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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49 views

Pauli Matrices multiplication with indicies

I am trying to write product of Pauli matrices in terms of its indicies. I am trying to find a proof of it. $\sigma^{z}_{\mu \nu}\sigma^{z}_{\alpha \beta}=\delta_{\mu \beta}\delta_{\nu \alpha}$ $\...
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23 views

Under what angle should we kick a ball at the foot of a hill in such a way that it falls back to us? [closed]

Under what angle should we kick a ball situated at the foot of a hill with incline $\varphi$ so it falls back to the starting point? Find the solution for the first rebound. Under what angle should ...
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1answer
38 views

Newtonian Mechanics - Pulley block system, finding acceleration [closed]

The question is to find acceleration of the block m1 in the above system (please look at diagram). So I took tension along String 2 to be T and thus Tension along String 1 would be 2T. Acceleration ...
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1answer
45 views

Are there no convection currents in ice-boxes and aerogel?

Technologies dealt with Ice-boxes have been used for a long time to prevent ice from melting for a longer time than keeping it in open. Aerogel is still an emerging technology (I came across it on ...
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2answers
49 views

Einstein's Calculation (Condensed Matter Physics) [closed]

(From The Oxford Solid State Basics by Steven H. Simon [Chapter 2.1]) Reading through a condensed matter textbook and struggling to see how the author progresses with the calculation in the chapter ...
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1answer
40 views

Which puck has the greatest kinetic energy at the finish line?

The question is: "Two pucks one with mass 3kg and the other with mass 1kg are pushed along a frictionless table with the same horizontal force from rest from the same starting point to the same ...
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1answer
51 views

Having trouble finding fundamental equation from $c_p$, $\alpha$ and $\kappa_T$

I'm having trouble finding que fundamental equation $u$ of a system, since my results don't match those that my professor provides for us. The exercise I need to solve, I think, would be difficult to ...
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1answer
42 views

How to find the equation of motion for a bead of mass $m$ threaded on a circular loop with dynamic friction coefficient $\mu_k$?

I have been working on a particular physics problem but am not sure if I have analyzed it correctly. Here is the problem: "A bead of mass m is threaded on a metal hoop of radius $R$. There is a ...
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35 views

Charge density of infinite sheet of negative charge in presence of external charge

A tiny hole is made in an infinite, conducting sheet of charge. Assume initial charge density to be $-\sigma$. We put a positive charge $+q$ in this hole. Find the charge density of the sheet now as a ...
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24 views

A pendulum consists of a rod with length L and a coin of mass m

A pendulum consists of a rod with length $L$ and a coin of mass $m$. The pendulum is held in a horizontal position and then is released with a minimum velocity needed to make a full circle. What'...
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1answer
35 views

A bar weighs $2N$ and is $5m$ in length. What is the weight needed to balance the bar?

A bar weighs $2N$ and is $5m$ in length. What is the weight($M$) needed to balance the bar? I think I understand that the equation not including the weight of the bar would have $$3*3=(5*1)+(2*M)\...
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2answers
40 views

Why there are three reactions at fixed beam in F.B.D?

It is fixed so no reactions will be present, then how three reactions at fixed beam in F.B.D? In F.B.D, we draw two reactions and moment reaction at fixed beam: Why there are three reactions at ...
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27 views

How small does a hole in a cup have to be to hold water without dripping? [duplicate]

I am creating a drain that lets water in but keeps pieces of plastic out. I need to know the size of a standard water droplet.
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1answer
62 views

Oscillating spring, speed close to the equilibrium: How is this answer not 1.5? [closed]

I have this question with the answer listed as $2.0\,\mathrm{m/s}$. "A $1.25\,\mathrm{kg}$ mass on a spring with a constant of $12.0\,\mathrm{N/m}$ is oscillating back and forth. Its maximum ...
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1answer
28 views

Does magnetic field make particle move in the direction of magnetic field(In circles)?

So my task says A particle with mass $m$ moves freely through space and there is no electromagnetic field. At moment $t = 0$ a uniform magnetic field is turned on with field strength $B$, and ...
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1answer
55 views

Pendulum attached to Oscillating Fulcrum

In the specific scheme, I would expect that by pulling the spring to the right, the pendulum due to inertia would have to move to the left quartile. In order to find the r vector: $$r = R + l$$ and ...
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2answers
112 views

What is the change of entropy for a resistor at constant temperature?

A 10 Ω resistor is held at a temperature of 300 K. A current of 5 A is passed through the resistor for 2 minutes. Ignoring changes in the source of the current, what is the change of entropy in (a) ...
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1answer
27 views

How to determine the error in the kinetic energy of a body when error in it's momentum is given

this is a question from my text book and I tried solving it with the various cases mentioned in the book (such as, if X=m+v then, deltaX = delta m+delta v) but I could not.
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4answers
255 views

When to apply Lorentz transformations and laws of time dilations and length contractions: explanations

In the laboratory we are observing the motion of a particle moving in the positive direction of the axis $x$ of a frame system attached to it. At the initial moment, the particle is in the origin and ...
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1answer
50 views

How to derive the $\Delta$-$Y$ formula for capacitors? [closed]

So, I've found a youtube video that first derives the formula for the resistors and then says the capacitance is the resistance^(-1). I was wondering if that would be the right approach.
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1answer
29 views

Magnetic field of an infinite hollow cylinder (with volume current)

Consider an infinite hollow cylinder with inner radius $a$ and outer radius $b$. The volume current density flows anti-clockwise across the surface of the cylinder ($\vec{J} = J\hat{\phi}$). The ...
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2answers
37 views

Confusion in conservation of angular momentum

Problem statment: A rod hinged at one end is released from the horizontal position. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then find the ...
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1answer
146 views

Magnetic field in a capacitor

If in a flat capacitor, formed by two circular armatures of radius $R$, placed at a distance $d$, where $R$ and $d$ are expressed in metres (m), a variable potential difference is applied to the ...
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0answers
31 views

qm problem with spin,angular momentum and parity

there is a particle A in the state $|J,M\rangle=|1,1\rangle$ where $J$ is the total angular momentum and $M$ the $z$ component, and has parity $=-1$. It decays in 2 particles B and C. B has spin $=1/2$...
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1answer
39 views

Two black holes in rotation - Energy conservation

I was looking at this problem: Let consider two black holes of mass $M$ rotating around a point $O$ (circular montion). The first black hole center is $M_1$, the second $M_2$. Each of them has ...
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2answers
58 views

What is the volume occupied?

What is the volume occupied by 1 mole of gas at $10^{−10}$ torr, the pressure inside an “ultra high vacuum” (UHV) chamber. How do I solve this problem without being given the temperature?
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3answers
50 views

Force between 2 plates of a capacitors , which approach is correct? [closed]

If I have a parallel plate capacitor with charge $Q$, to calculate the force on first plate we say the electric field of $\frac{Q}{2\epsilon_0 A}$ is created by the second plate and since the charge ...
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1answer
36 views

Finding $\mu(T,v)$ and $\mu(P,v)$ from fundamental equation $s(u,v)$

I need to find $\mu(P,v)$ (where $\mu$ is the chemical potential) and $\mu(T,v)$ for a system whose fundamental equation in the representation of entropy I do know. All the information I have is that ...
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2answers
35 views

Angular momentum and Gyroscopic precession of a top [closed]

A top is spinning in the counterclockwise direction as seen from above. Its axis of rotation makes an angle of 15º with the vertical. If frictional forces can be neglected, which of the following is ...
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0answers
26 views

Deriving expressions for momentum in relativistic elastic collision

I have the following question from D'Inverno book 'Introducing Einstein's Relativity': A particle of rest mass $m_0$, energy $e_0$, and momentum $p_0$ suffers a head on elastic collision with a ...
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0answers
31 views

How long does it take for this coil to stop? [closed]

Let's suppose there's a horizontal and uniform magnetic field $B$, and we introduce from below the field a square coil of mass $m$, side length $a$ and resistance $R$ in it with a inicial velocity $...
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1answer
67 views

Hard problem on dipole with $r^7 $ in denominator, I don't know how or why? [closed]

In an external electric field, a molecule is polarized. The dipole moment induced is given by $\vec P =\alpha \vec E$, where $\alpha$, is the polarizability constant and is a positive constant and $\...
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1answer
35 views

Change in potential energy of a parallel plate capacitor as a dielectric slab is moved in the space between plates

I was doing this question: If a parallel plate capacitor made of square plates of side L and separation D is connected to voltage source V. And then a dielectric slab of width D is introduced ...
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4answers
73 views

How does Newton's 3rd Law apply to arm wrestling? [duplicate]

I understand that when we refer to Newton's third law, forces do not cancel out because action-reaction pair forces are acting on different objects. I tried to apply this to arm wrestling, but I am a ...
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0answers
64 views

How to solve these coupled differential equations?

I am trying to solve for wavefunctions of 2D tilted Dirac systems, the Hamiltonian for which is: $$\hat H = v_{x}\sigma_{x}\hat p_{x}+v_{y}\sigma_{y}\hat p_{y}+I_{2}(v_{t}^{x}\hat p_{x}+v_{t}^{y}\hat ...
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0answers
32 views

Does the potential difference between two points remain the same if there spatial location is changed?

I was working through this particular homework problem. Where I am required to find out the current flowing through the resistor A (4 ohms). First of all I saw that the 2 resistors were in parallel ...
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3answers
89 views

Deriving SHM equation

i have derived SHM equation till here $$\sin\left( \frac{\sqrt k}{\sqrt m}\cdot t \right)$$ Now all the solutions (youtube and textbook) I'm looking are just stating intuitively $\frac{k}{m} = \text{...
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0answers
36 views

Phase of free neutron in a magnetic field

Let's consider two cases: A neutron with a spin fixed along $\hat{z}$ moves along $x$ with constant momentum $\vec{p} = p_0 \hat{x}$ under the influence of a magnetic field $\vec{B} = B_0 \hat{z}$. ...
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0answers
60 views

Tensor Notation - David Tongs Notes [duplicate]

I'm trying to understand the Maxwell's Equation example from David Tongs QFT notes. He uses the Lagrangian: $$ L = -\frac{1}{2}(\partial_{\mu}A_{\nu})(\partial^{\mu}A^{\nu})+\frac{1}{2}(\partial_{\mu}...
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0answers
14 views

How to calculate the differential cross section in the center-of-mass frame for a process $AB \rightarrow CD$?

I'm trying to do Exercise 4.2 in Halzen, Martin's "Quarks and Leptons" In the center of mass frame for the process $AB \rightarrow CD $, show that $$\begin{array} { c } { d Q = \frac { 1 } { 4 ...
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1answer
43 views

Deriving Planck's Constant from Wien's Displacement Law

So I'm reading an introductory book on Quantum Theory (David Park, 3rd ed.) and I am having trouble with the following question: "According to Wien's displacement law, the wavelength $\lambda_m$ at ...
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1answer
21 views

Difference between 'white light' and spectral light for rings of Newton

In my book of waves and optics, there's a chapter about the rings of Newton and as a question there is: how is the interference pattern when we use white light, considering me it's : there are rings ...
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0answers
50 views

Proving Poisson bracket relations $\{\phi, P^r\}=\Pi^r$ in Ticciati's “QFT for Mathematicians”

Let $\phi$ be a scalar field, and $\Pi$ be the conjugate momentum of $\phi$. Let $\cal L=\cal L(\phi, \partial_\mu \phi)$ be the Lagrangian density. Define the stress-energy tensor as $$ T^{\mu\nu}=\...
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0answers
67 views

Time after which the 3 particles will meet? [closed]

Problem is from Classical Mechanics: I am a beginner in Physics trying to understand the solution to the given below problem. Problem Statement: 3 particles are placed at the vertices of an ...
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1answer
76 views

Prove that a transformation is canonical by using $\mathbb{M}^T\cdot \mathbb{J}\cdot \mathbb{M}$ [closed]

So, I was given the following problem to solve: A system with two degrees of freedom is described by the following hamiltonian \begin{equation} H=p_1^2+p_2^2+\frac{1}{2}(q_1-q_2)^2+\frac{1}{8}(...
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3answers
34 views

The Lagrangian for gravitational potential energy in a double pendulum

For a double pendulum what would be the gravitational energy. I am trying to work out the Lagrangian for the double pendulum. I got the kinetic energy but I am struggling on the gravitational ...
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1answer
44 views

Damped forced Oscillation with variable external frequency

Consider that we have the following forced vibration with an input frequency $ω(t)$ variable in time. $$m\ddot{x}+c\dot{x}+kx = F_0 \sin{(\omega(t) t)}$$ Assuming that the solution must be a ...
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2answers
60 views

Hamiltonian in Piers Coleman - Introduction to Many-Body Physics book

In the book "Piers Coleman - Introduction to Many-Body Physics (2016, Cambridge University Press)" in page 491 When an electron pair is created, electrons can only be added above the Fermi ...
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1answer
30 views

What are typical atomic densities of solids and gases? [closed]

What are average values for the number of atoms per cubic cm for typical solids and gasses at atmospheric pressure?
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0answers
33 views

Seeking affine reparameterization of a curve [closed]

A ray of light propagates along the straight line $$x(p) = \frac{p}{\sqrt{3}}$$ $$y(p) = \frac{p}{\sqrt{3}}$$ $$z(p) = \frac{p}{\sqrt{3}},$$ where $p$ is a parameter. Reparameterize this curve with ...