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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How will Decreasing Velocity Affect Time Dilation? [duplicate]

Imagine that we have two observers, named $O_1$ and $O_2$. $O_1$ is traveling at a velocity of $\frac{c}{2}$ for $60$ seconds while $O_2$ is completely still. According to the equation for time ...
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How do I calculate the maximum separation between a chord and arc when I only know the length of each? [migrated]

If I know the length of a chord and I know the length of an arc that both have the same starting and ending points (A and B), how do I calculate the maximum separation between them? (D and D1) What is ...
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1answer
64 views

Proof that $U$ is an unitary operator [closed]

I have a function $f$ mapping a bit onto another bit, i.e. $f : \{0, 1\} \rightarrow \{0, 1\} $. The function f is either constant, so f(0) = f(1) or balanced, so f(0) $\neq$ $f$(1). The quantum gate ...
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2answers
41 views

Independence of kinetic energy with respect to $\rho$ when potential energy is independent of $\phi$

Reference material (free access right now): Shankar On page 81 of Shankar, (paraphrasing) he states that: $ 1: T$, the kinetic energy in polar coordinates, depends solely on $\frac{d}{dt} \phi$ if $\...
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2answers
64 views

Time Dilation + Length Contraction Scenario

I was bored today and went on a random learning binge (I haven't touched this topic before today in a good decade since high school), and got stuck with this scenario I created for myself: [I let ...
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2answers
620 views

Is this a Taylor approximation? How is it done? [closed]

I know what a Taylor series involves but you have to know the function; here $\mathcal{L}^*$ is just a function depending on $(v+w)^2$, any kind of function could be inside. How can the below ...
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1answer
35 views

Functional variation problem in Classical Field Theory (Non Relativistic) [closed]

An exercise of my Homework sheet make a statement about rotational variation on a scalar field $\phi(x)$:\ "Consider a scalar field $\phi(x,t)$ in a lagrangian $\mathcal{L}(\phi, \partial_t \phi, ...
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1answer
59 views

Why can we add in new things into system such that we have symmetry, exploit the symmetry and cancel out the fact that we added more things in end? [closed]

A cube made of insulating material has uniform charge distribution throughout it's volume. Assuming electric potential due to this charged cube at infinitely distant places to be zero, potential at ...
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2answers
60 views

How much energy is required to boil and maintain boiling water temperature for a set time period?

I am trying to calculate the amount of energy required to bring 1 litre of water up to boil (from 20 degrees C to 100 degrees C) and to maintain the water temperature at 100 degrees C for a period of ...
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How can I find the canonical transformation? [closed]

The Hamiltonian is $H=\frac{p^{2}}{2m}-Fq$, where $F$ is constant The transformed Hamiltonian is $K=P$ How do I find the canonical transformation? I know that $\dot{Q}=\frac{\partial K}{\partial P}=1$ ...
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1answer
35 views

How to infer about the volume of the body from measuring the mass of the object in 2 different liquids?

While solving a problem on hydro statics subject I saw a statement that argued that if I know the weight of the object in the air and then I know the weight of the object in the water.so when I ...
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Emf, terminal voltage, lost volt & internal resistance

When we insert neutral copper and zinc electrode in a battery containing $H_2SO_4$ the acid splits up.The hydrogen ions move towards the copper plate and the sulphate ions move towards the zinc plate....
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30 views

Double pendulum equations of motion using Newton's laws [closed]

I need help to understand this problem taken from Mechanical Vibrations by S. Rao I know that the equations of motion could be obtained in various ways, for example using the Lagrangian, but, at the ...
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1answer
32 views

The probability current of the complex scalar field, using the Noether theorem

According to wikipedia, then the Noether current for $$ L= \eta^{\mu\nu} \partial_\mu \phi^* \partial_\nu \phi - m^2\phi^*\phi $$ with invariant transformations: $$ \phi\to e^{i \theta}\phi\\ \phi^*\...
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2answers
91 views

Velocity Time Dilation Confusion [closed]

So I'm trying to understand velocity time dilation, even still after brushing it multiple times throughout university. I am doing so with the example of a spaceship travelling to Alpha Centauri [AC]. ...
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1answer
21 views

Inner product and projection in pseudo-riemannian manifolds

My question is about how to properly compute the projection of a tensor in a given direction using inner product product in a pseudo-riemannian manifold, since inner product isn't defined positive. ...
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2answers
431 views

Getting zero as solution to the 1D wave equation

I was solving an example of 1D wave equation with given BC and IC by separation of variables and Fourier series. $$\frac{\partial^2u}{\partial t^2}=c^2\frac{\partial^2u}{\partial x^2} $$ $$BC: u(0,t)=...
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2answers
133 views

Any boundary conditions missing from this problem? [closed]

Recently I was solving some boundary value problems in Electrostatics. I stumbled upon a problem with an infinitely long cylinder (axis along the $z$-direction and radius $a$) with a plate inside it (...
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4answers
62 views

Energy Conversion - Potential Energy to Kinetic Energy

In what form and by what way is energy converted when i, say lift a block to a height h above the earth's surface. If the said energy, say 5 Joules, is spent in ...
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0answers
13 views

What is the current in the circuit if the LED measures $2$ volts? [closed]

Draw a series circuit with a 6v battery, an LED and a 330 ohm resistor. What is the current in the circuit if the LED measures $2$ volts? I was able to successfully draw the circuit but I am not quite ...
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2answers
51 views

Confusion over the various equations of energy in basic special relativity

I have a fairly longstanding confusion over several different equations involving energy in special relativity and I struggle to see how they relate to each other. $E=mc^2$ $E=\gamma mc^2$ $E=mc^2+\...
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44 views

Variation of the kinetic term in modified gravity

Assume you have an action $S=\int \sqrt{-g}(R+p(X,\phi)) d^4x$. I want to calculate the perturbations for $\phi(t,x)=\phi_0(t)+\delta \phi(t,x)$ and the standard perturbed metric $ds^2=(1+2\Phi)dt^2-(...
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1answer
34 views

Minimum amount of Tritium for fusion reaction producing Tritium

I'm not studying physics. I only worked with basic dynamics and have no idea how to calculate this. It's likely that the answer to the question I'm asking is nonsensical, but, from my point of view, ...
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1answer
34 views

Change in ammeter's indication due to change in resistance [closed]

I stumbled on a problem in a textbook, where I was asked to describe the change in ammeter's indication due to change in resistance in circuit: rheostat's slider is moved or key is locked as indicated ...
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0answers
33 views

Capacity of a capacitor with multiple dielectrics [closed]

The question that I have is how should I calculate the total capacity of the capacitor described in the picture below: I tried taking Air, $C_1$,$C_2$ as parallel capacitors (They should have the ...
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1answer
38 views

How to derive the 2D asymmetric form of free Green function at large distance?

The free Green function: $$G(k)=\frac{1}{k^2+r}$$ I want to derive its form in real space(assuming the most trivial Euclidean metric) : $$G(x)=\int d^D k \frac{e^{-ik\cdot x}}{k^2+r}$$ for two-...
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2answers
109 views

Solutions to wave equation in 1+1D

This might seem like a silly doubt but I am confused about this. For what kind of waves is the wave equation in 1+1D satisfied? $$\frac{\partial^2 f(x,t)}{\partial x^2}=\frac{1}{v^2}\frac{\partial^2 f(...
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2answers
37 views

Interchange of indices [closed]

How to get the second equation, please? My result is wrong - I still have $(N-1)$. Thank you
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1answer
21 views

Problem with formula for cylindrical chandelier problem

The problem says: A cylindrical chandelier is hung on a wire and when it rotates around its siege an angle $\theta$ the twisting moment acting on it is $\tau$ = $−\theta$. The moment of inertia is ...
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3answers
62 views

Is friction different when viewed from a non-inertial frame?

I encountered this diagram when reading an explanation about why the front wheels of cars lift up when they accelerate. The diagram is in the reference frame of the car, so that there is a fictitious ...
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1answer
39 views

How to calculate the precise displacement of an object in projectile motion?

I am curious about how to calculate the precise location of a projectile. Assuming that acceleration due to gravity is $-9.81 \text{ms}^{-2}$, how would you calculate the displacement of a tennis ball ...
2
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2answers
62 views

Velocity of the touching point between 2 rotating circles

I'm trying to solve the following problem that I'm having a hard time with: We have circle ${\Sigma}_1$ with center $O_1$ and radius $a_1$. The center $O_1$ is also the center of the static ...
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2answers
47 views

Apparent depth WITH viewing angle [closed]

So i did one physics problem where I should find apparent depth of 3m deep pool(index between liquid in pool and air is (√7)/2) and we are looking at pool from 30° angle. I go to our favorite friend ...
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1answer
34 views

How to apply Doppler's effect in sound when source or observer is accelerating? [closed]

Q)A parachutist jumps from the top of a very high tower with a siren of frequency 800 Hz on his back. Assume his initial velocity to be zero. After falling freely for 12s, he observes that the ...
3
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4answers
91 views

Why should angular momentum be conserved in this case?

Consider two disks (not friction-less) with some moment of inertia ($I_1$ and $I_2$). Both of them are given angular velocities ($\omega_1$ and $\omega_2$) both in same sense. Now if we bring both ...
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0answers
74 views

Soap bubble with air blown in and charge distributed [closed]

So, I was trying to do this question and here is my attempt: I first tried work out the surface tension forces like so: I did $ F= PA$ $ P = 4 \frac{\gamma}{r}$ by laplace law so, $ F = 16\gamma \pi ...
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1answer
58 views

Internal energy of free two-dimensional electron gas

In our lecture, we had the following scenario: Suppose we have a 2D-free electron gas which is in a magnetic field $B$ perpendicular to the free electron system. Now the electron states have energies ...
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1answer
64 views

Pendulums in inertial and non-inertial frames

If I have a non-inertial frame accelerating with acceleration $A$ with respect to an inertial frame and if I have two pendulums, one in the inertial frame and the other in the non inertial frame, then ...
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1answer
24 views

Impact Mechanics

I have been looking at a paper modelling velocities and accelerations for dropped objects, in this case a perfectly elastic collision for an object hitting the ground. Where $v_1$ is the impact ...
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1answer
105 views

How do I analyse this pulley-trolley system? [closed]

"find a force F such that the blocks are stationary relative to the trolley. All surfaces, wheels and pulley are assumed to be friction-less" 1: This is a very common mechanics problem and ...
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1answer
69 views

Motion with air resistance [closed]

How to tackle real life problems in KINMEATICS in which air drag in some way is involved? I've attached one such problem in which I was stuck.
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1answer
42 views

Feynman Lectures, Chapter 4, Fig 4-3

From the Feynman lectures Chapter 4, Fig 4-3 "We lifted the one-pound weight only three feet and we lowered W pounds by five feet. Therefore W=3/5 of a pound." If there is a change of 3ft in ...
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0answers
31 views

Integral of a Vector [duplicate]

Let's say I have a vector like electric field now to find the electric field due to say a ring all of electric fields have different directions and we take the sin components and cos components in ...
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1answer
51 views

Using integrals in electric field in ring [closed]

When finding the electric field due to a ring. We take on the cos component as the sin component gets cancelled out. Now if we integrate the sin component of the electric field of the sin component ...
2
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1answer
56 views

How to derive Ehrenfest's theorem?

$$\frac{d\langle p\rangle}{dt}=-i\hbar \int_{-\infty}^{\infty}\frac{d\psi^*}{dt} \frac{d\psi}{dx}+\psi^*\frac{d}{dt}\Bigr(\frac{d\psi}{dx}\Bigr)$$ I didn't know the coding of partial derivative which ...
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1answer
30 views

Electron Plasma Frequency

Displayed is the context My question is, why doesn't the electric field from the electrons permeate throughout the cold plasma? Surely there will be flux on the RHS of the boundary as there is an ...
2
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2answers
49 views

What happens if I increase the magnitude of the centripetal force? [duplicate]

Suppose that a particle is in uniform circular motion and the magnitude of the centripetal component of the net force increases. Does this increase the tangential speed or decrease the radius of the ...
30
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3answers
838 views

Is 13 really the answer for the “Devil's problem” in physics (a rolling tube with a rod)? [closed]

Recently I chewed the fat with a physics student and got intrigued by him mentioning "the Devil's problem," which he described as a simply worded mechanics problem that is extremely ...
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1answer
31 views

Current flow rates in capacitors connected in series

In the following question, the capacitor $C_2$ is is initially charged to a potential difference to $2\epsilon$, when the switch was open. The solution to the problem takes the rate of change of ...
1
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1answer
62 views

Gravitational potential energy between a black hole and a mass [closed]

Let's think that there is a black hole with mass $M$ and matter with mass $m$. Two objects have distance $R$. What is the gravitational potential energy between the black hole and the mass? How can I ...