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0
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1answer
70 views

Finding resultant and direction of resultant

In this question- A motorboat is racing towards north at 25km/h and the water current in that region is 10km/hr in the direction of 60 degree east of south. Find the resultant velocity of the ...
0
votes
0answers
43 views

Plank stopping time

Problem: A plank of length $L$ and mass $m$ lies on a frictionless floor, if the plank has an initial velocity $v$, what is the stopping time of the block if it meets a floor with friction constant ...
0
votes
1answer
193 views

Toppling of a cylinder on a block

A uniform cylinder rests on a cart.The height and diameter is given.coefficient of static friction is given.How can i find the minimum acceleration of block such that the block topples? Morever what ...
0
votes
1answer
196 views

Free body diagram of rod in sphere

I was finding the free body diagram part of dynamics quite easy until I found this question , Here's how it goes : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw ...
0
votes
1answer
474 views

Rigid bar suspended by two ropes, tension of first rope after second rope is cut?

This is from a practice exam, I've been sitting here thinking about it for over an hour and can't convince myself of an answer, or write down any relevant exact equations. A bar of uniform density ...
-1
votes
0answers
30 views

Determine change in entropy - Please verify [closed]

Suppose 30 gram of metal gallium melts at 36°C. The melting temperature is 29.9 °C and specific heat of fusion is 80.3 kJ/kg. Explain if the melting of the gallium in this process is reversible or ...
-1
votes
1answer
337 views

Speed of a falling pencil [closed]

If you balance a pencil of length $d$ on its tip, and let it fall, how do you compute the final velocity of its other end just before it touches the ground? (Assume the pencil is a uniform one ...
-2
votes
2answers
3k views

Newton Laws of Motion + Effective spring Constant [closed]

! Can someone please help me in solving this question: What is the effective spring constant for the system of the two springs, perfect pulley, and string shown on the left for it to be modeled ...
8
votes
5answers
1k views

How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
6
votes
1answer
813 views

Lorentz Invariant Integration Measure [closed]

When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by $$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$ How can I show that ...
5
votes
0answers
219 views

Hamiltonian function for classical hard-sphere elastic collision

I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at x = 0. Everything I've read on the topic (e.g. this ...
5
votes
1answer
346 views

Do mutual eigenkets imply commutation of two operators?

I have been working on this question. I have solved it, and I would like to check whether my line of reasoning is right or wrong Question: Prove that if there exists a mutual complete set of ...
5
votes
1answer
287 views

Divergence theorem in complex coordinates

This question is related to Stokes' theorem in complex coordinates (CFT) but, I still don't understand :( Namely how to prove the divergence theorem in complex coordinate in Eq (2.1.9) in ...
5
votes
2answers
159 views

Generalizing a relativistic kinematics formula for spatial-acceleration dependence

I'm starting from this expression $$ \alpha dt = \gamma^3 dv $$ where $\alpha$ is proper acceleration of a point particle, $dv$ and $dt$ are coordinate differentials of velocity and time, and ...
4
votes
4answers
836 views

Can we add any two vectors?

Can we add any two vectors? If not, why is that so? I think this is not true, but I am not sure. My book says it is true, but I guess it is a misprint. For example, adding acceleration to velocity.
4
votes
3answers
201 views

Using 2D position, velocity, and mass to determine the parametric position equations for an orbiting body

I have a gravity-related question. I am programming an orbit simulator. I have everything up and running, but I would like to render the smaller body's orbital path (the larger body is fixed). To do ...
4
votes
1answer
958 views

Electric Field from Dielectric Shell

This is a question taken from a past E&M exam A thick spherical shell (inner radius $R_1$ and outer radius $R_2$) is made of a dielectric material with a "frozen in" polarization ...
4
votes
4answers
1k views

Why do we take small steps while walking on ice?

When we walk on ice we should take small steps. Small steps ensure: a.)larger friction. b.)small friction. c.)larger normal force. d.)smaller normal force. The correct ...
4
votes
1answer
103 views

Photon Escape Angle From Black Hole

Consider a photon source emitting photons near the surface of a Schwarzschild black hole. What angle, as a function of the source's radius from the event horizon, must the photons be emitted at such ...
3
votes
0answers
187 views

Wald problem 4 of chapter 4

I'm trying to derive equation 4.4.51 in Wald's GR book (the second order correction in $\gamma$ term for the Ricci tensor): where $g=\eta+\gamma$. So ...
3
votes
1answer
347 views

Fermi-Dirac distribution derivation?

I am trying to derive the Fermi-Dirac statistics using density matrix formalism. I know that $$<A>= Tr \rho A.$$ So I started from $$<n(\epsilon_i)>= Tr \rho n(\epsilon_i)=\frac {1}{Z} ...
3
votes
2answers
150 views

Proper Time with a non-zero Initial Velocity

I have a question regarding how to find the proper time for a body with an initial velocity to slow down to 0. For example, the equation I have been working with looks like: $$\int^\tau_0 ...
3
votes
2answers
422 views

Geodesic equations

I am having trouble understanding how the following statement (taken from some old notes) is true: For a 2 dimensional space such that $$ds^2=\frac{1}{u^2}(-du^2+dv^2)$$ the timelike geodesics ...
3
votes
1answer
479 views

Schrödinger equation for a harmonic oscillator

I have came across this equation for quantum harmonic oscillator $$ W \psi = - \frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + \frac{1}{2} m \omega^2 x^2 \psi $$ which is often remodelled by defining a new ...
3
votes
2answers
3k views

block slides on smooth triangular wedge kept on smooth floor.Find velocity of wedge when block reaches bottom

Find the velocity of the triangular block when the small block reaches the bottom: Here is what I did: The final velocity(at the bottom)of the small block of mass m is $\sqrt{2gh}$ along the plane ...
3
votes
1answer
451 views

Lab observation correct? As distance decreases, velocity increases, stderr decreases

The experiment goes like this: Allow a moving cart to move from the top of an incline plane ($x_0$) downwards. The time taken will be recorded by the picket fence (those things you see wired up). ...
3
votes
2answers
1k views

First integral of an equation of motion: $\mu\ddot r=-\frac{k}{r^2}$

I've got an equation of motion (EOM), which is $ \mu\ddot r=-\frac{k}{r^2} $ How do I find the first integral of this EOM? I'd appreciate it if someone could show me the steps involved. I should ...
3
votes
2answers
148 views

Derivatives of delta function and equation of continuity for a single charge…

For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are fiven by: \begin{equation} \rho(\textbf{r},t)= ...
3
votes
3answers
422 views

Braking distances on a rainy road

I am curious to find the braking distance for a car on a road. In attempting to find this out, I found that the braking distance for a car (on a flat road) is $$ d = \frac{v^2}{2\mu g} $$ where ...
3
votes
2answers
1k views

What potential energy functions are mostly used in Schrodinger equation?

In the time-independent Schrodinger equation $$\left(-\frac{\hbar^2}{2m}\Delta+V(\mathbf{r})\right)\psi(\mathbf{r})=E\psi(\mathbf{r})$$ What functions $V(\mathbf{r})$ are mostly used in research ...
3
votes
2answers
2k views

Simple harmonic motion problem

Problem: An object is undergoing simple harmonic motion with period 1.2s and amplitude 0.6m. At $t=0$, the object is at $x=0$. How far is the object from the equilibrium position when $t=0.480$s? ...
2
votes
1answer
60 views

The relation between energy quanta of an Einstein solid and the equipartition value of heat capacity

Consider an Einstein solid with quantized energy values $U=q\epsilon$ and $N$ oscillators. I calculated some values of an Einstein solid numerically through a function in R (at the bottom of the ...
2
votes
1answer
126 views

Relation between electric potential and wavelength of an electron

"An electron that is accelerated from rest through an electric potential difference of $V$ has a de Broglie wavelength of $\lambda$. Investigate the relationship between $V$ and $\lambda$." I had two ...
2
votes
1answer
175 views

RMS Free Path vs Mean Free Path

I am trying to determine the mathematical difference between mean free path and root-mean-square free path. For an ideal gas, the relaxation time is $$\tau=\frac{1}{\sqrt2 \pi nd^2 \bar v}$$ and the ...
2
votes
0answers
298 views

Equation of motion for a falling rod (with one end touching a frictionless surface)

I have a quick question about the equation of motion for a falling rod (with one end touching a frictionless surface). The end touching the surface is not fixed. I am given the moment of inertia about ...
2
votes
1answer
113 views

prove: $[p^2,f] = 2 \frac{\hbar}{i}\frac{df}{dx}p - \hbar^2 \frac{d^2f}{dx^2}$

I need to prove the commutation relation, $$[p^2,f] = 2 \frac{\hbar}{i}\frac{\partial f}{\partial x} p - \hbar^2 \frac{\partial^2 f}{\partial x^2}$$ where $f \equiv f(\vec{r})$ and $\vec{p} = p_x ...
2
votes
2answers
1k views

How To Use Ladder Operators?

I'm studying for a test in quantum mechanics and I'm having a hard time understanding how to use ladder operators. There are no examples in my text book, only definitions that I can't understand how ...
2
votes
0answers
276 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, ...
2
votes
2answers
232 views

Mathematical model for this graph of a simplified binary star system?

Unnecessary background for question: I had a school assignment asking us to relate a quadratic equation to a real life example relating to our future dream career, making sure to express the accuracy ...
2
votes
1answer
182 views

Gravitational binding energy and integrated potential energy not the same?

Before looking up the formula for the gravitational binding energy of a uniform sphere, I simply figured that the general formula for binding energy of an arbitrarily-shaped mass distribution would be ...
2
votes
2answers
290 views

Would this box on the floor rotate based on friction?

There is a floor that friction is proportional to its velocity (like $F=-kv$) and there is a box with its width as $l$ and its height as $h$. (you may assume that $l$ is longer than $h$). It is on the ...
2
votes
2answers
312 views

Pendulum Hits a Mass and Spring

I think this problem’s solution is on the web but after a few days of searching, I can not find it. Can anyone give me a reference? Thanks in advance. A mass and spring are resting on a frictionless ...
2
votes
2answers
222 views

Proper time for an accelerating object

As far as I have read so far, proper time is the time measured on the clock of an inertial frame moving uniformly with respect to another inertial frame. The concept and the mathematical expression ...
2
votes
1answer
387 views

Derivation of hyperbolic motion in Special Relativity

My question pertains to the equation of hyperbolic motion in special relativity: $$x^{2} - c^{2}t^{2} = c^{4}/\alpha^{2}.$$ As far as I am aware, this equation is the key to calculating coordinate ...
2
votes
1answer
721 views

Special Relativity and Constant Acceleration

My question pertains to the concept of a constantly accelerating rocket as it approaches the speed of light. The scenario is as follows: A rocket is constantly accelerating at 1g to reach Andromeda. ...
2
votes
1answer
133 views

Does a 27 hp engine output the same amount of energy as lifting a 1 ton stone block almost 3 meters per second?

I’m trying to get a sense of how much energy a 27 horsepower engine outputs. 27 hp $=$ 20 133 watts (joules/second). Potential energy can be calculated as $E = mgh$ where $g = ~9.8\ m/s^2$ on earth. ...
2
votes
2answers
3k views

Calculating the field of an infinite flat sheet of charge using the superposition principle

I am trying to calculate the field of an infinite flat sheet of charge (a plain with uniform charge density $\sigma$) using the superposition principle. I know that the field of an infinite line ...
2
votes
1answer
604 views

After normalizing a wavefunction I don't know how to calculate probability on an interval (-0.1 + 0.1)

This is quite large homework where I 1st had to normalize the wavefunction $\psi = Axe^{-x^2/2a}$ and I got a constant $A=\sqrt{2/(a\sqrt{\pi a})}$. How do I calculate the probability now for the ...
2
votes
2answers
377 views

2 protons collision (both with different kinetic energies) - I don't know what to put in for $p^2c^2$

The problem statement: Two protons with kinetic energies $W_{k1}=4GeV$ and $W_{k2}=2GeV$ colide and form new particles. What is the mass of newly born particles? There are as many as possible ...
2
votes
2answers
182 views

$\left(H^\dagger H\right)^2$ is invariant under $U(1)\times SU(2)$?

Is it true that $\left(H^\dagger H\right)^2$ is invariant under $U\left(1\right) \times SU\left(2\right)$ where $H$ is the Higgs field $(1,2,1/2)$? Does this invariance imply that its hypercharge ...