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1answer
115 views

Normal Coordinates for Quantum Coupled Oscillators

Thanks if you take the time to read this. Here is the problem statement: The problem I'm getting is that I'm not getting the kinetic energy diagonal when I convert to the coordinates that ...
2
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0answers
179 views

Conservation of energy in a quantum harmonic oscillator after a sudden change in spring constant

At a given instant of time, a harmonic oscillator undergoes a sudden change in spring constant from $k$ to $k'$. Show that for energy to be conserved in the accompanying transition, $\sqrt{k/k'}$ must ...
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3answers
677 views

Basic vector addition problem [closed]

This is the entire problem: A student adds two vectors with magnitudes of 200 and 40. Taking into account significant figures, which is the only possible choice for the magnitude of the resultant? ...
-2
votes
2answers
51 views

Finding out the potential [closed]

According to me, if we want to find out the potential the the equation will be, $$dV = \int \frac{dQ}{4 \pi \epsilon_0 x}$$. But the answer is given is on the basis of $$dV = \int \frac{dQ}{4 ...
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1answer
94 views

Momentum representation of a function with discontinuous derivative [closed]

Consider the following wave packet $$\psi = Ce^{2\pi i p_0x/h}e^{-|x|/(2\Delta x)}$$ where $h$ is the Planck's constant and $C$ is the normalization constant. The derivative of this function is ...
2
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1answer
203 views

Volume quotient in Carnot-cycle

Problem: One kilomole of an ideal, monatomic gas undergoes a reversible Carnot-processes between temperatures 300 °C and 20 °C. The work done during one cycle is 1500 kJ. a) Find the ...
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3answers
766 views

Block and inclined plane (INPhO Problem)

The figure shows two blocks on an inclined plane of mass 1kg each.The coefficient of static as well as kinetic friction is $0.6$ and angle of inclination is $30^\circ$ . Find the acceleration of the ...
0
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1answer
174 views

Simple exercises about U-tubes

I want to solve some exercises involving U-tubes, like You pour two non-mixing fluids with densities that go like 1:2 into a U-tube. The fluid is 5cm higher in one arm than in the other. Where is the ...
2
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1answer
521 views

Deriving an equation involving Killing vectors

I'm currently studying Carroll's GR book Spacetime & Geometry, and ran into some trouble understanding the text. When discussing Killing vectors, Carroll mentions that one can derive ...
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0answers
71 views

Angular Momentum with Upper Index

I am asked to show $[L^2,L_i] = 0 $, but with the definition : $L^2 \equiv L_i L^i$ I tried this: $[L_i L^i,L_i] = L_i [L^i,L_i] + [L_i,L_i]L^i$ We know that : $[L_i,L_i]$ = 0 , so we have, $[L_i ...
0
votes
1answer
87 views

Interpretation of Free Damped Vibrations

I'm studying vibrations; so I'm using Beer-Johnston-Cornwell Dynamics book. I am worry about the equation for Underdamped Vibration, which in the book it is: $$x_{(t)}=x_0e^{-\lambda ...
0
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1answer
167 views

x-coordinate of the ball when it's velocity is perpendicular to projection velocity

We have a ball projected at 20 m/s at an angle $\pi/6$ from the x-axis. Now we have to calculate x-coordinate of the ball when it's velocity is perpendicular to projection velocity. I am thinking ...
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2answers
505 views

Calculate the acceleration of a moving elevator [closed]

An elevator is moving down with uniform acceleration. A man inside the elevator who wants to measure the acceleration drops a coin as soon as the elevator starts. The coin is 6ft above the floor of ...
1
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2answers
58 views

Unitary Confirmation

I am asked to show that an new defined operator: $$U_{\beta} = \exp(\displaystyle\frac{i\beta L_z}{\hbar})$$ is unitary, where $$L_z = -i\hbar\,\,(x\displaystyle\frac{\partial}{\partial y} - y ...
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votes
1answer
107 views

Vector analysis query [closed]

I cannot understand how and why those two expressions are coming (the ones I have highlighted). Please explain.
0
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1answer
92 views

Classical mechanics problem for two boxes [closed]

![enter image description here][2] This question is truly annoying, and I have been stuck for an hour on part D, would greatly appreciate if anyone could shed a light on this problem. Why ans for ...
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0answers
118 views

Calculating journey time of a spacecraft from one planet to another planet

I don't know if this is the correct place to ask =/ I have been trying to make an animation of a spaceship travelling from one planet to another. The animation being this: ...
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1answer
1k views

Cylinder rolling down slope problem [closed]

A uniform cylinder of mass $m$ and radius $r$ is rolling down a slope of inclination $\theta$. The cylinder rolls without slipping. You may take the acceleration due to gravity to be $g$. At what rate ...
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3answers
205 views

Homework question about electric field between two spheres

I was helping a friend of mine with the following question from Knight's book and I was not able to answer part (c). Here is what I think I know: (a) I expect $V_1 = V_2$; the two spheres are in ...
3
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1answer
56 views

Virial of a system

I had obtained $$\overline{E_{kin}} = -\frac{1}{2}\overline{\sum_j\mathbf{r}_j\cdot\mathbf{F}_j}$$ and was asked to show that if the forces are conservative then $$\overline{E_{kin}} = ...
2
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0answers
111 views

How to calculate angular momentum per second for a photon beam? [closed]

Given a photon polarization state $$|\phi\rangle = \frac{3}{5}|x\rangle + \frac{4i}{5}|y\rangle,$$ a beam of photons transmit $N$ photons per second in such a state. An L-polarized photon has an ...
0
votes
1answer
930 views

Calculating a 2D collision between two perfectly circular disks [duplicate]

Assume I have two disks, $p_1$ and $p_2$, of radius $r$, with their own velocities (preferably in $(x,y)$ form, but $(m, \theta)$ works too) and masses (unit-less, but same unit) collide in two ...
2
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0answers
43 views

Acceleration of 2 bodies tied with a string [closed]

Find the acceleration of the block of mass M shown in the figure . The co-efficient of friction between the 2 blocks is μ1 and that between the bigger block and ground is μ2. Could someone help ...
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0answers
22 views

How far will the first spacecraft travel before the second one catches up to it? [closed]

A spacecraft leaves the point of origin and has a maximum acceleration of 30 m/s. It can only maintain this rate for 10 minutes before it runs out of gas and then proceeds to drift at a constant ...
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0answers
46 views

Movement of a gyroscope with non-fixed axis

Assume one has a gyroscope rotating around an axis with both ends leaning on a dedicated semiplane as shown on the picture below. There is no friction either between the rotor and the axis or between ...
5
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1answer
552 views

Orthonormality of Radial Wave Function

Is the radial component $R_{n\ell}$ of the hydrogen wavefunction orthonormal? Doing out one of the integrals, I find that $$\int_0^{\infty} R_{10}R_{21}~r^2dr ~\neq~0$$ However, the link below says ...
2
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0answers
277 views

Loop-the-Loop with Friction [closed]

Let's consider a track that begins vertically becomes a 450 degree loop, and level off. (See diagram) We drop a block from height $H$ that falls and goes around the loop. Ignoring air resistance, ...
1
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1answer
1k views

Uncertainty in Acceleration given the uncertainty in position

I had a motion detector record the position of a dynamics cart and automatically plot Position vs Time and Velocity vs Time plots in Logger Pro on the computer. If the instrument uncertainty in ...
1
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1answer
610 views

Writing a Wavefunction as a Linear Combination of Eigenstates

We have the following wavefunction for the hydrogen atom: $$\psi(r,\theta,\phi)=\frac{1}{\sqrt{4\pi}}\frac{1}{(2a)^{3/2}}\frac{r}{a}e^{-r/2a}\sin(\theta)\sin(\phi)$$ where $a$ is the Bohr radius. ...
1
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1answer
140 views

Resistance and current

I'm not a current student at any school, but I am learning a new profession, and some of it is a basic understanding of elecrticity. I have some knowledge, but definitely not enough, and I have had to ...
3
votes
2answers
125 views

Circumference of a circular path

Suppose a car moves with a constant speed of $20 \text{m/s}$ a quarter of a circle, and completes the quarter in $5$ seconds. One way to calculate the circumference is simply $20 \cdot 5 \cdot 4 = 400 ...
1
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1answer
148 views

Thin lens formula workout method (Query)

In order to workout the method for establishing the formula of thin lens, my teacher says that the optical path is: $PA + AQ = PS_1 + nS_1S_2 + S_2Q$ ($n$ is the refractive index of the ...
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0answers
96 views

Circuit Analysis: Help getting the Thevenin equivalent [closed]

I am attempting to solve this problem which requires me to get the Thevenin equivalent of a circuit, and I've gotten as far as getting the equivalent resistance of the circuit (which I believe is 5 ...
1
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2answers
79 views

Charged spheres - help with method to work these out? [closed]

Can anyone demonstrate how to get the answers to these questions? I'm just interested in the method I need to use in order to obtain the correct answer no matter what the values are. Three small ...
1
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1answer
91 views

Objects falling on Slopes [closed]

An object falls on a slope and then rebounces....and it is known it hits the slope again...how do I calculate it's second point of contact with the slope....how can a projectory equation be used in ...
1
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1answer
313 views

Refraction Vector (Ray tracing)

I am doing ray tracing and I do the refraction of the ray using the following relation (I got it from PDF called "Reflections and Refractions in Ray Tracing"): But I have seen it in another PDF as ...
1
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1answer
86 views

Analytic solution of particle in electric field [closed]

This is homework and I need some guidance. The question I struggle with is: Place a particle with $m=2$ , $q=3$ in a constant electric field $\vec{E}=(5,0,0)$ Choose $\vec{r}(0)=(0,0,0)$ and ...
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2answers
159 views

How to work out the acceleration of an object

I got given this question and im just lost. An object that weighs 25 kg experiences two perpendicular forces of 80N and 50N respectively. What's the acceleration that object gets? What i ...
1
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0answers
112 views

Lenses and Magnification [closed]

A $2.05\text{ cm}$ tall object is placed $30.0 \text{ cm}$ to the left of a converging lens with a focal length $f_1 = 21.0\text{ cm}$ . A diverging lens, with a focal length $f_2 = -42.5\text{ cm}$ , ...
0
votes
2answers
734 views

Friction problem having two blocks on separate inclined planes connected by a string

This is a question I found in my old high-school textbook(I'm revising the topics for a course).Two blocks A and B of masses $1kg$ and $2kg$ are placed on a fixed triangular wedge by a massless ...
2
votes
1answer
64 views

Infinite period in Simple Harmonic Motion

I'm studying the Simple Harmonic Motion, and I am hesitant about, how to get mass values for infinite period? When mass is 0. When mass is infinite. With $\tau=2\pi/\sqrt{k/m}$.
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0answers
267 views

Orthonormality of Radial Wave Function in the Hydrogen Atom

Question: Show that the radial wave function for the hydrogen atom are orthogonal with no exceptions. Attempt: We know that ...
2
votes
1answer
97 views

Textbook Problem: Free energy expression

In Klotz, Introduction to Chemical Thermodynamics, Ex. 8.2 requires me to derive $$ dG = V \left( \frac{\partial p}{\partial V} \right)_V dV + \left[ V \left( \frac{\partial p}{\partial T} ...
1
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1answer
186 views

Math / Physics Help - Barrel Pressure and Velocity

Back in 1993 I derived the following equations to calculate projectile velocity and barrel pressure. Recently, I have noticed that I need to double the calculated results in order to obtain real word ...
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votes
2answers
122 views

Elementary physics question…requires calculus?

A 2500.0kg car is going at a constant velocity of 14.0 m/s and hits the breaks to stop. It skids 25m. What is the coefficient of friction of the tires to the ground? So I have acceleration = -4.0 ...
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2answers
203 views

What does “along the handle of the cart” mean? And how does one calculate weight?

A horizontal force is used to pull a $5.0\text{ kg}$ cart at a constant speed of $5.0\text{ m/s}$ across the floor. The force of friction between the cart and the floor is $10\text{ N}$. ...
0
votes
1answer
126 views

Find current in a nontrivial circuit

Let us assume that we have this circuit: We know that: $$I_1 = I_2 + I_3$$ $$I_1R_1 + I_3R_3 = V$$ $$I_1R_1 + I_2R_2 + \dfrac{q_c}{C_1} = V$$ Therefore we can write: $$I_1 = k_1 - k_2*q_c$$ ...
4
votes
4answers
1k views

Example in the book: A simple accelerometer

A simple accelerometer You tape one end of a piece of string to the ceiling light of your car and hang a key with mass m to the other end (Figure 5.7). A protractor taped to the light allows you ...
2
votes
1answer
132 views

Problem Of Lazy Fish [closed]

Fish achieve neutral buoyancy (so they don't have to swim constantly to stay in place) via a swim bladder. A swim bladder is a little internal sack that they can inflate/deflate with air, which ...
4
votes
1answer
65 views

Problem Of Pumping Rubber [closed]

One can work out by either lifting weights or using a tension band, which is like a big rubber band. If we model the rubber band as a big spring with spring constant $400 N/M$ how far in meters must I ...