ is exhausted with the axial piston pump. It pumps $\Delta V$ of volume per one working cycle. After how many cycles does the pressure in the gas tank reduce by $K$ times? ...
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1answer
34 views

Linearizing Equations (Question given below): [on hold]

This question is mainly asking to rewrite a different graph equation (maybe parabolic, curved, etc) and changing it to a normal linear equation in the form y = mx+b. The question 5 and 6 can be seen ...
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0answers
23 views

Method of resolution of forces numerical Question [on hold]

The resultant of two forces F1 and F2 is at right angles to F1. Determine the angle between the forces.
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0answers
22 views

A block of mass M bound to a weightless bar is hit by a projectile. How many laps does the block travel? [on hold]

I have solved the following problem, but the solution is not available to me, so I'd like to know I made any mistakes. A block of mass "M", initially still, is bound to a weightless bar of length "b"....
2
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2answers
239 views

A simple calculation about surface gravity in classical GR

I am reading An Introduction to General Relativity Spacetime and Geometry by Sean Carroll, but simple calculations stop me. At page 245, a formula for the surface gravity is given $$\kappa^2=-\frac{1}...
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1answer
53 views

Show Galilean invariance of Schrödinger eq

I'm trying to show the Galilean invariance of the (time-dependent) Schrödinger equation by transforming as follows: $$ \left\{\begin{eqnarray}\psi(\vec{r},t) &=& \psi(\vec{r}'-\vec{v}t,t),\\ \...
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1answer
6k views

How to calculate uncertainties of a natural exponential function?

(I apologize if this should be posted in mathematics, however I chose to post it here as it's technically about physics) I conducted an experiment in which position of items were shifted on an object,...
2
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1answer
38 views

How to convert $\rm kg/m^3$ to $\rm J/m^3$ for natural gas and biogas?

I want to convert from mass density to energy density: Natural gas has a density of $0.8\: \rm kg/m^3$. Biogas has $1.15\:\rm kg/m^3$. I want to convert them into $\rm J/m^3$ so that I can ...
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0answers
13 views

Momentum of neutrino and beta particle [on hold]

In carbon-14 decay beta particles with end point energy 0.155MeV are emitted. A beta particle with 0.025MeV energy is emitted at 135 degree to the direction of motion of recoiling nucleus ,calculate ...
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0answers
53 views

Taylor expansions giving different answers before and after applying Euler-Lagrange equation

I have the Lagrangian $$\alpha(\boldsymbol{\dot{r}} -\boldsymbol{v}(\boldsymbol{r}))^{2} + \beta \nabla \cdot \boldsymbol{v}(\boldsymbol{r}),\tag{1}$$ where $\boldsymbol{r}$ is the position and $\...
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0answers
16 views

Evaluating the radius of a spherical cavity that will make a glass cube just sink in water [on hold]

A glass cube of side 5cm having spherical cavity within just sinks in water. If the specific gravity of glass is 2.5, what is radius of spherical cavity?
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2answers
9k views

Given airplane mass, velocity of air under wing, and a wing area, find velocity of air over wing

I attempted to solve this problem as a tutor for a student and struggled, but want to be convince the professor didn't provide enough information. The problem is essentially: We wish to maintain a ...
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0answers
24 views

Calculate the time taken for a body to hit earth's surface [on hold]

Find the time taken for an iron cube of dimensions 0.1m × 0.1m × 0.1m, whose density is 7.85 g/cm³ to reach the earth's surface released from a height of 10m from earth's surface, provided gravity = 9....
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0answers
16 views

Electric field inside a homogenous distribution for slightly different Coulomb's law

I am trying to show that the electric field inside a homogeneous distribution of superficial charge is of the order of magnitude of $\delta$, with: $$V(\textbf{r})=\int d^3\textbf{r'}\frac{\rho(\...
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1answer
65 views

Kinematics problem, only energy related approach [on hold]

I read this question: From the top of a tower, a stone is thrown up and it reaches the ground in time $t_1$. A second stone is thrown down with same speed and it reaches the ground in time $t_2$. A ...
6
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6answers
4k views

What is the electric field flux through the base of a cube from a point charge infinitesimally close to a vertex?

I'm having some trouble with the following problem: A charge $q$ is placed on the body diagonal of the cube very close to one of the corners (distance $\delta$ from the corner, $\delta$ tending to ...
2
votes
1answer
63 views

Distance between two drops [on hold]

2 drops are thrown away simultaneously in $t=0$, with initial velocity of $v_i$ and in angle of $\theta_i$ in opposite directions as seen in the picture. What is the distance between them as a ...
-1
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0answers
33 views

Interference questions [on hold]

non reflecting surfaces are made by coating very thin films of transparent materials . find the maximum thickness of such coating is u=5/4 and l= 5.5*10-5 cm. What does it mean by maximum thickness?
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4answers
2k views

Covariant Derivative of Kronecker Delta

I am reading Carroll's book on GR right now, and I ran into a little trouble in his chapter 3 on curvature. He is establishing the properties of the covariant derivative, and claims that the fact that ...
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2answers
65 views

Calculating gravitational force with multiple planets [on hold]

I have a question regarding the following problem: Given the following system of planets (see image), calculate the total gravitational force acting on $m_3$. ($m_1 = 2 \cdot 10^{20}kg;$ $m_2 = 1 \...
1
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0answers
66 views

Simple/elementary explanation for $\mathbf{3} \otimes \mathbf{\bar{3}} = \mathbf{8} \oplus \mathbf{1}$? [duplicate]

I am preparing a talk on the Eightfold Way, and am attempting to explain the spectra of the light mesons/baryons via representation theory. It will be delivered to students who have never seen ...
5
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5answers
1k views

Somewhat unusual projectile motion question

A stone must fly over two walls of height $h_1$ and $h_2$ $(h_2~ > ~h_1)$ from the side of the lower wall. The distance between the upper points of the two walls near which the stone's trajectory ...
7
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1answer
513 views

General motion of a cone on an inclined surface

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight? I know that its motion depends on the ...
6
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1answer
1k views

Homopolar motor and Lorentz force

My second grader thought making a homopolar motor for her science experiment would be fun. And, it was. Now I am trying to explain how it works and the Lorentz force. Please help me by giving me a ...
1
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0answers
49 views

Rigid body dynamics exercise

Yesterday I came across this exercise and I can't really find a way to get the correct answer. Exercise A rigid homogeneous rod that weighs $M=5\,\mathrm{Kg}$, has length $l=0.8\,\mathrm{m}$ and a ...
5
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1answer
272 views

How the Poisson bracket transform when we change coordinates?

I'm studying the book Geometric Mechanics by Darryl D. Holm and there's one exercise in the book I'm not quite getting what has to be done. The same discussion the author makes in the book is made on ...
5
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1answer
186 views

Examples of central forces on the path of orbit?

In solving a problem from Goldstein (3.13), I solved for multiple properties of a circular orbit with the attractive central force where the path of orbit crosses the point of the force (at origin). ...
0
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1answer
379 views

Coordinate transformation problems

Two questions here, both related to one another. SOLVED Question 1. I am looking to transform a dual vector $p_a$ from spherical polar coordinates to Cartesian coordinates. My dual vector is given ...
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0answers
21 views

Determining the z-component of the electric field at a point near a plate [on hold]

I'm struggling with all three parts a,b,c. Any help would be great, thanks. Regards Roy Browning
8
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3answers
6k views

Basic Thermodynamics: Quasistatic Adiabatic Process

I'm going through the exercises in a Thermodynamics book, just to revise and build my intuition. Right now, I'm working on: Show that for a quasistatic adiabatic process in a perfect gas, with ...
2
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0answers
50 views
+50

To find the probability of the direction of the velocity after impact lying between given limits

I'm trying to understand Maxwell's "Illustrations of dynamical theory of gas" puts forward the argument of equal scattering probability. The area between the spherical zone is not very clear. How does ...
0
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0answers
23 views

Tension due to unequal forces on a massless spring [duplicate]

When a massless spring is pulled by 5N on both sides the tension in the spring is 5N (proved by considering COM at rest and breaking the spring into two springs of 2k each)...what if the forces ...
0
votes
1answer
162 views

Stagnation points of combination of line sink and line source

I've got the complex potential of a flow consisting of a line sink at $z=-a$ and a line source at $z=a$ both of equal strength. I want to find the stagnation points but when I differentiate I get no ...
0
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1answer
37 views

Simple harmonic motion qsn [on hold]

Have been stuck with this question from classical mechanics under the simple harmonic motion the question is saying that if $$y=a\cos(\omega t)+b\sin(\omega t)$$ show it represents simple harmonic ...
-2
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3answers
227 views

The use of the commutators in quantum mechanics: explanations [duplicate]

Considering that I've never studied quantum mechanics before I have need to understand the operator commutator. My start is: $[A,B]=AB-BA \tag{a}$ Now, why must be $$\left[\frac{\partial }{\partial ...