Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright.
11
votes
1answer
571 views
Mechanics + Thermodynamics: Bouncing Ball
In preparation for an exam, I'm revisiting old exam questions. This one seems neat, but also quite complicated:
A soccer ball with Radius $R=11cm$ is inflated at a pressure of $P =9 \times 10^4 ...
9
votes
4answers
363 views
Trace and adjoint representation of $SU(N)$
In the adjoint representation of $SU(N)$, the generators $t^a_G$ are chosen as
$$ (t^a_G)_{bc}=-if^{abc} $$
The following identity can be found in Taizo Muta's book "Foundations of Quantum ...
8
votes
9answers
6k views
What's the core difference between the electric and magnetic forces?
I require only a simple answer. One sentence is enough... (It's for high school physics)
7
votes
3answers
146 views
Where does the extra equation come from to determine the forces from an object on a table?
I have a question about basic statics but somehow I cannot manage to find the answer on my own (btw, this is not a homework. It's been so many years since school for me...).
The problem is very ...
7
votes
1answer
252 views
One strategy in a snowball fight
Here's a common college physics problem:
One strategy in a snowball fight is to throw a first snowball at a
high angle over level ground. While your opponent is watching the
first one, you ...
7
votes
2answers
846 views
Transformation of angles in special relativity
My question is about the problem below
Depicted are two space ships (the USS Voyager and the USS Enterprise), each with velocity $v=c/2$ relative to the space station (Babylon 5).
At the exact ...
7
votes
2answers
271 views
Equivalence principle and radiation from falling particle
I am currently having a hard time solving a problem of GR from Lasenby's book.
I can't make it more clear than by quoting the exercise:
7.2 A charged object held stationary in a laboratory on the ...
6
votes
4answers
3k views
Derivation of self-inductance of a long wire
Currently I am stuck, trying to derive the self-inductance of a long wire. According to literature it should be
$$L=\frac{\mu_r\mu_0l}{8\pi}$$
and in literature its derived by looking at the energy ...
6
votes
4answers
133 views
Integrating radial free fall in Newtonian gravity
I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
6
votes
2answers
144 views
Radioactive Decay
Problem:Nuclei of a radioactive element $\Bbb X$ having decay constant $\lambda$ , ( decays into another stable nuclei $\Bbb Y$ ) is being produced by some external process at a constant rate ...
6
votes
2answers
149 views
Why does the quantum Heisenberg model become the classical one when $S\to\infty$?
The Hamiltonian of the spin $S$ quantum Heisenberg model is
$$H = J\sum_{<i,j>}\mathbf{S}_{i}\cdot\mathbf{S}_{j}$$
I have read that when the spin quantum number $S\to\infty$, quantum fluctuation ...
6
votes
3answers
1k views
Charge density in concentric spheres
Question:
If there are two conducting spherical shells and the inner shell is grounded, what will be >the charge density in the inner shell if there is a charge Q placed on the outer shell?
...
6
votes
2answers
749 views
How do Leptons arise from Lambda decay?
I have a question for an assignment:
Use your understanding of the quark model of hadrons and the boson model of the weak nuclear interaction to explain how leptons can arise from lambda decay, ...
6
votes
2answers
235 views
Conservation of energy in a non-linear oscillator
I have a homework question about a "non-linear oscillator". I actually have an answer to this question, but the answer I get is stronger than what is needed according to the question. The question ...
6
votes
0answers
225 views
exponential potential $ \exp(|x|) $
For $a$ being positive what are the quantization conditions for an exponential potential?
$$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$
with boundary conditions $$ y(0)=0=y(\infty) $$
I ...
6
votes
0answers
224 views
Capacitance of this unusual capacitor
This capacitor is composed of two half spherical shelled conductors both with radius $r$. There is a very small space between the two parts seeing to that no charge will exchange between them.
...
5
votes
3answers
316 views
Why isn't average speed equal to displacement over time?
I'm in an introductory Physics course and I need help!
During a one-hour trip, a small boat travels 80.0km north and then travels 60.0km east. What is the boat's average speed during the one-hour ...
5
votes
2answers
5k views
What is the relationship between kinetic energy and momentum?
I can't seem to figure out the relationship between $E_k$ and $p$ or $F$.
I understand that the units are pretty different. But for example:
A bullet with a mass of 10.0g is moving at the speed of ...
5
votes
3answers
114 views
Horizontal $E$-field for a charged conducting disk
For part of a simulation I am writing, I need to know the electric field emitted from a charged conducting disk. If the disk was laid out in the $x$-$y$ plane, I am interested in the field in that ...
5
votes
3answers
207 views
experimental technique for measuring temperature of an ant
I am taking a course on thermodynamics. I have a question from my text(halliday & resnick,physics-1). They asked me to measure temperature of an ant or an insect or a small body,like a small ...
5
votes
3answers
230 views
Force between two charged rods?
Suppose that we have two rods of length $l_1, l_2$ connected at one end but free to rotate. These rods have charge density $\lambda$ uniformly distributed, so the total charge of rod $i$ is $\lambda ...
5
votes
1answer
5k views
How do you find the uncertainty of an weighted average?
The following is taken from a practice GRE question:
Two experimental techniques determine the
mass of an object to be $11\pm 1\, \mathrm{kg}$ and $10\pm 2\, \mathrm{kg}$.
These two ...
5
votes
2answers
285 views
relativistic acceleration equation
A Starship is going to accelerate from 0 to some final four-velocity, but it cannot accelerate faster than $g_M$, otherwise it will crush the astronauts.
what is the appropiate equation to constraint ...
5
votes
2answers
176 views
Can the process $u\overline{u} \rightarrow s\overline{s}$ be mediated by the EM interaction?
I’m working on a homework problem which asks for the dominant contribution (e.g. EM, strong, or weak) to the process $p + \overline{p} \rightarrow \Lambda + \overline{\Lambda}$).
I know that the EM ...
5
votes
3answers
3k views
Weight on carpet vs. hard floor
Will the scale say I weigh more, less, or the same on a carpet as compared to a hard floor?
You can assume the scale works via spring mechanism. Free body diagrams encouraged!
5
votes
3answers
501 views
Relationship between height and velocity in conservation of mechnical energy
I'm a high school physics student, and we recently did a lab on the conservation of energy where we measured the speed of a marble at varying heights on a rollercoaster track. We were supposed to ...
5
votes
2answers
275 views
Gauge invariant Chern-Simons Lagrangian
I have to prove the (non abelian) gauge invariance of the following lagrangian (for a certain value of $\lambda$):
$$-\frac14 F^{\mu\nu}_aF_{\mu\nu}^a + ...
5
votes
2answers
152 views
Boy and box on ice
I have a troubles. Can you help me?
I have a task, called "slippery activity".
Boy (he has $m=45kg$) Stands at ice and tries to move a big box ($M=90kg$) with a string (rope). Boy's Slip ratio is ...
5
votes
2answers
470 views
High school double lens optics question
This is a first year high school homework question (in the Finnish high school), and I'm having serious trouble solving it. I apologize for possible non-standard terms: I'm doing the translation from ...
5
votes
1answer
180 views
Thermo homework (HW) problem
I do not believe this question can be solved with the thermodynamics knowledge that I have learned thus far, but someone correct me if I am wrong:
A 0.2-m³ tank containing helium at 15 bar and ...
5
votes
1answer
206 views
What is the change in flux through a loop that has been rotated?
We have a number of field lines perpendicular to one loop of wire with an area $A = 10\textrm{ cm}^2$. The magnetic field is$B= 7.2\times10^{-5}\textrm{ T}$.
You turn the loop and the flux decreases ...
5
votes
1answer
184 views
few fermions in a harmonic trap — position density matrix from diagrammatics
I'm trying to calculate the momentum distribution of a 1D system of non-interacting identical fermions in a harmonic trap.
Given Feynman's answer (from his Statistical Mechanics book) for the ...
5
votes
3answers
813 views
Charge Distribution on a Parallel Plate Capacitor
If a parallel plate capacitor is formed by placing two infinite grounded conducting sheets, one at potential $V_1$ and another at $V_2$, a distance $d$ away from each other, then the charge on either ...
5
votes
0answers
126 views
Find $x$ operator given $p$
This is problem $1.2$ of Molecular Quantum Mechanics by Atkins, 4th edition. I'm given the momentum operator
$$p=\sqrt{\frac{\hbar}{2m}}(A+B)$$
with
$$[A,B]=1$$
and I need to find $x$ in this ...
5
votes
1answer
268 views
Lagrangian density for a Piano String
So I'm trying to do this problem where I'm given the Lagrangian density for a piano string which can vibrate both transversely and longitudinally. $\eta(x,t)$ is the transverse displacement and ...
5
votes
1answer
413 views
Magnetic field from a half-cylinder [closed]
I am preparing for an exam, on this problem I had the opposite direction of the magnetic field.
A conductor-cylinder with radius R has been cut in half ($\phi \in [0,\pi]$)
A DC current $I$ runs ...
4
votes
2answers
1k views
Help me get out of a speeding ticket
I was driving uphill from a complete stop for a distance of .4 miles estimated to take 1 minute in a navigation app. I was pulled over right after cresting the hill. The cop had me on radar going ...
4
votes
5answers
358 views
The approximate uncertainty in $r$
The volume of a cylinder is given by the expression
$V=\pi r^2 h$
The uncertainties for $V$ and $h$ are as shown below
$\begin{align}
V&\pm 7\%\\
h&\pm 3\%
\end{align}$
What is the ...
4
votes
3answers
2k views
Why can't a single photon produce an electron-positron pair?
In reading through old course material, I found the assignment (my translation):
Show that a single photon cannot produce an electron-positron pair, but needs additional matter or light quanta.
...
4
votes
5answers
3k views
What would be the effective resistance of the ladder of resistors having n steps
I'm a tutor. This is a high school level problem. In high school, every one have might have solved a problem of effective resistance of a ladder of resistors having infinite steps. Now the problem is ...
4
votes
2answers
830 views
Make a semi transparent mirror with copper
The question:
How would you make a semi transparent mirror (50% reflection, 50% transmission) with glass with a layer of copper. For light $\lambda$ = 500nm Try to be as realistic as possible
What ...
4
votes
2answers
92 views
What's the physical difference between the quantities $\langle v_{i}v_{j}\rangle$ and $\langle v_{i}\rangle\langle v_{j}\rangle$?
What's the physical difference between the quantities $\left\langle v_{i}v_{j}\right\rangle $ and $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle $?
Where $\left\langle ...
4
votes
2answers
204 views
Is the proper interpretation of temperature missing in this book?
In Randall T. Knight’s textbook “Physics for Scientists and Engineers” in the first chapter on thermodynamics (Ch. 16: A Macroscopic Description of Matter) one of the first conceptual questions is ...
4
votes
3answers
238 views
How does capacitance work?
I have a circuit whit a AC source a capacitor and a resistance all in series. I find that the difference of potential between the capacitor leads begin to change after some instants as it should. But ...
4
votes
2answers
147 views
A four-dimensional integral in Peskin & Schroeder
The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660:
...
4
votes
4answers
135 views
How to prove that the symmetrisation Operator is hermitian?
Let $\mathcal{H}_N$ be the $N$ particle Hilbert space. So a quantum state $\left| \Psi \right>$ may be representated by
$$\left| \Psi \right> = \left| k_1 \right>^{(1)}\left| k_2 ...
4
votes
2answers
397 views
Uniform chain falls off table Diff EQ
I really need some assistance setting up this problem. any assistance would be a Godsend:
a uniform heavy chain of length a initially has length ...
4
votes
4answers
2k views
Infinitely charged wire and Differential form of Gauss' Law
I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get
$$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty ...
4
votes
2answers
98 views
Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$
I know how to derive below equations found on wikipedia and have done it myselt too:
\begin{align}
\hat{H} &= \hbar \omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)\\
\hat{H} &= ...
4
votes
2answers
163 views
A wonky gravitational potential and its critical points
I have tough problem I am not sure how to solve:
For this question, we are confined to a plane. Consider a gravitational field that is proportional to $\frac{1}{r^3}$ instead of $\frac{1}{r^2}$, and ...
