# Tagged Questions

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 questions.

277 views

402 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 ...
447 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 ...
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 ...
401 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). ...
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 ...
145 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: \rho(\textbf{r},t)= ...
412 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 ...
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 ...
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? ...
49 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 ...
92 views

### Elastic collision of point particle and rod

A 1 meter long rod on the ice with mass $m_2=1$ kg is perpendicularly hit on one end by a point particle with mass $m_1=0.1$ kg. The collision is elastic and the point particle is bounced back in ...
91 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 ...
138 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 ...
246 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 ...
235 views

### Wave function of a particle in a gravitational field

Suppose we have a particle with mass $m$ and energy $E$ in a gravitational field $V(z)=-mgz$. How can I find the wave function $\psi(z)$? It should have an integral form on $dp$. Any help would ...
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 ...
237 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, ...
223 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 ...
172 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 ...
273 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 ...
306 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 ...
359 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 ...
681 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. ...
130 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. ...
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 ...
574 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 ...
1k views

### Calculating specific orbital energy, semi-major axis, and orbital period of an orbiting body

Is it possible to calculate the specific orbital energy $ϵ$, the semi-major axis $a$, and the orbital period $T$ (or $P$) without any of them being available to you? The values I do have available to ...
337 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 ...
179 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 ...
116 views

368 views

### My math says this is wrong, but what part of energy conservation am I violating?

Basically energy of conservation says it doesn't matter what path I take, energy will be the same from before as it is after. So I took the block at the top's energy equal to the energy when it ...
818 views

### Free Body Diagram of Fluid Statics Problem

I need help determining the forces, and the direction of them in this fluid statics problem. A hollow cylinder with closed ends is 300mm in diameter and 450mm tall. It has a mass of 27kg and a tiny ...