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.

Filter by
Sorted by
Tagged with
0
votes
1answer
59 views

Solid in Liquid Heat Transfer (Temperatures/Entropy Changes)

Suppose we have a solid of temperature $T_s$ and heat capacity $C_p$ submerged into a pool of water that has temperature $T_w$. If $T_s \gt T_w$ and the pressure of the isolated pool-solid system is ...
0
votes
2answers
36 views

Why can I use conservation of momentum to understand a bag getting dropped on a moving truck, if the ground provides an external force?

Please help me with this sat question from released test A toy truck with a mass of $0.6$ kg initially coasts horizontally at a speed of $2$ meters per second. A child drops a beanbag with a mass ...
0
votes
1answer
63 views

Normalizing a set of eigenfunctions with different domains [closed]

Maybe it seems so easy, but it is not! How can we obtain the normalization constant $N$ for a set of eigenfunctions with different domains? For example, we have $\psi_{1}=N(f_{1}e^{-\kappa x}+g_{...
3
votes
2answers
213 views

Normalization constant of a planar wave

As we know for the plane waves ( $ae^{i k x}+b e^{-i k x}$), the normalization constant can be easily obtained from the integral $\int^{x_{2}}_{x_{1}}\psi^{*}\psi dx=1$ by the relation $|a|^{2}+|b|^{2}...
1
vote
2answers
34 views

Constrained motion of the vertices of a quadrilateral

There is this square of side length $a$. It's opposite vertices are being pulled in opposite directions with a constant velocity $u$. The question here is what is the velocity of the remaining pair of ...
1
vote
0answers
32 views

Obtain an expression for pressure difference [closed]

The question is "For the two-liquid manometer, shown below, obtain an expression for $p_1 – p_2$. Let $\mathcal A$ be the area of each tank and $\mathcal S$ the area of the tube. Let $S_3$ be the ...
1
vote
0answers
33 views

From a potential energy equation, how can we determine whether or not the particle undergoes circular motion?

(I realise this may be considered a homework question but I have read the rules.) I'm working through an introductory book on classical mechanics and there is this question: Consider a particle of ...
2
votes
0answers
56 views

Reading symmetry out of Lagrangian

Consider the Lagrangian: $$\mathcal L=\mathcal L_{kin}+\frac{1}{2}m_a^2(\phi^2_1+\phi^2_2+\phi^2_3)+\frac{1}{2}m_b^2(\phi^2_4+\phi^2_5)+\lambda_a(\phi^2_1+\phi^2_2+\phi^2_3)^2+\lambda_b(\phi^2_4+\phi^...
0
votes
2answers
57 views

Accurately calculating the work to move a charge? [on hold]

I'm applying a force $F_{me}$ to move the charge $q_2$ towards $q_1$. If they are both equal charges, I'm assuming a repulsive force $F_R$ opposing me. In order to get $q_2$ to the final position ...
0
votes
2answers
48 views

How is the angle same in friction force? [closed]

How is the angle $\theta$ of the plane and between the $mg$ (attraction due to gravity) and component of $mg$ is same? In the figure $\theta$ between the $mg$ and its component $$mg\cos\theta$$ is ...
1
vote
0answers
47 views

$bc$-system energy momentum tensor

I have a (maybe silly) question regarding the expression of the energy momentum tensor of the $bc$-system in equations $(2.5.11a)$ and $(2.5.11b)$ in Polchinski's String Theory, page 50. I know that ...
0
votes
0answers
43 views

Calculation of 3-point function given a generating funcional $Z[J]$

With: $$\ln Z[J]= \int dt \frac{J^2(t)}{2} f(t) + C \int dt \frac{J^3(t)}{3!}$$ I am asked to calculate the 3-point funcion. Attempted solution: The 3-point funcion is given by $\frac{ \delta^3 }{\...
2
votes
1answer
105 views

In this pulley-block system, acceleration of blocks-A and B is same then how is their displacement different?

In the given arrangement, Block C begins to move down at a constant speed of $7\ \rm{cm/s} $ at time $t=0$. At the same instant, Block A is made to start moving down at constant acceleration. When it ...
3
votes
1answer
41 views

Path of sound in ocean where sound speed varies linearly with depth

In an ocean, described with $x-y$ Cartesian coordinates where $y=0$ on the sea bed, the sound speed varies linearly with $y$: $$v(y)=c+by$$ A textbook says that, if sound wave is emitted on the sea ...
1
vote
1answer
28 views

Inconsistency regarding two charge elements on a uniformly charged disk

Let us say we have the following uniformly and positively charged thin disk: Suppose also that the total charge on the disk equas $Q$, with which we could define a constant charge density $\sigma$ ...
3
votes
0answers
77 views

Is it possible to guess this solution just by looking at the system? [closed]

Show that, if a projectile is shot from a height $h$ with speed $v_0$, the maximum range is obtained for launch angle $\theta=\arctan\left(\dfrac{v_0}{\sqrt{2gh+v_0^2}}\right)$ For the problem shown ...
0
votes
0answers
16 views

How can I calculate magnetic field strength of a variable gap magnet?

I am currently doing an experiment where an aluminium pendulum is passed through a variable gap magnet (creating eddy currents). The variable I am changing is distance between the two grade N35 ...
1
vote
1answer
40 views

Work done by friction on an inclined plane

A rough inclined plane is placed on a cart moving with a constant velocity u on horizontal ground. A block of mass M rests on the incline. Is any work done by force of friction between the block and ...
1
vote
0answers
72 views

Articulated rod falling [closed]

I'm studying for a university entrance exam (you can think of it as the Brazilian version of IIT JEE) and came across a problem I can't get the same answer from the book and I would like to know if ...
-1
votes
1answer
47 views

Work done by charged particles [closed]

A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments; one in which the charged particle is also a proton and in another, ...
0
votes
2answers
46 views

Can magnetic field change kinetic energy?

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. ...
0
votes
1answer
88 views

Common observables and associated operators: operator momentum [duplicate]

Starting from my previous question Commutators in quantum mechanics and considering that the commutator $$\left[i\hbar\frac{\partial}{\partial x},x\right]=i\hbar, \tag{1}$$ the associated linear ...
1
vote
1answer
58 views

Why does $k_\text{B} T \ll \hbar\sqrt{k_\text{Hooke}/m}$ imply that vibrational motion is negligible?

I want to estimate the heat capacity of a diatomic molecule whose movement has been constrained to a 2-dimensional plane. I can assume that $$ k_\text{B} T ~\ll~ \hbar\sqrt{\frac{k_\text{Hooke}}{m}} ...
2
votes
1answer
43 views

Particle moving on ellpse with foci as origin

I'm reading the book "An introduction to Celestial Mechanics" by Forest Ray Moulton. In the first chapter, I got stuck on the following problem: A particle moves in the ellipse whose parameter and ...
0
votes
2answers
102 views

Isn't friction on an incline coefficient of friction times the Reactional force?

Question - "As shown in figure a body of mass 1 kg is shifted from A to D on inclined planes by applying a force slowly such that the block is always in contact with the plane surfaces. ...
1
vote
0answers
35 views

Problem related to combination of lens & equivalent focal length and lens maker's formula [closed]

in between two equiconvex lens( made of glass) of focal length of 20cm there is a layer of water which also acts as a convex lens.The whole figure is surrounded by air. Find out it's equivalent focal ...
0
votes
1answer
75 views

Simple question on quantization of EM field

This is part of the lecture note of QFT by Tong: I have a question on the last part of (6.27). Why does it hold? Actually this question is not about QFT and is about just integral. The typical way to ...
0
votes
1answer
26 views

A thin rod is standing on a smooth surface [closed]

A uniform thin rod of mass m and length l is standing on a horizontal surface. A slight disturbance causes the lower end of the rod to start falling. find the velocity of the centre of mass of the rod ...
0
votes
2answers
57 views

Null electric field at infinity? How? [closed]

Suppose there are two charges (4uC each) fixed in the horizontal axis. One is in x=0 and the other in x=8m. I've obtained the electric field: $E=-k\cdot4\mu C \cdot [\frac{1}{x^2}+\frac{1}{(x-8m)^2}]...
0
votes
1answer
78 views

Angular Speed of Disk after Throwing Stone [closed]

A person of mass $M_2$ stands on the edge of a disk of mass $M_1$ and radius $R$. The disk can rotate freely about its center without friction, and there is enough friction between the disk and the ...
0
votes
0answers
52 views

Proving an equivalent [duplicate]

Can anyone help me prove the following equivalent found in Peskin & Schroeder on page 27. $$ \frac{1}{4\pi^2} \int_{m}^{+\infty} dE \sqrt{E^2-m^2} e^{-iEt} \sim_{t \to \infty} e^{-imt}$$ The ...
1
vote
4answers
122 views

A man with a rifle shoots bullets at a speed [closed]

Hello all So I was doing this question. I had a doubt that, initially as both the (man and rifle ) system and the bullet were at rest we put 0 instead of m1u1 + m2u2 in equation of conservation of ...
0
votes
1answer
52 views

Calculate how thick the continent is [closed]

I have a task that I'm stuck on: For simplicity's sake, we assume that a continent consists of an even thick surface of granite that floats in peridotite. If a continent protrudes 5.0 km above the ...
-1
votes
1answer
30 views

Projectile motion problem with only angle and distance given [closed]

I have a cannon that shoots a projectile at an angle of 30°, the projectile hits a wall at 2.5m and it does so when the velocity only has a an horizontal component. I need to find the initial speed, ...
1
vote
0answers
66 views

Classical definition of number of particles in a volume

In "Relativistic Transport Equation" by Lindquist (1966), they use the "classical" result $$ \mathrm{d}N = f(x,p,\alpha) \, \mathrm{d}E \, \mathrm{d}\Omega \, \mathrm{d}V \,,$$ where $N$ is the ...
0
votes
1answer
31 views

Bound states and parity for a arbitrary potentials

If we are given an arbitrary potential, and we are asked to find bound states and parity, what would be usual strategy to do that? Let's we have a potential given: $$-\frac{A}{y^2+a^2} -\frac{A}{(y-...
0
votes
2answers
71 views

Explanation of Kinetic Energy Terms [closed]

I'm reviewing some classical mechanics and came across a problem from Colombia Universities physics Ph.D. qualification exam. The question is this: A mass $m$ slides down a circularly curved ...
2
votes
0answers
29 views

Polarization operator of fermi system

I misunderstand the following derivation. The polarization operator is given by the integral: $$\Pi(\omega,{\bf k})=-2i\int\frac{d\epsilon}{2\pi}\frac{d^3p}{(2\pi)^3}G(\epsilon_+,{\bf p}_{+})G(\...
2
votes
3answers
53 views

Understanding the Born-Mayer binding potential for ionic crystals

what was supposed to be a simple question, turned out to be a conundrum. I am asked to plot the Born-Mayer potential energy for a single pair of positive and negative ions. The potential energy is ...
-2
votes
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 ...
1
vote
0answers
39 views

Why am I getting two different expressions for capacitance? [duplicate]

The question is: A capacitor of capacitance C1 is connected to a battery of potential V0. The battery is then disconnected and a second capacitor of capacitance C2 is connected to the first ...
0
votes
2answers
25 views

How to determine the minimum force in these questions?

Take a look at this example The author mentioned that the shortest path when the angle is 90 which is clearly obvious. Now take a look at the following problem from the same book The author has ...
0
votes
4answers
71 views

What happens to the pressure and the temperature of a gas compressed adiabatically?

The set-up is basic. There is a piston that goes down, reducing the volume. The process is adiabatic, so the acquired energy is kept inside the gas. The ideal gas law states that as the volume ...
0
votes
1answer
41 views

Basic mechanics, motion in one dimension [closed]

I've just started to read Physics by Serway et al. In the problems section in chapter 2 there's the following question: The driver of a car slams on the brakes when he sees a tree blocking the road....
-2
votes
1answer
55 views

Reconciling Wikipedia and textbook descriptions of ladder operator method #2

I'm trying to reconcile the work in my textbook, Quantum Field Theory and the Standard Model by Schwartz, which I'm finding difficult to follow, with the Wikipedia article for the ladder operator ...
7
votes
2answers
696 views

Approximating an expression for a potential

In a problem which I was doing, I came across an expression for the potential $V$ of a system as follows $$V = k\left(\frac{1}{l - x} + \frac{1}{l + x}\right)\tag{1}\label{1}$$ where $k$ is a constant,...
0
votes
1answer
26 views

Tension about disk

A uniform disk of mass $M = 8.0 \;\mathrm{kg}$ can rotate without friction on a fixed axis. A string is wrapped around its circumference and is attached to a $m = 6.0 \;\mathrm{kg}$ mass. The string ...
1
vote
1answer
96 views

Does time evolution preserve parity?

Let $\psi(t_0, \cdot)$ be the state of a quantum system corresponding to a Hamiltonian $H$ in the position representation at time $t_0$. Assume $\psi(t_0, -x) = \psi(t_0,x)$, that is $\psi(t_0, \cdot)$...
0
votes
1answer
58 views

At the Point where Force is being applied, why at that point net force should be zero? [closed]

1st image is of question.2nd is of how i solved the question by considering the F.B.D there. I got the answer which was stated in the book. My doubt is that in the 3rd diagram of 2nd image, i had to ...
2
votes
1answer
182 views

Coupled oscillators in Hamiltonian formalism - problem with diagonalization

I have a problem with simple coupled oscillator system. I tried to solve single oscillator with Hamiltonian, and then coupled system of two, but when I try to put coupling constant $k^\prime=0$ in my ...