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2
votes
1answer
155 views

Strömgren Sphere of Sun

I have a homework problem: The Sun emits $ \sim5 x 10^{23}$ photons per second with $hν > 13.6$ $eV$. If the density of hydrogen atoms in interplanetary space is $n =$ $109 m^{-3}$, what ...
4
votes
1answer
125 views

Integrating Radial Vector Fields

Given a integral $$\int_vd^3{r} \;\vec{r}\;\rho(r)$$ and How do you convert it to spherical coordinate system, noting that $\rho(r)$ is indeed as it is without vector, i.e. it is spherically symmetric ...
1
vote
1answer
85 views

Classical mechanical problem

I have two planes, one characterized by equation $$\phi_1=f(x)-z=0$$ and another $$\phi_2=\alpha y-z=0$$ where $\alpha$ is arbitrary. In their line of intersection(we assume it exist and is continous) ...
1
vote
2answers
406 views

I don't understand the idea of perpendicular vectors being independent of each other?

So problem 71-75 is about vectors. The problem says: A river has a current flowing with a velocity of 2.0 meters per second due east. A boat is 75 meters from the north riverbank. It travels at ...
1
vote
3answers
157 views

A satellite in orbit fires it's engines for a short interval. Is the new orbit closer or further away?

A satellite is in a circular orbit when its engines turn on to exert a small force in the direction of the velocity for a short time interval. Is the new orbit further or closer to the Earth? The ...
8
votes
2answers
266 views

What is the physical meaning of $|f''(\xi )|\leq\frac{4(f(b)-f(a))}{(b-a)^{2}}$ where $f(t)$ is position as a function of time?

Here is the full problem: I was able to prove the given expression; but the interpretation part is giving me a bit of trouble. Here is my interpretation: The average acceleration in $(a,b)$, is ...
1
vote
0answers
240 views

How to calculate the radius of a rain drop with variable mass? [closed]

I need help with the following problem, please help me get started as I do not know where to begin with One spherical raindrop is falling in the atmosphere. Mass of the raindrop increases ...
1
vote
0answers
248 views

Anharmonic oscillator solution function

I am solving a CLASSICAL an-harmonic oscillator problem with Hamiltonian given by $H= (1/2)\dot{x}^2+(1/2)x^2-(1/2)x^4$ with all the constants (k's) and mass being taken as 1 (one). I find that $x= ...
1
vote
1answer
97 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
votes
0answers
174 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 ...
0
votes
1answer
153 views

Filament in a lightbulb, thermal radiation

I'm trying the following: The filament inside a 100 W lightbulb has an absorption coefficient of 0.25, and while operating, it is at a temperature of 2,573 K. What's the size of the surface of the ...
2
votes
1answer
130 views

Possible Outcomes from Measuring a Hydrogen Atom

A hydrogen atom is characterized by the wavefunction $$\mid \psi \rangle =\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$ ...
-2
votes
2answers
48 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 ...
2
votes
1answer
159 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 ...
-3
votes
1answer
74 views

Are all solids mono-atomic? Is there not any di-atomic metals or compounds? [closed]

I want to know whether all solids are mono-atomic or not, and if there was diatomic solids or not,and if there was compounds of solids.
5
votes
1answer
129 views

Force problem related to adhesive and bonding

I have two PCBs (printed circuit board), and they are glued by adhesives, as show in the pictures. And the location of the adhesives are indicated on the picture (please notice that NO adhesive is ...
0
votes
1answer
153 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 ...
0
votes
0answers
70 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
129 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 ...
0
votes
1answer
92 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 ...
-1
votes
2answers
395 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 ...
0
votes
1answer
81 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 ...
4
votes
1answer
160 views

Conserved topological charge for d=3 Yang-Mills. G=U(2)

Consider a pure Yang-Mills lagrangian density $$\mathcal{L}=-\frac{1}{4}F^{\mu\nu}_aF^a_{\mu\nu}$$ with gauge group $U(2)$. Take the generators for $U(2)$ to be $t_0$, $t_i \ i=1,...,3$ with ...
2
votes
1answer
226 views

Probability current vs. direction of wave function

I did an exercise for my Quantum-Mechanics Lecture: Let $\hbar$=2m=1. A particle in 1 dimension has $j(x)=2\ Im(\overline{\psi} (x) \ \psi'(x))$ and it's to show that there are superpositions $\psi ...
2
votes
1answer
470 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 ...
1
vote
2answers
55 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 ...
1
vote
3answers
584 views

A question on Bernoulli's principle

Which is more appropriate regarding Bernoulli's principle fast moving air causes low pressure or lower pressure causes fast moving air.
-3
votes
1answer
103 views

Vector analysis query [closed]

I cannot understand how and why those two expressions are coming (the ones I have highlighted). Please explain.
0
votes
4answers
287 views

How to end up with Newtons in the calculation of the lift force

In another StackExchange Physics question, @Rego had found the following equation to calculate the lift force generated by a simple rectangular blade. $$F = \omega^2 L^2 l\rho\sin^2\phi$$ in ...
0
votes
0answers
116 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: ...
0
votes
3answers
578 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? ...
0
votes
1answer
90 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 ...
0
votes
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 ...
2
votes
0answers
102 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 ...
2
votes
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 ...
1
vote
3answers
201 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 ...
1
vote
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 ...
1
vote
0answers
44 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
votes
1answer
442 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 ...
1
vote
1answer
78 views

Simple QM question about Sy matrix

Given a spin 1/2 particle in state $|\alpha\rangle=\begin{bmatrix}a \\b\end{bmatrix}$, what is the probability of it being measured in the $S_{y+}$ state. Is this equivalent to, if $S_y$ is measured ...
2
votes
0answers
232 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
vote
1answer
474 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. ...
3
votes
1answer
54 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}} = ...
1
vote
1answer
128 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 ...
1
vote
0answers
94 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
vote
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 ...
0
votes
4answers
5k views

Power dissipated in Series versus Parallel

Do two resistors in parallel dissipate more heat per unit time for an applied voltage when compared to two resistors in series?
0
votes
1answer
107 views

Why do I get inconsistent answers with the kinematics equations?

The initial velocity is 14 m/s the final velocity is 0. The distance is 9.0 m and the time is 1.5 s. When solving for the acceleration, why do I get different values when using different kinematic ...
1
vote
1answer
85 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
vote
1answer
255 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 ...