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2
votes
2answers
80 views

Integration of 3-momentum

During a lecture that I missed, I was trapped when the lecturer uses the relation $$dp_x~ dp_y ~dp_z ~=~d^3\mathbf{p} ~=~ 4\pi p^2 dp.$$ Can I know how is this relation derived please?
0
votes
1answer
86 views

Vector Summation [closed]

When two vectors are sketched from a single point, the angle between them is θ. Show that the size of their vector summation is given in the expression: $ \sqrt{A^2 + B^2 +2ABcosθ} $. Any ...
-4
votes
2answers
357 views

Basic Physics Question [closed]

I'm having a difficult time answering this question. I think I'm just converting the units wrong somewhere: You're the CEO of a courier company, and you decide to select an electric car for your ...
2
votes
2answers
126 views

Scalar QFT Fock Space

I want to demostrate the following relation of the normal ordered product: $\Omega\equiv:\exp{\left(-\int d^3k~a^{\dagger}(k)a(k)\right)}:=|0\rangle\langle0|.$ I proved the commutation relation ...
0
votes
1answer
96 views

How does volume of water in closed system relate to humidity at 25(C) degrees

If I have a closed system with a volume of 100L, at ~24(C) or ~75(F) degrees, what volume must be filled with water to reach a humidity of 90%? I imagined if you fill it 100% with water, humidity is ...
0
votes
1answer
78 views

Loop Rule Parts Problem

[Loop Rule Diagram] The problem is thus: Apply the loop rule to abcdefghia and find the expression which adds to zero. I tried this, but I was not able to get it correct. I know that when crossing ...
2
votes
2answers
258 views

Would this box on the floor rotate based on friction?

There is a floor that friction is proportional to its velocity (like $F=-kv$) and there is a box with its width as $l$ and its height as $h$. (you may assume that $l$ is longer than $h$). It is on the ...
0
votes
3answers
3k views

Calculate average acceleration without time? [closed]

I have a question about a flea jumping, for which I need to show that the average acceleration is around 1000 $ms^{-2}$. I know that to calculate average acceleration you can use $\frac{dv}{dt}$, ...
2
votes
3answers
5k views

How to establish relation between flow rate and height of the water column of the tank?

Suppose a water tank has 1" diameter drain at the bottom and is filled with water up to one meter height above the drain. What time it will take the tank to drain out completely. Now say, the tank is ...
1
vote
1answer
147 views

Finding the tangential force experienced by a bob of mass m on a simple pendulum via the gradient/nabla operator)

The problem was posed as follows. Given a pendulum of length $L$ with a mass $m$ attached to it, which forms an angle $\theta$ from the y-axis to the direction of swinging. First we had to find the ...
1
vote
1answer
127 views

Doubt in solving question related to photoelectric effect?

Question:- When a beam of $1.06eV$ photon of intensity = $2.0 W/m^2$, falls on a platinum surface of area $1.0*10^{-4}m^2$, and work function $5.6eV$, $0.53$% of incident photons ejected photo ...
-2
votes
0answers
39 views

Mathematical physics help appreciated [closed]

Is anyone able to help me answer the following questions? What is the method? a) Monochromatic light is incident on a slit of width 0.200 mm. On a screen 1.43 m beyond the slit, the first-order dark ...
1
vote
2answers
750 views

Determing time to complete known distance with constant acceleration [closed]

Answer: $a=v^2/d$ is the formula I needed. This is a problem in a programming assignment, I haven't taken physics. I have a starting speed (0 m/s), an final speed (208.33m/s) and the distance it ...
0
votes
1answer
215 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: ...
2
votes
1answer
243 views

Given wave function at $t=0$, what is the process of deriving time dependent wave equation? [closed]

Suppose $$\Psi (x, t=0)=Ae^{i\alpha _1}\psi _1(x)+Be^{i\alpha _2}\psi_2(x)+Ce^{i\alpha _3}\psi_3(x).$$ If $\psi _n$ are the energy eigenfunctions how would I derive $\Psi (x,t)$? I am having trouble ...
1
vote
1answer
194 views

How to determine the positions of two points in a radial line by an intensity level dB?

The following is the question from my school. A source emits sound uniformly in all directions. A radial line is drawn from this source. On this line, determine the positions of two points, 1.00m ...
0
votes
1answer
144 views

Antimatter collision - Energy Released

I think it's about time for me to ask this question, as I've been contemplating this for a while. $$E = mc^2.$$ This is Einstein's most famous equation. But what does it mean? On my own, I had to ...
2
votes
1answer
905 views

Overlap integral and probability

I have a question regarding how to extract probability from an overlap integral. Specifically, I am calculating the probability of a particle in a bound state in a delta potential $V=-\alpha ...
4
votes
1answer
78 views

Problems with dimensions when solving an ODE

I'd like to solve the following differential equation: $$\frac{dQ}{dt}=\frac{k_BT}{m}-\frac{\alpha Q}{m}$$ where $Q$ has units of $\text{m}^2\text{s}^{-1}$, $k_B$ is Boltzmann's constant, $T$ is ...
1
vote
1answer
773 views

Calculating the frictional force

Here's my problem and the work I've done. The time is already past for me to submit the answer, but I want to know where I went wrong and why I was wrong. The 2-kg box slides down a vertical wall ...
1
vote
0answers
65 views

Can I transfer electricity through induction?

If I place a solenoid connected to a bulb inside a bigger solenoid which is connected to a power source, will the bulb glow?
1
vote
0answers
355 views

projectile that splits into two fragments of equal mass

I am studying for an exam, and this is part of a problem in my book. A projectile is launch from level ground and is intended to hit a target 100m away. Instead, it explodes into two fragments of ...
7
votes
2answers
199 views

A problematic integral in calculating the entanglement entropy in 1+1 D free massive bosonic field theory

I encountered a curious integration identity when I was reading the paper by Pasquale Calabrese and John Cardy on the entanglement entropy of 1+1D quantum field theory (arXiv). The identity is given ...
-1
votes
2answers
112 views

Vectors question? [closed]

I am stuck on this vectors question I have for home work. Does anything think they can help point me in the right direction on how to solve this? An explorer is caught in a whiteout (in which the ...
1
vote
1answer
168 views

Coulomb force on the center of a hexagon?

Six point charges $q$ are at the corners of a regular hexagon that has sides of length $a$. What is the force on another charge $Q$ which is located in the center of the hexagon? What is the force on ...
0
votes
4answers
3k views

Finding equivalent resistance in complex circuit

In my previous Phys.SE question, situated here, I asked about finding the equivalent resistance of the following circuit : I got some very good answers and some tips. Now what if the same circuit is ...
1
vote
1answer
194 views

$t_1$, $t_2$, $t_3$ Hermitian generators of $SU(2)$

What is the exact $SU(2)$ representation to which these Hermitian generators belong? \begin{equation} t_a=\{t_1,t_2,t_3\}=\left\{\frac{1}{\sqrt{2}}\begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & ...
3
votes
5answers
361 views

Ball rolling into a bowl - where is its maximum KE (speed)… given there is friction. See diagram

Please examine this diagram and answer the apparently trivial questions. I am particularly interested in reasoned answers for part (a)(ii) - where is the maximum Kinetic energy? I say it is at B ...
1
vote
4answers
423 views

Lead in ice block

This is a strange question I would like to have some explanation accompanied with: We have an ice block, with in it a lead block. This entire block is put into a glass of water, resulting in a rise ...
1
vote
3answers
389 views

Simple Quantum Mechanics Question about The Commutator of Translation Operators

Say there is $\hat{J} = \exp[-i \hat{p} l/ \hbar]$ and $\hat{U}= \exp[-i\hat{H}t/ \hbar]$, where $\hat{H}$ is time-independent. Can we say anything about $[\hat{J},\hat{U}]$? Is it zero? How do we ...
3
votes
1answer
1k views

Example where angular momentum and angular velocity are not parallel

I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel.
0
votes
1answer
138 views

taking the trace

could anyone show me the first couple of steps in taking the trace of something like this, im not sure how to start. 'Tr[$\gamma($$\gamma k + $$\gamma p + $$\gamma q + m) $$\gamma ($$\gamma k + ...
1
vote
2answers
71 views

Capacitor's voltage

Imagine I have two plates that form a capacitor, so the magnitude of the charge in each plate is, let's say, $Q$. So, the force, in respect to the distance $d$, is gonna be: $$F(d) = ...
5
votes
3answers
255 views

Calculating the uncertainty of $r$, when $1/r^2$ is used

I have tried to search through the forums and the Internet, however I haven't been able to find a source I was able to understand fully. I have a distance $r$, with an uncertainty of $\mathrm{±\ ...
1
vote
1answer
70 views

Spring with changing equilibrium

Suppose that we have two cars on a track, each with a different mass. Now suppose that the cars are connected with a spring. We smack one car. I would like to write down the equations of motion for ...
5
votes
1answer
285 views

Quantum tunneling effect in a potential of the kind $V(x)=A\frac{x^2}{1+x^4}$

Given a potential: $$V(x)=A\frac{x^2}{1+x^4}$$ with $A\gt 1$ and a quantum particle inside the well around the point $x=0$. I'm stuck on the calculation of the transmission and reflection coefficients ...
2
votes
1answer
242 views

Lorentz Force Law and cycloid motion

The question I have is from Intro to Electrodynamics by Griffiths (Page 206, Example 5.2) http://imgur.com/a/sfBlt When using the initial conditions $y(0) = z(0) = 0$, I get: $y(0) = 0$ implies ...
1
vote
1answer
170 views

Is this a series or parallel connection?

I am confused how the capacitors in this circuit are connected. $C_4$, $C_6$ and $C_5$, $C_3$ appear to be parallel, but both $C_4$ and $C_6$ seem to be in series with $C_1$ as do $C_5$ and $C_3$. Am ...
3
votes
1answer
82 views

Van der Waal's gas satisfies $U = \int_{0}^T C_VdT - a/V + K$ (constant)

I need to show that a Van der Waal's gas satisifes $$U = \int_{0}^T C_VdT - \frac{a}{V} + K$$ where $K$ is constant. The equation of state of a VDW gas is $$\bigg(p + \frac{a}{V^2}\bigg)(V - b) ...
0
votes
1answer
85 views

About the three point function at one loop order

Could someone explain how exactly do you calculate the trace of the three point function of one loop in QED. in the following link the expression from 1. a (2) ...
2
votes
1answer
81 views

How to derive following thermodynamic relation?

I'd would like to derive the following $$\bigg(\frac{\partial U}{\partial V}\bigg)_T = T \bigg(\frac{\partial p}{\partial T}\bigg)_V - p$$ What I know is that the internal energy $U$ is a function ...
1
vote
3answers
200 views

Coordinate transformations of the metric tensor

Let's have metric (it describes the space-time of uniformly accelerating observer in Minkowski space-time) $$ ds^2 = v^2du^2 - dv^2. \qquad (.0) $$ I need to find expressions for $u = f(x, t), v = ...
1
vote
1answer
42 views

Decrease in Intensity [closed]

A beam of particles pass through a target made of thin foil of a very small thickness $\Delta x$ having $N$ particles per unit volume. Let the collision cross section be $\sigma$ . If the intensity of ...
0
votes
0answers
185 views

Current Carrying Wire Loop near Current Carrying Long Wire

A rectangular wire loop of (width $a$ and height $b$) carrying clockwise current $I_1$ is a distance $d$ below a horizontal infinitely long wire carrying a current $I_2$ to the right. What is the ...
1
vote
3answers
699 views

Calculate for Multiple Resistors with a Bridge

Background A circuit is constructed with five resistors and a battery as shown. The battery voltage is V = 12 V. The values for the resistors are: R1 = 78 Ω, R2 = 150 Ω, R3 = 132 Ω, and R4 = 83 Ω. ...
2
votes
0answers
198 views

How should I think about reciprocal lattice and Miller indices?

When I hear someone talking about a (100) plane or a (111) plane or an (hkl) in general, my first thought is, is the system cubic. The reason I think this is because I tend NOT to think of the planes ...
0
votes
3answers
203 views

Projectile motion formulas

Assuming: The equations for the vertical and horizontal components of my initial velocity. Are: $v_{x,i} = v_i \cos\theta$ and $v_{y,i} = v_i \sin\theta$ And the displacement components are ...
1
vote
0answers
127 views

A basic question about Heisenberg State Kets (in particular the simple harmonic oscillator)

I know base kets in the Heisenberg picture are $U^\dagger |{a}\rangle$ but if the base kets are the base of the hamiltonian, and the hamiltonian is independent of time, are all of the base kets ...
1
vote
0answers
31 views

Trouble evaluating an integral arising from particle collision

Assume we have two charged particles colliding. He have particle 1 with mass $m_1$, charge $Z_1 \cdot e$ which travels in $x$-Direction passing by a STATIONARY particle 2 (mass $m_2$, charge $Z_2 ...
4
votes
1answer
819 views

Wien's displacement law in frequency domain [duplicate]

When I tried to derive the Wien's displacement law I used Planck's law for blackbody radiation: $I_\nu = \frac{8 \pi \nu^2}{c^3} \frac{h \nu}{e^{h\nu/k_bT}-1}$ Asking for maximum: $\frac{dI_\nu}{d ...