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2answers
390 views

Angular Momentum commuting with Hamiltonian

I've been given an assignment where I have to prove that the angular momentum operators $L_j = \varepsilon_{jkl}q_{k}p_{l}$ commute with the Hamiltonian, given as $H = \frac{p^2}{2m} + V(r)$. Now, I ...
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2answers
352 views

Derivation of relativistic uniformly accelerated motion

I'm trying to understand solution of the following problem from Landau, Lifshitz, Classical Theory Of Fields: (ending skipped). What I see when I "write out the expression for $w^iw_i$", using ...
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1answer
185 views

Principle of relativity and motion perpendicular to the direction of light beam

consider you are in a train that moves with a speed of $c/4$. A bulb is hanged from the ceiling. A light beam leaves the bulb downward. Exactly under the bulb on the floor is a detector. According to ...
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1answer
249 views

Variable Tension in the string [closed]

A body of mass $m$ is hanging with a string having linear mass density $\lambda$. What is the tension at point $A$ as shown in the figure. I am aware of the scenarios in which string is ...
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4answers
1k views

Velocity of 2 balls with different masses on a moving train after the train brakes

Question This is from my textbook: There are 2 balls of the same size made of rubber and iron respectively kept on the smooth surface of a moving train. Which ball will move faster when the train ...
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2answers
175 views

Velocity of an object undergoing homogenous acceleration

So I was considering the following problem within the context of Special Relativity: Given an object O, with initial velocity v, undergoing constant acceleration at a rate of a, I want to express the ...
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1answer
623 views

Energy required for ionizing Helium

The energy required to remove both electrons from the helium atom in its ground state is 79.0 eV. How much energy is required to ionize helium (i.e., to remove one electron)? ...
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0answers
478 views

How to calculate Riemann and Ricci tensors for a sphere? [closed]

Let's have the metric for a sphere: $$ dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right). $$ I tried to calculate Riemann or Ricci tensor's ...
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2answers
791 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 ...
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1answer
109 views

Maximum separation when 2 unlike charges shot apart

I want to compute the maximum separation when 2 unlike charges are shot apart from each other ...
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1answer
432 views

Ratio of Size of Atom to Size of Nucleus

I have the following problem: In nuclei, nucleons exists in nuclear energy levels and in atoms, electrons exist in atomic energy levels. The order of magnitude of nuclear energy is 1MeV whereas ...
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1answer
173 views

Path Integrals Page Peskin

Hi this problem relates directly to path integrals but I imagine it is a maths trick that I am missing. One has an expression such as $$\int dx \exp\left[i\frac{(p)^{2}}{2}-iV(\frac{f}{4})\right] $$ ...
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0answers
122 views

Use of Principle of Equivalence

Let $x^\mu$ be the coordinates of a reference frame, $K$, where all bodies feel the same constant and uniform acceleration $\textbf{a}=\textbf{g}=-\nabla\varphi$; let $\xi^\mu$ be the coordinates of a ...
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5answers
2k views

How to get the angle needed for a projectile to pass through a given point for trajectory plotting [closed]

I am trying to find the angle needed for a projectile to pass-through a given point. Here is what I do know: Starting Point $(x_0,y_0)$ Velocity Pass-through point $(x_1, y_1)$ I also need to ...
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0answers
315 views

Point charge moving towards a conducting plane

A point charge $q$ of mass $m$ is released from rest at a distance $d$ from an infinite grounded conducting plane. Show that the charge hits the plane after an amount of time given by: $ \Delta t= ...
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1answer
2k views

Rolling bowling ball with slipping

If a bowling ball is moving with some initial velocity while slipping, how far will it move before it begins to roll once it experiences static friction? $\ddot{x} = \mu_{kf}g$ And there is also a ...
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1answer
299 views

Intercept a moving object

Object A can move at 50km/h, wants to intercept object B (currently $15^{\circ}$, east of north from A) moving at 26km/h, $40^{\circ}$ east of north. What angle should A take to intercept B? AB is ...
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1answer
1k views

Newton 2nd Law: Does vertical force (mass) affect the horizontal acceleration?

I learnt before that if 2 forces are perpendicular to each other, they should not affect each other. However in a recent experiment setup (asked in another question): I believe the theoratical ...
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2answers
4k views

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 ...
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1answer
582 views

What is physics of a normal jump?

What is the physics behind a normal human jump ? when a normal human wants to jump. First, some energy is stored in their thighs and The elastic tendons Just like a spring. In mechanics and ...
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1answer
141 views

Determine the flow and amplitude equation for thermal energy (with Del operator)

It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
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1answer
124 views

Gravitation and equilibrium (…and similar problems) [closed]

One problem that I'm having trouble with (as opposed to the other): The Messenger is a probe that orbits Mercury $700 \rm km$ from the surface. What is the tangential velocity it should be ...
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1answer
1k views

Calculation for force generated by a rotating rectangular blade

When trying to calculate the lift force generated by a simple rectangular blade, I've found the following equation: $$F = \omega^2 L^2 l\rho\sin^2\phi$$ in which $\omega$ is the angular velocity, $L$ ...
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1answer
1k views

How to calculate the charge and the potential across a charged capacitor charging an uncharged capacitor?

Initially, there is a single capacitor $A$ attached to a power source that charges it to a certain voltage $V$. Once it is charged, it is instantaneously removed and placed in a circuit with an ...
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1answer
218 views

Lenz' law versus $-\frac{d\Omega}{dt}$

I am preparing for an exam, on one problem my answer differ from the solution. The current $i(t)=I_0e^{-\alpha t}$ runs in a long straight conductor along $\hat z$. Point A,B,C,D forms a triangle. ...
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3answers
110 views

Time dilation in special relativity

Suppose a star ship is moving with some velocity. Two light pulses one in direction similar to star ship another opposite to it is shot towards the space ship. Then how time inside space ship adjust ...
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2answers
26 views

Calculating the Probability Current of a Travelling Wave

Calculate the probability current density vector $\vec{j}$ for the wave function : $$\psi = Ae^{-i(wt-kx)}.$$ From my very poor and beginner's understanding of probability density current it is : ...
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0answers
32 views

How can we show that a map is a completely positive map? [migrated]

I am doing a homework problem where I have to find whether the map $$ \rho ~\rightarrow~ {\rm tr}(\rho) I - \rho $$ is completely positive. If the map is not completely positive, a counter-example ...
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1answer
60 views

Integrating for speed [closed]

Trying to determine the speed of a falling body with respect to traveled distance and initial speed. I've been provided with the following equation for acceleration as a function of distance and the ...
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1answer
57 views

Density Matrix Characterization

I am working a two dimensional Hilbert space with basis {$|0\rangle, |1\rangle$} and I am trying to show that the density matrix is characterized by 3 real numbers and show that these three numbers ...
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2answers
44 views

Homework Question involving Momentum [closed]

I'm trying to solve a homework problem as review for an exam I have tomorrow and I was wondering if someone could help explain it to me. It is as follows: You are at Lowe’s shopping for bricks ...
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0answers
40 views

Determining impact velocity over long distances [duplicate]

Everything I have found concerning impact velocity from a given height deals with constant acceleration due to gravity. I would like to know how to work in varying acceleration into the equation. So, ...
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2answers
127 views

2 bodies separated by a rope [closed]

Say you have two bodies connected by a "weightless" rope, one hanging from a ledge on a pulley (classic pulley problem). If the body that is on the surface and being pulled by the object hanging ...
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2answers
193 views

Understanding field representation of force [duplicate]

I am reading the book The Evolution of Physics. I have a doubt in the topic "The field as representation". In this topic authors give the example of gravitational force represented as a field. In the ...
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1answer
69 views

Problem understanding a step in derivation of Lorentz Transformation

I need to understand a step in the derivation of Lorentz Transformation. I cannot understand how can we equate the equations 1 and 2. I am talking about the relation between ct, x, y, z. Where ...
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2answers
99 views

Is my free diagram of a spring stretched on one end and attached to the wall on the other end correct? [closed]

Consider the following figures. The top one shows the construction of a spring where its left end is attached to the wall and its right end is stretched by a force. The bottom one is supposed to be ...
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1answer
141 views

Centrifugal force acting on ring [closed]

Take for example the case of a rod rotating about an axis passing through its centre of mass and perpendicular to it. It has a ring hung from one of its sides. The rotation of the rod causes the ring ...
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1answer
294 views

Inverse Square Law in Beta Radiation

Setup: A radioactive source is placed at alternating distances from a Geiger Counter. Counts per second for 10 different distances (each spaced 1 cm apart) were taken for preset times ranging from 200 ...
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2answers
263 views

Reflection formula for spherical surface from Fermat's principle (Query)

The snip shows a part of the method shown by my teacher, to describe the reflection formula for spherical surface. However I do not understand how the relation of AB and BI (which I have ...
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1answer
163 views

Working with a Routhian for a specific system

I asked a more general question earlier about the Routhian, but I'm still having trouble working with it. Here's my specific case. Given the following Lagrangian: ...
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1answer
573 views

Expectation value of total energy for the quantum harmonic oscillator [closed]

A particles unnormalized wavefunction is given as $$\psi(x)=2\psi_1+\psi_2+2\psi_3.$$ How can I find $\langle E\rangle $ without calculating $\langle T\rangle$ or $\langle V\rangle $ ...
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2answers
205 views

Anticommutatorrelation in Bogoliubov-de Gennes Hamiltonian

I almost solved the problem Equivalence of Bogoliubov-de Gennes Hamiltonian for nanowire. In the next steps I used the notation by arXiv:0707.1692: $$ \Psi^{\dagger} = ...
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1answer
133 views

EM vector potential

We can write the electromagnetic field tensor as $$\begin{bmatrix} 0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & 0 & ...
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1answer
85 views

Pauli matrices identities

There are some definitions and properties for Pauli matrices and their combinations: $$ \varepsilon^{\alpha \beta } = \varepsilon^{\dot {\alpha} \dot {\beta} } = \begin{pmatrix} 0 & 1 \\ -1 & ...
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3answers
727 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 ...
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2answers
181 views

How does symmetry allow a rapid determination of the current between $A$ and $B$?

The following was originally given to me as a homework question at my physics 2 course: Consider the following circuit The difference of potentials between the point $V_{1}$and the ...
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2answers
101 views

Hamiltonian equations: can I divide a solution of motion for a constant?

I'm solving an exercise about Hamiltonian equations. I have followed the proceeding below. The results given by the book are different to mine because its first result is the half of mine (and the ...
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2answers
115 views

Computing $\Delta m$ in $\beta^-$ decay

$\require{mhchem}$What is the energy $Q$ released when $\ce{^131_53I}$ decays and $\ce{^131_54 Xe}$ is formed? The atomic mass of $\ce{I}$ is $130.906118~u$ and the atomic mass of $\ce{Xe}$ is ...
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3answers
848 views

Solve for Initial Velocity of a projectile given Angle, Gravity, and Initial and Final positions?

I've found equations http://www.physicsclassroom.com/Class/1DKin/U1L6a.cfm for solving everything (and rearranged to solve everything) to do with projectile motion EXCEPT this, even though it should ...
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0answers
145 views

Wave equations for two intervals at Potential step

Lets say we have a potential step as in the picture: In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$. Let me ...