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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18
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3answers
3k views

Problem understanding the symmetry factor in a feynman diagram

I am trying to understand a $1/2$ in the symmetry factor of the "cactus" diagram that appears in the bottom of page 92 In Peskin's book. This is the diagram in question (notice that we are in $\phi^4$ ...
10
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4answers
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A simple derivation of the Centripetal Acceleration Formula?

Could someone show me a simple and intuitive derivation of the Centripetal Acceleration Formula $a=v^2/r$, preferably one that does not involve calculus or advanced trigonometry?
2
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1answer
379 views

Recovering QM from QFT

Reading through David Tong lecture notes on QFT. On pages 43-44, he recovers QM from QFT. See below link: QFT notes by Tong First the momentum and position operators are defined in terms of "...
5
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2answers
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Does the normal reaction shift when a force is applied?

I started learning rotational mechanics and while looking at a solution for one of the problems in the book, I came across this statement In the absence of any external force in horizontal ...
8
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4answers
29k views

Internal energy according to the van der Waals equation

I am trying to derive the internal energy of a gas which obeys the van der Waals equation. I have however encountered some problems. I calculate the integral of $dU$ from $V=0,T=0$ to $V=V, T=\infty$ ...
5
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2answers
2k views

Orthochronous Lorentz transformations are time-preserving and $SL(2,\mathbb{R})$

Let's consider the pseudosphere/hyperboloid in $\mathbb{R}^{1,2}$ given by $$x^2+y^2-z^2=-R^2.$$ We know that the Lorentz group $$O(1,2)=\{ A \in Mat(3,\mathbb{R}): A^tGA=G \},$$ where $G=diag(-...
10
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4answers
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Relativistic Doppler effect derivation

This is about a step in a derivation of the expression for the relativistic Doppler effect. Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is ...
5
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2answers
13k views

block slides on smooth triangular wedge kept on smooth floor.Find velocity of wedge when block reaches bottom

Find the velocity of the triangular block when the small block reaches the bottom: Here is what I did: The final velocity(at the bottom)of the small block of mass m is $\sqrt{2gh}$ along the plane ...
9
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5answers
3k views

A conical pendulum. A textbook claims one can start the circular motion in an unintuitive way

A textbook claims that if you hang a mass from a string that's attached to a rod (so that the string is parallel with the vertical axis) and you spin the rod fast enough, you can put the mass into ...
6
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3answers
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Energy loss in Capacitors

We have this formula in our textbook for loss of energy when two capacitors are connected together. They mention that it is due to heat dissipation. However, we have not considered any such term in ...
5
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1answer
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Bessel function representation of spacelike KG propagator

Preliminaries: In their QFT text, Peskin and Schroeder give the KG propagator (eq. 2.50) $$ D(x-y)\equiv<0|\phi(x)\phi(y)|0> = \int\frac{d^3p}{(2\pi)^3}\frac{1}{2\omega_\vec{p}}e^{-ip\cdot(x-y)...
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2answers
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Equations for an object moving linearly but with air resistance taken into account?

I know (from Kinematics) that for an object moving linearly with an acceleration and without air resistance the following equations can be used to determine v(velocity) or x(position of the object) at ...
5
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2answers
941 views

5D Ricci Curvature

As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper http://arxiv.org/abs/1107.5563. I was wondering if there is some special ...
9
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1answer
5k views

Schwarzschild metric in Isotropic coordinates

As one wants to jump to Isotropic coordinates in order to write the Schwarzschild metric in terms of them, one does this coordinate transformation: $$r=r'\left(1+\frac{M}{2r'}\right)^2$$ So we start ...
5
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4answers
11k views

Electric field and electric potential of a point charge in 2D and 1D

in 3D, electric field of a piont charge is inversely proportional to the square of distance while the potential is inversely proportional to distance. We can derive it from Coulomb's law. however, I ...
5
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1answer
5k views

Is there a simple way of finding the eigenstates of the creation and annihilation operator in QM?

How can I find the eigenstates of creation and annihilation operator in QM? My attempt: Such eigenstate will obey: $$ a^{\dagger} |\psi \rangle = \alpha |\psi \rangle. $$ We can expand $|\psi \...
3
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2answers
6k views

Proving the Lorentz invariance of the Lorentz invariant phase space element

I have been looking around for a satisfactory answer to prove that $$\frac{d^3\vec{p}}{2E_{\vec{p}}}$$ where $E_{\vec{p}}=+\sqrt{(|\vec{p}|c)^2+(mc^2)^2}$, is Lorentz invariant. The standard answer ...
2
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2answers
949 views

How do you prove that $L=I-V+1$ in $\lambda\phi^4$ theory?

It is known that the number of loops in $\lambda\phi^4$ theory is given by the formula $$L=I-V+1$$ where $L$ is the number of loops, $I$ the number of internal lines and $V$ the number of vertices. ...
9
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3answers
37k views

Equivalent resistance in ladder circuit [closed]

I have stumbled upon a given question I really have a hard time to solve. Basically I need to find an equivalent resistance in some form of "ladder" configuration. Where the chain is an infinite ...
6
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4answers
9k views

Infinitely charged wire and Differential form of Gauss' Law

I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get $$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty \...
5
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3answers
2k views

What is the binding energy of a neutron star?

Neutrons which constitute a neutron star have a rest mass that is greater when separated from the star because they are bound with a certain potential energy. This potential energy causes the system ...
4
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3answers
1k views

How to derive $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$

Wikipedia indicates that the following relation is "easily shown": $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$, however I'm having some trouble showing it. I think I'm just ...
3
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5answers
9k views

How to use Ampere's Law for a semi-infinite wire with current?

Suppose that there is a semi-infinite wire which extends to infinity only in one direction. There are no other circuit elements at the other end(finite end) of the wire and the current does not loop. ...
11
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2answers
450 views

Stable muon density inside a white dwarf star?

It occurs to me (though I'm hardly the first) that the decay $$ \mu^- \to e^- + \bar \nu_e + \nu_\mu $$ should be forbidden in electron-degenerate matter, since there must be an empty state available ...
7
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2answers
1k views

Invariance of canonical Hamiltonian equation when adding the total time derivative of a function of $q_i$ and $t$ to the Lagrangian

The following is exercise 8.2 in 3rd edition (and exercise 8.19 in 2nd edition) of Goldstein's Classical Mechanics. Adding the total time derivative of a function of $q_i$ and t to the Lagrangian ...
6
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3answers
722 views

What was the density of the universe when it was only the size of our solar system?

What was the density of the universe when it was only the size of our solar system? Did it approach neutron star density? Is it physically correct to even ask such a question?
5
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2answers
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Particle in infinite potential well which is doubled in size at $t_0$

I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding. The Problem: A Particle sits in an infinite potential well ...
5
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2answers
1k views

Variation in measurements of $g$ on the Earth's surface due to the Moon's gravity

A book, Exercises for the Feynman Lectures on Physics, has recently been published. It consists of homework problems to provide practice with the techniques and concepts used in the famous Feynman ...
5
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3answers
15k views

Does Earth's Rotation Affect Its Shape?

The question I am working on is, "Consider the following. (a) Find the angular speed of Earth's rotation about its axis. rad/s (b) How does this rotation affect the shape of Earth?" I am ...
5
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3answers
13k views

Calculating time to reach certain velocity with drag force

I was given a problem for homework where we needed to calculate the time for a falling object to reach a certain velocity when accounting for drag force. I did it by setting up acceleration as a ...
3
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2answers
643 views

Why uncertainity is minimum for coherent states?

While reading for quantum damped harmonic oscillator, I came across coherent states, and I asked my prof about them and he said me it is the state at which $\Delta x\Delta y$ is minimum. I didn't ...
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3answers
38k views

Work, Energy & Power - Body slides down a hemisphere

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$. There is no friction between the surface of the block and the hemisphere. The height at which the body loses contact ...
1
vote
1answer
103 views

How do I handle elastic contacts in a simulation with friction [closed]

I'm trying to simulate a wheel as it hits the ground. Problem 1 Suppose a disc is dropped from a height. It has initial velocity of $-x,-y$ caused by throwing and gravity. It has no initial angular ...
9
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1answer
2k views

Why solids expand on heating

I came upon the following question: A solid expands on heating because: a) the potential energy of interaction between atoms in the solid is asymmetric about the equilibrium positions of atoms;...
5
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4answers
1k views

How big is an excited hydrogen atom?

Suppose an empty universe with the exception of a single hydrogen atom (1 proton, 1 electron). The electron may be in its ground state or it may be excited a certain number of levels. Suppose it is at ...
4
votes
1answer
53k views

Calculation of pressure from flow rate of water

Anybody kindly help me to find how to calculate pressure in bar from flow rate. I have a pipe and from that I am transferring water at a constant flow rate of 5ml/min. At this flow rate, with a 0.5 cm ...
2
votes
1answer
2k views

Estimate the reaction force on each leg of a 4-legged table

Assume you have a table with four legs with a weight placed somewhere inside the boundary created by the legs. The task is to determine the reaction force at each leg. Here are the problem ...
1
vote
1answer
294 views

How to compute the inertia tensor ${\bf{J}} _{\Omega}$ of a body of revolution

Suppose that $\Omega$ is a body of revolution of the function $y=f(x), a\le x \le b$ around the $x$-axis, where $f(x)>0$ is continuous. How to compute the inertia tensor ${\bf{J}} _{\Omega}$? ...
0
votes
1answer
810 views

Radially symmetric charge distribution (dipole moment) [closed]

a) There's a radially symmetric charge density $\rho(r)$ centered around the origin. Determine the dipolemoment of that charge density. b) Let $\rho(r)$ be an arbitrary charge density now. Under ...
7
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2answers
486 views

Escape velocity from a rotating black hole

Under Newton, the escape velocity is $$v_{esc} = \rm c \ \sqrt{r_s/r}$$ where $\rm r_s=2 \ GM/c^2$. In the nonrotating relativistic case (the Schwarzschild case) the radial escape velocity is the ...
5
votes
5answers
1k views

The approximate uncertainty in $r$

The volume of a cylinder is given by the expression $V=\pi r^2 h$ The uncertainties for $V$ and $h$ are as shown below $\begin{align} V&\pm 7\%\\ h&\pm 3\% \end{align}$ What is the ...
5
votes
2answers
5k views

Velocity of an satellite in an elliptical orbit

Consider some some satellite of mass $m$ around earth, traveling in an elliptical orbit about a focus (earth). Let's suppose at one point $A$ the satellite is a distance $a$ units away the focus at ...
3
votes
2answers
2k views

Newton's third law does not apply to the kinetic energy formula?

Here is a classic problem: A 60kg boy and a 40kg girl are sitting in front of each other on skateboards on a frictionless horizontal surface. The boy pushes the girl and the girl gains a velocity ...
2
votes
3answers
588 views

What is the meaning of natural line broadening?

I have recently found one exercise in an exercise book: During the transition from the first excited state of a hydrogen atom into the ground state, photons with a wavelength of 121.5 nm are ...
2
votes
1answer
868 views

Deriving relativistic Doppler shift in terms of wavelength? [closed]

Consider a star moving with velocity $v$ at an angle $\theta$ with respect to its line of sight to Earth. Show that the relativistic Doppler shift is $$\lambda_{obs} = \frac{1 - \frac{v}{c} cos(\...
2
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3answers
2k views

Unit conversion help (school) [closed]

Can someone please help me explaining how to convert units in problems like the one below? I've done many things, but I am very unsure of all my methods. Could you tell me what steps should I take? $$...
2
votes
2answers
18k views

The potential and the intensity of the gravitational field in the axis of a circular plate

Calculate the potential and the intensity of the gravitational field at a distance $x> 0$ in the axis of thin homogeneous circular plate of radius $a$ and mass $M$. Could anybody describe how to ...
1
vote
2answers
853 views

velocity of an object after leaving a ramp

at point no. 2 in the diagram, let the object accelerates to a velocity v1 (just along the direction of the slope) due to rolling down the ramp. Now, v1 has a x-component as well as y-component. Now, ...
1
vote
1answer
3k views

How is circular motion possible on a banked road when there is no Friction?

It is given here that the maximum safe speed of a vehicle on a banked road having coefficient of friction $0$, is $V =\sqrt{R g \tan \theta}$, where $\theta$ is the angle of banking. I can't ...
1
vote
2answers
7k views

What will be the relative speed of the fly? [duplicate]

It has happened many times and i have ignored it everytime. Yesterday it happened again . I was travelling in a train and saw a fly (insect) flying near my seat. Train was running at a speed of ...