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Relation between speed of sound and compressibility

We know that $c^2=\frac{\partial p}{\partial ρ}$ The adiabatic compressibility is defined as: $\beta_S=-\frac{1}{V}\frac{\partial V}{\partial p}$ such that the subscript "S" stands for "adiabatic" ...
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1answer
220 views

Optimal selection of generalized coordinates in Lagrangian system

EDITED: The number of bonds is actually 2, not 1 (look at edit history). Fixed for archiving purposes. Problem: The edge A of an homogeneous rod (of length $\ell$ and mass $m$) is performing a smooth ...
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0answers
114 views

Need to find the Vab of this circuit! [closed]

Find Vab in the circuit http://imgur.com/IqZ7Yis I uploaded a picture of the circuit. I tried adding 10 and 5 (top) because they appear to be in series. I also added 10 and 15 (bottom two) because ...
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3answers
250 views

Commutators involving functions

I am looking for the commutator: $$[e^{aq},p]$$ My approach is to Taylor expand the function: $$[\sum_n \frac{1}{n!}(aq)^n,p]$$ I know that $[q^n,p]=ni\hbar q^{n-1}$ So how do I account for $n$ ...
4
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1answer
104 views

Simple Commutator question

For some reason this is really tripping me up: $$[q_rq_sp_r,q_sp_rq_s]$$ Where $r$ and $s$ are different. Is this just zero because $p_r$ on $q_s =0$. I am trying to simplify this and I feel like 0 ...
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3answers
337 views

Finding the energy eigenvalues of Hydrogen using WKB approach

I need help to find the energy eigen values of Hydrogen atom using WKB approach. So far I know, the radial equation is given by $$\frac{1}{r^2} \frac{\partial }{\partial r} \left( r^2 \frac{\partial ...
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1answer
90 views

Diffraction problem - How do I interpret

Here is a problem on diffraction - Diffraction pattern of single slit of width 0.5 cm is formed by a lens of focal length of 40 cm. calculate the distance between first dark and next bright fringe ...
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1answer
162 views

Contradiction regarding friction of a rolling cylinder in an inclined plane

I came upon this while wondering whether the friction of a rolling cylinder on an inclined plane depends on the value of friction coefficient. now, $$f\leqq\upsilon N$$ Again after calculating I ...
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1answer
183 views

Frequency of rotating coil

Given a coil initially in the x-y plane, rotating at angular frequency $ \omega $ about the x-axis in a magnetic field in the z-direction. This uniform time varying magnetic field is given by $B_z ...
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133 views

Why does Hydrogen bubbles gather in anode instead of cathode during electrolysis?

Just wondering when water undergoes electrolysis why does oxygen goes towards cathode and hydrogen towards anode why not the other way round
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83 views

Perturbation of a Hydrogen Atom in a Quadrupole Field

Question: A hydrogen atom is located in a quadrupole field, which gives it a perturbation $$H_1=A(x^2-y^2)$$ where $A$ is some constant. Calculate the ...
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3answers
2k views

Why does the tension on the pulley in an Atwood machine not equal $(m_1 + m_2)g$?

Consider the following simple Atwood machine with an ideal pulley and an ideal string According to my textbook, the tension on the clamp that holds the machine to the wall equals $2T$. I don't ...
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1answer
205 views

Synchronizing Pendulums

Assume we have a frictionless pendulum of length $l$ with mass $m$. This pendulum hangs from some weightless contraption, which is itself bolted to a platform. This platform can move horizontally in ...
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1answer
206 views

Electrical Potential Energy and Electric Force [closed]

Under certain circumstances, potassium ions $(K+)$ move across the $8.0 nm$ thick cell membrane from the inside to the outside. The potential inside the cell is $−70 mV$ and the potential outside is ...
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1answer
71 views

Regarding the centrifugal force in a 3-body system

In our lecture about general mechanics, we have treated the simplified 3-body system consisting of the Sun, the Earth and the Moon. We assumed that the moon does not have any influence on the Sun or ...
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2answers
127 views

A question about canonical momentum and arbitrariness for potential in magnetism

The following question confuses me: There exists magnetic field $B_z =- \beta x$ where $x > 0$, and a particle is incident from origin point $(0,0)$ with pisitive charge $q$, mass $m$, and ...
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0answers
37 views

What is $p$ in this candidate solution for the motion of N masses?

In this problem: Consider the system of $N$ masses shown in the figure (see picture 1). a) Using the approximation for small angles, write the equation of transverse movement for the n-th ...
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0answers
22 views

Speed and Velocity Worksheet [duplicate]

What is the formula we use to calculate average speed?
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1answer
191 views

Calculate integral of motion condition with Poisson brackets

Problem statement: The Hamiltonian of a system is given by the formula: \begin{equation*} H = \frac{p_r^2}{2m} + \frac{p_\theta^2}{2mr^2} + V(r,\theta). \end{equation*} Under what condition is ...
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1answer
244 views

Example of application of creation/annihilation operators in matrix form

I was wondering how it would sound like the creation/annihilation of particles that we usually do in the context of Dirac formalism, with matrices and vectors. As a reminder we know that: ...
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0answers
54 views

Problem with experiment results on drag force

I am trying to investigate the relationship between velocity and drag force of falling object in air. I used video analysis from logger pro to determine the displacement of the falling object at ...
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0answers
61 views

Modeling with First Order Equations [closed]

A ball with mass 015kg is thrown upward with initial velocity 20m/s from the roof of a building 30m high. There is air resistance of magnitude v^2/1325 directed opposite to the velocity , where the ...
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1answer
116 views

No valid Feynman diagram for processes

This will likely be easy for anyone experienced in particle physics, but I'm not. I'm asked to explain why it is impossible to construct a valid Feynman diagram using Standard Model vertices for the ...
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1answer
140 views

2D Harmonic Oscillator Commutators

So I am given a 2-dimensional harmonic oscillator with $H=H_1+H_2$ where $$H_i=\frac{p_i^2}{2m}+\frac{1}{2}m\omega^2x_i^2$$ Additionally, $$L=x_1p_2-x_2p_1$$ If we define ...
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2answers
310 views

How do I combine three resistors which are in parallel with each other?

For this circuit (a and b are connected by a battery), Will I be able to find the total resistance of the circuit by adding resistors that are in series and combining resistors that are in ...
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0answers
652 views

Find initial velocity when given max height of 100m [closed]

A ball is thrown straight up. The height of the ball above the ground in (m) is given by the function: $$h(t)=-5t^2 + vt + c$$ What is the initial velocity if you want the ball to reach a max height ...
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1answer
119 views

Uniform Circular Motion Confusion

Having some problems when calculating this problem: A fly lands on an old record player, while a 7'' O.D. 45 RPM record is playing. If the fly lands on the edge of the record, determine the records ...
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1answer
91 views

How to find the equillibrium points using Jacobian and Hessian?

Given that I have Jacobian and Hessian matrices of three particles interacting with each other in a harmonic trap through Coulomb's law in a 2D plane, how do I find the equilibrium points of them (I ...
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1answer
52 views

Using $A = {\lambda}N$ to find when a the amount of a radioactive source becomes constant

The question and mark scheme I will write in bold and my own thoughts in normal sized text. I'm told that: When a $\bf{_{92}^{235}U} $ nucleus is exposed to free neutrons it can absorb a neutron. ...
6
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1answer
227 views

Integral in $n$−dimensional euclidean space

I've asked this question in Mathematics Stack Exchange, but unfortunately there is no answer yet. I repost it because this integral comes from QFT and maybe someone here did it before or could help ...
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1answer
126 views

Slope of a channel

I have a trapezoidal channel like this: The question is to get the slope of the channel such that we have a Chézy coefficient of 64 $m^{1/2}/s$. Given: $B= 76\: \mathrm{m}$, $y = 10\: ...
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1answer
75 views

How to include Damping in a Simple harmonic oscillator

Im designing a model for Kelvin Method. Some of my calculation results are as follows: Radius of the membrane : 50 micron thickness of the membrane : 3.25 micron resonate frequency : 1.32MHz ...
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1answer
147 views

photon polarization, uncertainty in Energy

A beam of red light is sent along the $z$ axis through a polaroid filter that passes only $x$ polarized light. The beam is initially polarized at $30$°, and the total energy is $10$ Joules. Estimate ...
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0answers
219 views

Stationary Perturbation Theory : Estimating higher order corrections for anharmonic oscillator

Note $\hbar = 1$. $$H = H_0 + \lambda V =\frac{p^2}{2m} + m\omega^2x^2 + \lambda m^2\omega^3 x^4$$ Supposedly the perturbation expansion diverges. We are supposed to estimate for what order we have a ...
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309 views

Inclined plane problem

FOR THE GIVEN PROBLEM AND SOLUTION BELOW 1) The problem statement, all variables and given/known data: A student pulls on a box up an incline of 10 degrees. The student pulls with a force of 180 ...
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1answer
117 views

Block on cart, equation of motion

Consider a rigid block of $b \times h$ having mass $m$ on cart (as depicted below). The cart is given an acceleration $a$, this leads to overturning of the block. The angle of rotation is indicated by ...
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2answers
73 views

Why is there no way to make electric field at point P zero by changing quantity and sign of charge of $q_1$? [closed]

q1 = -2.4μC and q2 = 8.9 μC, q3 = 2.3 μC, d is 6.2cm. Suppose that we want to make electric field at point P zero. We leave everything about q2 and q3 as they were before, but we are allowed to ...
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1answer
2k views

Calculate work done in an inclined plane [closed]

How can you calculate the work done by a force (of unknown quantity) exerted on a 10kg block on an inclined plane. The force is pointing upwards and parallel to the incline (which is inclined 30 ...
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0answers
75 views

Spring Force in a Dynamic Equation

I am working on dynamic simulation of a bipedal robot, I have dynamic equations of a preliminary structure. But Now I have to add some springs to the dynamics. I am having a problem of how to account ...
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0answers
128 views
4
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1answer
164 views

Continuity domain for momentum operator

I know this is essentially a mathematic question, but I received no answer on math SE. Moreover it has a direct application in physics, so I thought to ask this here too. The momentum operator in one ...
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1answer
81 views

Oscillator, angular frequency equation

I found the highlighted equation on the Wikipedia on angular frequency, however it doesn't say how it was obtained, could someone please explain that? Also, it says that the spring is massless, if ...
3
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1answer
355 views

If the k of a wave is negative, is the wavelength negative too?

My friend went to an interview for a reputed scholarship program and was asked this question. A wave has an equation $a\sin(\omega t-kx)$. Sometimes k surely can become -ve. We know that ...
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1answer
134 views

Rope on an inclined plane problem

My book says the answer is (a)zero but i don't understand how it came zero. What will the acceleration if horizontal level of the two ends of the rope are different?
1
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1answer
73 views

How to apply conservation of angular momentum with a shock? [closed]

I got this tricky question, need help. A uniform rod of mass $M$ and length $L$ is attached to an axis at its top, a bullet with mass $m$ traveling at speed $U$ (horizontal) hits the rod at $2L/3$ ...
2
votes
1answer
260 views

Is there a better choice of coordinates for a bead on a rotating helical wire?

A bead of mass $m$ is threaded around a smooth spiral wire and slides downwards without friction due to gravity. The $z$-axis points upwards vertically. Suppose the spiral wire is rotated about the ...
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1answer
221 views

Apply Gauss' Law to find Electric Field around nonconducting plastic sheets

The question: Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities $\sigma_1$,$\sigma_2$,$\sigma_3$ and $\sigma_4$ on their surfaces, as shown in the ...
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2answers
106 views

How can I find the amplitude?

Prove that the motion of a mass $m$ on a linear spring with constant $k$, has the form $$y (t) = A \sin(wt+f),$$ where $t$ is the time and $A, w, f$ are constants. We know that for $t = 0, y(0)=y_{0}$ ...
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2answers
148 views

Finding the height of a power-line

Question: To find the height of an overhead power line, you throw a ball straight upward. The ball passes the line on the way up after 0.80sec , and passes it again on the way down 1.5sec after it was ...
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2answers
103 views

Acceleration at two points on a rigid body

The rod AB is falling while sliding on the friction-less wall and the floor. I need to find the acceleration of the points A and B. I am sure that the point A is freely falling, so its acceleration ...