Questions tagged [homework-and-exercises]

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. Please READ THE GUIDANCE IN META before asking homework-like questions.

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22
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8answers
1k views

Shape of a rotating rope with one free-end [closed]

One end of a uniform rope (with total mass $M$) is fixed on the edge of a cylinder. The cylinder has a radius $R$ and rotates with angular velocity $\omega$. The axis is vertical in a gravitational ...
0
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1answer
34 views

“dielectric constant” or “electrical permittivity”?

What are the differences between "dielectric constant" and "electrical permittivity"? By searching on the net, I found permittivity = absolute permittivity, which is the measure of capacitance that ...
0
votes
1answer
70 views

Can a heat pump have efficiency greater than 100%?

A heat pump has an efficiency greater than 100%. Does this violate the laws of thermodynamics? My answer: I'm assuming that "heat pump" means heat engine. $e>1$ $\displaystyle\implies\frac{W}{...
6
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0answers
146 views

Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)

I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
0
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1answer
39 views

Pulley getting pulled [closed]

I cannot seem to figure out the mistake in my work when attempting to solve this problem. I have drawn out the force vectors in this image Now, based on intuition, I know that the block on top will ...
0
votes
0answers
40 views

Diffeomorphisms on Polyakov action

The Polyakov action is invariant under arbitrary transformations of the sort: $$ \sigma^{\alpha} \rightarrow \tilde{\sigma}^{\alpha}(\sigma). $$ How do I show that the metric will transform like a ...
1
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1answer
28 views

Are constraint relations valid on friction

I was doing a question in Newton's laws of motion where I came across this question . The question said there was same frictional coefficient between all surfaces and there is no acceleration of the ...
1
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0answers
30 views

Finding friction on a banked road [closed]

Problem: A turn of radius $20m$ is banked for the vehicle of mass $200kg$ going at a speed of $10ms^{-1}$. Find the direction and magnitude of frictional force acting on a vehicle if it moves with a ...
1
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1answer
37 views

Electric field for two coaxial, infinite thin, infinite long cylinders

Problem: calculate the Electric Field for two coaxial (along z-Axis), infinite thin and infinite long charged cylinders with $r_1 < r_2$ and surface charge density $-\sigma \frac{r_1}{r_2}$ ...
0
votes
1answer
63 views

What would be the direction of force exerted on two stationary posts by pivoting levers which are spring loaded? [closed]

I am having a difficult time with visualizing/determining what would be the direction of force exerted on two stationary metal rods by two pivoting levers which are spring-loaded. To help explain ...
-3
votes
1answer
215 views

How do we find the equation for the gyrating motion of a particle in a uniform magnetic field and a non-uniform Electric field? [closed]

Considering the gyrating motion is not negligible and also retaining the guiding center drift, how do we get the trajectories x(t),y(t),z(t) of the particle? In this case is the variation in the ...
0
votes
2answers
27 views

Amplitude of Shm if Constant External force is applied

In the attached picture, is the spring mass system in equilibrium with a constant force $F$? My question supposes that the system is slightly displaced from equilibrium (let's say to the left). Is ...
3
votes
0answers
56 views

Weyl transformation of Ricci tensor

We define the Weyl transform as, $$ \tilde{g}_{\mu\nu}=\Omega^2g_{\mu\nu}, $$ wherein $\Omega^2$ is a scalar function of space-time $x$. The Weyl transformed Christoffel symbol can be obtained by ...
0
votes
0answers
61 views

Time evolution of harmonic oscillators with changing spring constant [closed]

Let's consider a simple harmonic oscillator with spring constant $k$. It has hamiltonian $$ H=\frac{1}{2}(p^2+k^2x^2), $$ Where $k$ is time dependent. $k=k_0+\lambda t$. Now, imagine that at $t=0$, ...
2
votes
2answers
39 views

Where can pseudo-force be used?

I was doing this question and eventually got the answer but I had a thought :- It being a non inertial frame , can we apply pseudo force on it? But as the question says both are travelling with ...
3
votes
1answer
101 views
+50

Importance of an extra total derivative term in Liouville theory

In this paper on boundary Liouville theory, the authors have introduced an extra term, $-\partial_{\sigma}^2\phi$, (the last term in the equation below) in defining the stress tensor of the Liouville ...
0
votes
3answers
59 views

If the speed of electron (in space) is increased, will the magnitude of current also increase? [closed]

Electrons are emitted by a hot filament and are accelerated by an electric field, as shown in the figure. The two stops at the left ensure that the electron beam has a uniform cross-section. (a) ...
0
votes
1answer
37 views

Deriving enthalpy equation from $c_P$ and $v(T,P)$?

I'm getting frustrated finding my mistake, because I get the exact same answer as my professor, except for a constant. The problem is the following: For a system, we know that $c_P = c + \frac{2aP}{...
2
votes
2answers
165 views

Why is $x^n \psi^{(m)}(x)$ zero at infinity? [duplicate]

Prove: Product of any polynomial of $x$ with $\psi(x)$ or any of its derivatives goes to zero in the limit $x\to\pm\infty$. This comes from a footnote written by the professor in his quantum ...
0
votes
1answer
34 views

Why is this derivation of rotational kinetic energy wrong?

I was trying to derive the rotational kinetic energy of a solid sphere with radius $R$ using the following idea. Each infinitesimally small shell volume $4\pi r^2 \cdot dr$ at radius $r$ within the ...
1
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1answer
47 views

Charges redistribution in Conducting Plates

Lets Suppose there is Conducting plate X and charge Q is given to which means +Q/2 and +Q/2 on each side . Now lets suppose plate Y (uncharged at first) (exactly similar to plate X (area and material ...
-2
votes
1answer
41 views

Pressure variation in liquids with varying densities [closed]

There is a question mentioned in my textbook which is given below Equal masses of three liquids are kept in 3 identical cylindrical vessels A, Band C . The densities are Da,Db and Dc with Da < ...
1
vote
2answers
31 views

Pressure at the bottom of the fluid (fluid mechanics) [closed]

There is a question given my book which is stated below The three vessels shown in figure have the the same base area. Equal volumes of a liquid are poured in the three vessels the force on the ...
1
vote
0answers
38 views

Calculating heat current through a spherical shell [closed]

I have a spherical shell with inner radius $a$ and outer radius $b>a$. There is a temperature difference of $\Delta T$ between the inner and outer shells. The thermal conductivity is $k$. The ...
1
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0answers
45 views

Having some tension about the Tension in Atwood's Machine

I was thinking about how the tension force is equal in a massless String. While the explanation that the String would accelerate crazy, crazy, crazy fast if there was an actual difference makes sense, ...
18
votes
5answers
5k views

Does friction always oppose motion?

Recently I had the following misconceptions: Static friction always opposes the motion of body. The force of friction cannot initiate motion in a body. Now I came to know that my understanding was ...
0
votes
0answers
62 views

Is this a valid solution for the underdamped wave equation?

The loss factor and the wave number are replaced by an expression depended by the damped frequency. Could the last expression be a valid solution for the underdamped wave equation when the initial ...
3
votes
3answers
63 views

Why is mass totally neglected when center of gravity is shifted? [closed]

A square sheet of metal has a square of one quarter of the original area cut from one corner as shown in the figure. Which of the following statements is true about the position of the centre of ...
0
votes
1answer
20 views

Mott Scattering

I had this old homework that I never completely understood. A scatterng experiment is performed with electrons ($E_0=450$MeV) colliding at an atomic nucleus.Following form factor is measured $\left |F(...
0
votes
0answers
35 views

Uncertainty regarding MTW Exercise 3.6 and 3.9

I am currently working through the exercises in "Gravitation" by MTW. I am a little unsure about my approach to Exercise 3.6 and I feel stuck at Exercise 3.9: Exercise 3.6 reads: An observer with 4-...
0
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0answers
16 views

Problem with wind (Doppler Effect)

Mi physics book has a problem that states The C note has a frequency $\nu=261,6$Hz. In an open concert wind blows from the stage to the audience vith speed $v_o=6m/s$.What is thefrequency heard by ...
0
votes
2answers
41 views

The internal energy of a system is a single-valued function of the state variables viz. Pressure, volume, temperature etc

In case of gas, any two of the variables P, T, V are sufficient to define completely its state. Why so?
1
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1answer
46 views

The relation between Chern-Simons Theory and Yang-Mills Theory

So from this page, I know that there is a relation between Chern-Simons Theory and Yang-Mills Theory, but I have difficulty proving the identities in the document. I was going to prove $$\partial_\...
0
votes
1answer
42 views

Soldiers and artillery guns [closed]

I have a question in my homework which says: Soldiers who fire artillery guns never stand behind the gun. Why? What could be some good reasons for this and which of Newton’s laws would cause this ?
-4
votes
3answers
62 views

Electromagnetism Physic [closed]

Hiii guys please help me. The question is that Mary and her friends are camping in Kuala Woh. While they are hiking in the jungle, they lost their way. They have a compass but the marking on it has ...
2
votes
1answer
56 views

Necessary and sufficient conditions for a pure state

I've seen some claims that idempotency ($\rho^2=\rho$) is necessary and sufficient to guarantee the existence of some state $\psi$ such that $\rho=|\psi\rangle\langle\psi|$, as well as claims on the ...
1
vote
1answer
44 views

Compactness of product

Let $Q$ be a position operator and $P$ its conjugate momentum. We would like to show that $f(P)g(Q)$ is compact if $f$ and $g$ are sufficiently smooth operator-valued functions and have compact ...
2
votes
0answers
34 views

Suppose A and B represent two vectors (insame order), the angle between them being 60 degrees, then why is the resultant wrong? [migrated]

Let's say there are three points A,B and C: A represents the displacement between points A and B (4 cm to the east) and B represents the displacement between the points B and C (3cm to the northwest)....
0
votes
0answers
26 views

Heat Capacity for Conduction Electrons in a Metal

This is a problem from one of the past papers that I am doing in preparation a resit exam that is coming up soon: Consider the derivation of the heat capacity for conduction electrons in a metal. a) ...
0
votes
0answers
35 views

Einstein Solid Question

[From The Oxford Solid State Basics by Steven H Simon] (2.1) Einstein Solid a) Classical Einstein ( or "Boltzmann") Solid: Consider a three-dimensional simple harmonic oscillator with mass m and ...
1
vote
1answer
87 views

Relativity and differential equation

I have a question regarding Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973), Gravitation ISBN 978-0-7167-0344-0. It is a book about Einstein's theory of gravitation. In page 166 of ...
0
votes
1answer
33 views

Stuck on determining velocity? [closed]

The main question was: A car travelled 50 metres in 5 seconds with constant acceleration and initial velocity being zero. What will be the velocity after 15 seconds? I tried to solve by this way, $...
-1
votes
0answers
17 views

Dimension of distance travelled in $n$th second and velocity [duplicate]

Why is the dimensional formula of distance travelled by a particle in nth second of time same as that of velocity? It's really confusing for me to understand this, after all it's distance but still ...
1
vote
1answer
42 views

Why is it so that some of the paper pieces get stuck to it while others drop instantly when they stick?

When we rub a comb on our head and held it near pieces of paper then they get attracted because of induced opposite charge.
-1
votes
1answer
61 views

Change in kinetic energy of pendulum [closed]

"An object of mass m is tied to a string of length L and a variable horizontal force is applied on it which starts from rest and pulled slowly until the string makes an angle $\theta$ with the ...
0
votes
1answer
86 views

Mathematical Model for a Pendulum in an Electric Field

I am studying Higher Level Physics and for my Physics IA I am doing an experiment determining the effect of the voltage between two parallel plates on the on the frequency of a pendulum in between the ...
0
votes
1answer
119 views

Neutron capture calculation

So, the problem state is: Neutron beam radiates sample A with initial number of atoms $N_0$. With neutron capture nuclei (cores) of A are transitioning to nuclei B (they are just one neutron richer ...
2
votes
0answers
41 views

Solving the Euler-Lagrange equation with the Axion Lagrangian

I am trying to show that for a constant axion field $\theta(\textbf{x},t)=const.$ the axion Lagrangian $\mathcal{L}_\theta=-\frac{\kappa\theta}{4\mu_0}F_{\mu\nu}\tilde{F}^{\mu\nu}$ does not lead to a ...
0
votes
1answer
24 views

Newtonian mechanics (elevator problem)

The question is to find the reading of the spring balance. I want to solve it without using pseudo forces. What should be the method to go about using relative acceleration from ground frame? It would ...
0
votes
0answers
22 views

Dual of an antisymmetric tensor

Consider the construction of the dual of $F_{ik}$, which is an antisymmetric tensor. The dual is given by the expression $$F^{*lm} = \frac{1}{2} \epsilon^{iklm} F_{ik}\tag{1}$$ The question I'm ...