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
1answer
41 views

How does quantum tunneling work in a bigger mass?

im trying to figure out the probability of a 9 y/o kid going right through an object. im trying to do this with a compacted form of schrodingers equation: e^(-2*(m*v/H/2pi)*l) where l = 22,34mm, h = ...
1
vote
1answer
51 views

A balloon popped in a room

This question is Question 23 from CAP exam 2017. An inflated balloon, filled with a gas of temperature T, is held in a room with the same temperature. If we make a small hole on the side of the ...
1
vote
0answers
15 views

Magnetic field due to a double tape line

I have been asked to calculate the inductance of a double tape line : Now we know that $$ N\phi = LI$$ So let's calculate the magnetic field by assuming an amperian loop like this: $$\int B.dl = ...
2
votes
0answers
69 views

Calculate the matrix size for ground states BEC using difference with Gross–Pitaevskii equation

The Ground states BEC at $0$ temperature can be described by Gross–Pitaevskii equation as $(-\frac{\hbar^2}{2m}\nabla^2+V(r)+g|\psi|^2)\psi(r)=\mu\psi(r)$ We limit the BEC in 2D where $V(r)=\frac{1}{...
0
votes
0answers
48 views

Derivation of Coulomb's law from classical field theory

In the section on Coulomb's law in QFT by Schwartz, he expands $-\frac{1}{4}F_{\mu\nu}^{2}$ to get $-\frac{1}{2}(\partial_{\mu}A_{\nu})^{2} + \frac{1}{2}(\partial_{\mu}A_{\mu})^{2}$, can someone ...
1
vote
0answers
38 views

Interesting astro/particle/quantum/experimental physics investigations for gifted pre-calculus students? [closed]

TL;DR What are interesting applications that I could work through with pre-calculus level students? I'd like to go from pop science explanations to an actual building of physical intuition and ...
0
votes
2answers
61 views

Classical period of Morse potential [closed]

A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential: $$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$ From the only other question I ...
0
votes
1answer
37 views

What is the final pressure of steam in a tank, if we allow some steam to exit?

Consider $m_1 = $ 100 kg of steam at pressure $P_1$ and temperature $T_1$ in a 3 $m^3$ insulated tank, closed off by a valve. We open the valve and allow 50 kg of steam to exit. What is the final ...
0
votes
0answers
35 views

Leaking potential [closed]

I'm trying to model the leaking of a probability from a semi-infinite well into free space. I'm not sure exactly what potential to start with are what form of the wave function to go with. I'm making ...
2
votes
1answer
58 views

Time period of an oscillatory motion [closed]

The question: A particle of mass $m$ is executing oscillation on the $x$-axis. Its potential energy is $U(x)= K|x|^3$, where $K$ is a positive constant. If the amplitude of oscillations is $a$, ...
3
votes
1answer
85 views

Perturbed Ricci tensor due to metric perturbation i.e. $R^{(2)}_{\mu\nu}[h]$ in Linearized theory of Einstein field equation

This is an equation (7.153) from Chapter-7 of Sean Carroll's An introduction to General Relativity: Spacetime and Geometry book. I think all of you who studied GR and went thorugh Carroll's book have ...
0
votes
0answers
18 views

Finding enthalpy of an isentropic compression given pressure, specific volume, $\gamma$ and $R_{sp}$ [closed]

For an isentropic compression from state 1 (pressure: 1200 Pa, specific volume: 71.75 $\frac{m^3}{kg}$) to state 2 (pressure: 7200 Pa, specific volume: 19.9526 $\frac{m^3}{kg}$ with $\gamma$ = 1.4 ...
-2
votes
0answers
36 views

Capacitor and electric field [closed]

I know the electric field would remain same but why and how to arrive at the result Secondly, if it remains same then why wouldn't force be equal to Eq ie electric field times charge on other plate ...
0
votes
1answer
23 views

Longitudinal magnification

I want to prove that if an object is small in length and lying along the principal axis then $M = -\frac{dv}{du} = -\left(\frac{v}{u}\right)^2$ where $M$ is the longitudinal magnification
0
votes
0answers
30 views

Canonical commutation relations for a real scalar field

I am taking my first course in QFT and have come across this problem From the canonical commutation relations for a real scalar field $\hat{\phi}$ show that $$[\partial_i \hat{\phi} , \hat{\phi}...
0
votes
1answer
54 views

Determine phase difference of harmonic oscillators

I am not understanding what I am doing wrong here. Please see the question below: Two harmonic oscillators are made using identical springs with identical masses and are set up side by side. You ...
0
votes
1answer
37 views

Driving force and mean of a particle wave function [duplicate]

I am currently undergoing a course on introduction to quantum mechanics and we took the historical approach. I'm currently at DeBroglie wavelength. He introduces the wave particle duality in matter, ...
1
vote
1answer
29 views

Divergence of current density and electric field within a wire

In the following exercise: I concern myself with the validity of my interpretations of (b). Here I am more confident slightly. The divergence of the current density is merely $- d \rho / dt$, so as ...
0
votes
1answer
46 views

Minimum separation between two bodies [closed]

Let Bodies A and B be kept at two points in the x-y plane. They are allowed to move in the x-y plane. Suppose the velocity of B is constant, and the speed of body A is fixed, how must the body A ...
0
votes
0answers
54 views

A Question About Vector Superfield

My reference is section 5.2 of BUSSTEPP Lectures on Supersymmetry, page 46. A Vector superfield $V$ is a scalar superfield which satisfies the reality condition $$V=\overline{V},$$ where the bar ...
-3
votes
1answer
56 views

5.61b University physics with modern physics [closed]

$$ \sum F_{y} = 0 $$ $$ \sum F_{y} = T_{1y} + T_{2y} - mg $$ $$ mg = (4400N)\sin{60} + (4400N)\sin{40} $$ $$ mg = 6640N $$ Why is this wrong? solution $T_{1x}$ has to be equal to $T_{2x}$ $$T_{1x} ...
5
votes
5answers
4k views

Why do I get negative height?

A baseball is thrown from the roof $50.1^\circ$ above the horizontal. The initial velocity is $11.5\ \mathrm{m/s}$. I'm trying to find how high the ball goes. I choose positive direction upwards. $$...
4
votes
2answers
96 views

Number of GPS satellites required to give 100% coverage

I am a Belgian school student in sixth grade of secondary school (the Belgian equivalent of High school). Together with two class mates we were assigned to write some kind of essay about the Global ...
2
votes
1answer
82 views

How do time-like separated points preserve temporal ordering under orthochronous Lorentz Transformations?

How do time-like separated points preserve temporal ordering under orthochronous Lorentz Transformations? This question has already been asked in this Phys.SE post but I want to derive this result in ...
-1
votes
0answers
13 views
0
votes
0answers
20 views

Motional EMF with a rod in a closed loop

Let me preface this by saying that while this is a problem which came from my college physics class, it was not a graded assignment, it was optional study material (and you can see from the photo I've ...
1
vote
1answer
59 views

How much did the universe expand since recombination time? [closed]

Assuming adiabatic expansion, and a temperature at recombination time of $2700^{\circ} C$, how much has the universe expanded if the temperature today is $2.7K$? My idea is to use $\frac{dQ}{dt}=A\...
0
votes
1answer
36 views

Probability of finding hydrogen atom in its ground state given an initial state

So I came across this question that asked what is the probability of a hydrogen atom which is prepared in an initial state $\Psi (\vec{r},t)$ to be in the ground state $\psi_{100}(\vec{r}) =2exp(-r)Y_{...
0
votes
0answers
25 views

How to choose the method of circuit analysis?

I was just doing some revision, and I was wondering how to figure out which method to use for solving a given circuit? I tried using mesh analysis on the attached circuit but I got it completely wrong....
1
vote
0answers
29 views

Stability of charges [closed]

Problem: Consider a circular ring of uniform positive charge density. Discuss the stability of a positive charge placed at centre of this ring. What can you say about the stability of a positive ...
4
votes
7answers
855 views

Inductor and Capacitor in Parallel

I've been staring at this for 10 minutes and I'm soooo confused. Hopefully, you guys can help! So, let's say we close the switch. From what I understand, the capacitor will charge up to $10V$ almost ...
0
votes
0answers
18 views

Formula for total current and phase angle in function of given currents and phase angles in the branches of a parallel RLC circuit

Consider this parallel RLC circuit powered by an sinusoidal alternating voltage and two branches, one containing an ohmic resistance $R_1$ and a capacity $C$, the other one containing an ohmic ...
2
votes
1answer
29 views

Cubic Power of Supercovariant Derivative

Let $\bar{D}_{\dot{\alpha}}=\bar{\partial}_{\dot{\alpha}}-i(\bar{\sigma}^{\mu})_{\dot{\alpha}\beta}\theta^{\theta}\partial_{\mu}$ be the supercovariant derivative. How to prove the following identity? ...
2
votes
2answers
108 views

Weak Energy conditions for Perfect fluid derivation

I want to derive the restraints $$\rho + p \geq 0\qquad\text{and}\qquad \rho \geq 0$$ which correspond to applying the weak energy condition ($T^{\mu \nu} v_\mu v_\nu \geq 0$ for $v_\mu$ timelike) on ...
1
vote
3answers
47 views

Rotational KE vs Translational KE [closed]

Q. Horizontal electric field E = mg/q exists as shown in the figure and a mass m is attached at the end of a light rod. if mass m is released from the position as shown in the figure. find the angular ...
2
votes
0answers
37 views

Formula for all the Lorentz boosts that result in $E$ parallel to $B$?

This is a follow-up question to a previous question regarding a minimum-energy invariant of the electromagnetic field. @ChiralAnomaly showed that there is indeed an invariant minimum energy density ...
-1
votes
1answer
49 views

I was unable to solve this mechanics/physics exercise and I can't find anything close to have a base [closed]

Mass in G = 500 kg. What's the force in AD? (1 ft = 0,3048 m) For me, there's not enough information. I don't have all the coordinates or angles to do a complete free body diagram and I'm not sure ...
1
vote
1answer
37 views

How to calculate second-order correction to the energy from matrix elements of perturbation?

A particle is in the one dimensional harmonic potential $V(x)=\frac{1}{2}m\omega^2x^2$ with a small perturbation $V'$. I want to calculate the first- and second order correction to the ground state ...
2
votes
1answer
63 views

How would you calculate the half-life of a source with one long measurement?

I'm working on a project, and I understand that half life of a source is typically calculated with time intervals (eg 5 sec intervals for 20 minutes) and then using that data to find the decay ...
0
votes
1answer
25 views

Rolling on a track in vertical plane

A sphere of mass m and radius r is released from rest at point A on a track in vertical plane. The track is rough enough to support rolling between A and B and from B onwards it is smooth. My ...
4
votes
3answers
913 views

Why isn't acceleration always zero whenever velocity is zero, such as the moment a ball bounces off a wall? [duplicate]

The answer to this homework problem is $\left(\text{D}\right) :$ I understand why we rule out options $\left(\text{A}\right)$ and $\left(\text{B}\right)$ first. However, I don't get why $\left(\...
0
votes
2answers
78 views

Finding the eigenstates of an operator [closed]

I am currently taking a course in QM and can't see how the eigenstates have been found for examples like this one: Question Let $\phi _1$ and $\phi _2$ be two normalised wavefunctions orthogonal onto ...
3
votes
1answer
64 views

Diffusion equation with time-dependent boundary condition

I was trying to solve this 1D diffusion problem \begin{equation} \dfrac{\partial^2 T}{\partial \xi^2} = \dfrac{1}{\kappa_S}\dfrac{\partial T}{\partial t}\, , \label{eq_diff_xi} \end{equation} with ...
1
vote
1answer
48 views

Picking the Right Reference Frame

A space vehicle travelling at $3860 \ \text {kmph}$ w.r.t Earth sends its exhausted rocket motor backward with a speed of $125 \ \text{kmph}$ w.r.t the command module. The mass of the rocket motor is $...
1
vote
1answer
37 views

Minimum Angular Velocity

A bead is free to slide on a vertical circular frame of radius $R$ comes to equilibrium when $\cosθ = g/Rω²$. The minimum value of angular velocity comes out to be $\sqrt{g/R}$, which we can find out ...
-1
votes
2answers
74 views

Expressing Maxwell's equations as scalar equations involving differentials in Euclidean space

I am trying to convert Maxwell's equations from the well known differential form (found on Wikipedia https://en.wikipedia.org/wiki/Maxwell%27s_equations) into scalar equations involving partial ...
1
vote
1answer
50 views

Thermodynamics - please check my proof that $\partial C_p/\partial p$ = 0 for an ideal gas

Prove $$\left(\frac{\partial C_p}{\partial p}\right)_T = 0$$ for an ideal gas. All the $\partial$s are partial derivatives Please check to see if this makes sense. We know that $$C_p = \left(\...
0
votes
1answer
37 views

How to calculate energy loss of falling object [closed]

I've done an experiment where I dropped 3 balls from a meter high and I want to record the energy loss they get once they bounce. I have height measurements for the first fall and the bounce. How ...
1
vote
0answers
29 views

Finding displacement using dampened oscillations (an attempt) [closed]

A cubical box of mass $10$ kg with edge length $5$ m is free to move on a frictionless horizontal surface. Inside is a small block of mass $2$ kg, which moves without friction inside the box. At time $...
0
votes
0answers
24 views

Vibrational Energy at T = 0 K using the Debye model

I mm trying to estimate the vibrational energy at $T=0$ for a 3-D lattice using the Debye model. My plan is to sum over all the frequencies using: $$U = \int_0^{\omega_D} d\omega D(\omega)\epsilon(...