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3
votes
1answer
141 views

Chain with mass gradient problem

This is the problem, basically. Now my question is about the approach. Mine, and my teacher's. I would like some help as to which one is correct... Mine: As the whole chain is in equilibrium, the ...
3
votes
2answers
149 views

Eigenenergies and eigenkets given the Hamiltonian

For a two level system the Hamiltonian is: $$ H=a(|1\rangle \langle1|-|2\rangle\langle2|+|1\rangle\langle2|+|2\rangle\langle1|) $$ where $a$ is a number with the dimension of an energy. I need to ...
1
vote
1answer
115 views

From Lagrangian to equations of motion [closed]

I have a given Lagrangian: $$L= e^{st}\cdot\frac12\cdot(mv_y^2-ky^2)$$ And are asked to identify the equations of motions, the constants of motions and physical system. Without the exp-time-term, ...
3
votes
3answers
158 views

A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$ [closed]

I have complications to do the following problem: A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$. Find its velocity and acceleration vectors. My first idea was ...
0
votes
2answers
86 views

Maximum range for projectile thrown from a mountain [closed]

I have doubts with the following problem: A projectile is fired from the top of a mountain that has a downward slope with angle $\phi$ from the horizontal. The initial velocity of the projectile is ...
5
votes
1answer
117 views

Pendulum with a rotating point of support from Landau-Lifschitz

I found this problem in Landau-Lifschitz vol.1 (Mechanics) A simple pendulum of mass $m$, length $l$ whose point of support moves uniformly on a vertical circle with constant frequency $\gamma$. ...
3
votes
0answers
71 views

Virasoro Operators commutation relations

For the commutation relation in quantising the bosonic string $\left[L_n,L_{m}\right]=(n-m)L_{n+m}+\frac{D}{12}n(n^2-1)\delta_{n+m,0}$ we can then calculate this for $m=-n$ in between the vacuum ...
3
votes
2answers
109 views

Maximum permissible speed while going down a ramp

So, I was playing hill climb racing and I noticed that if we move with high speeds towards a ramp going down we just jump it off. While lower speeds, help us to stay in contact with the ramp. ...
0
votes
1answer
58 views

Butterfly inside the accelerated train [duplicate]

Suppose there is a train moving right with constant acceleration and there is a butterfly inside the train which moves opposite to direction of motion of train i.e. towards left. The butterfly always ...
3
votes
2answers
280 views

What is the expected distance of the electron from the nucleus in the hydrogen atom?

Specifically, I would like to know the general formula, in terms of $n$ and $l$, assuming the electron is in an orbital (i.e. simultaneous eigenstate of $H$, $L^2$, and $L_z$). I understand that it ...
-2
votes
2answers
114 views

Newtonian Mechanics problem? [closed]

The ball of mass $m$ is given a speed of $v_a = \sqrt{3gr}$ at position $A$. When it reaches $B$, the cord hits the small peg $P$ after which the ball describes a smaller circular path. Determine ...
2
votes
0answers
129 views

Equations of motion of the double pendulum by vector methods [closed]

I wanted to know if anyone of you do know a book or article on the Internet in which the equations of motion of a double pendulum is deduced, only using vector methods (i.e. Newton's 2nd law as ...
1
vote
1answer
213 views

Electric field from current without Maxwell's law of induction

A long, straight wire carries a current that decreases linearly with time. What is the direction of the induced electric field outside the wire? I would interpret this as follows: a current ...
0
votes
1answer
81 views

Product of ρ and φ [closed]

Consider a charge distribution $ρ_1(r)$ and the potential $φ_1(r)$ due to it. Consider another charge distribution $ρ_2(r)$ and $φ_2(r)$ due to it. Both distributions have finite extent, but are ...
1
vote
0answers
67 views

Finding the induced EMF on a bar - Faraday's law

I have a couple of questions about the following problem: A conducting bar of length L moves with velocity v, in a rectangular region with a uniform and stationary magnetic field B_1. Near the bar, ...
3
votes
0answers
154 views

Practice AP Physics B Exam Question regarding Momentum

I am trying to review momentum for the AP exam coming up. I will be taking the AP Physics C exam for Mechanics, but I was just practicing on any free response questions I could find and I came across ...
5
votes
2answers
89 views

Physical position eigenfunction normalisation

We know that the Dirac function $$\delta(a)=\lim_{a \rightarrow 0} \delta_{a}(x)$$ can be written as an infinitesimally narrow Gaussian: $$ \delta_{a}(x) := \frac{1}{\sqrt{2\pi a^2}}e^{-x^2/2a^2}$$ ...
1
vote
1answer
640 views

Magnetic field in a cylinder with an off-axis hole

Take a long cylinder of radius $ a$. It has a long cylindrical hole of radius $b$ parallel to the cylinder axis. The distance between the two axes is $d$. If the cylinder has a uniform current density ...
1
vote
2answers
52 views

Temperature limit on entropy of a paramagnet

We have $$S=Nk_B[\ln(2 \cosh(x)) - x \tanh(x)]$$ where $$x = \frac{\mu B}{k_BT}$$ In need to show that at low temperatures entropy $$S \approx Nk_B2xe^{-2x}$$ I wrote out the $\cosh(x)$ in terms of ...
0
votes
2answers
122 views

Problem with horizontal projectile motion questions

I don't really understand horizontal projectile motion. Suppose I throw a ball horizontally. Given $\theta$ = 0 degrees, time = 0.5 seconds, horizontal range = 15.5 metres, the "initial horizontal ...
0
votes
1answer
87 views

The Shell Theorem and A Problem Related to it

The shell theorem states that: A uniform spherical shell of matter attracts a particle that is outside the shell as if all the shells mass were concentrated at its center. Now, I have to solve a ...
0
votes
1answer
127 views

Maximum Weight Sustained by wire / Breaking limit of wire [closed]

I know that breaking stress depends on material of wire, not on the diameter or the length of wire. and also that Breaking load depends on the area of cross section of wire. But still i have a ...
0
votes
1answer
125 views

Infinite motion on a 3D curve

Suppose we had a curve defined by $$\underline{r}(s) = \alpha \cos(s) \underline{i} + \gamma s \underline{j} + \alpha \sin (s) \underline{k}$$ with $\alpha^2 + \gamma ^2 = 1$ and suppose we had a ...
-1
votes
0answers
16 views

The magnitude of the resultant? [closed]

The two structural members, one of which is in tension and the other in compression, exert the indicated forces on joint O. Determine the magnitude R of the resultant R of the two forces and the angle ...
5
votes
2answers
239 views

A calculation problem on Conformal Field Theory

This problem is on Di Francesco's book I. It's exercise 7.1: Calculate the norm of the following vector, where $\lvert h\rangle$ is the state of highest weight. $$L_{-1}^n\lvert h\rangle$$ I have ...
5
votes
1answer
118 views

Relativistic Doppler effect on gamma rays

I'm trying to solve the following problem : An electron-positron pair annihilates, creating two photons. At what speed must an observer move along the line of the photons in order that the ...
1
vote
1answer
41 views

Obtain rate as a function of position for a force $F=-b\left( \frac{\partial x}{\partial t} \right)^{2}$

I have trouble getting the speed as a function of position for a force of the form: $$F=-b\left( \frac{\partial x}{\partial t} \right)^{2}$$ I had thought to use Newton's second law, so: ...
1
vote
0answers
262 views

Numerical solution of two coupled second order differential equations of motion [closed]

Is there a numerical algorithm for solving a pair of coupled second order differential equations? This question arises from a homework problem that I have that involves two dimensional projectile ...
0
votes
2answers
55 views

Molecules of a solid [closed]

Question: Molecules of a solid : (a) are always in a state of motion (b) move only when heated (c) move because they are loosely bound (d) do not move at all My attempt: I ...
0
votes
1answer
62 views

Propulsion force [closed]

My physics instructor gave us a general problem A box is sitting motionless on a rough, horizontal patch of ground. You give it a good kick, so that it slides to the right with an initial speed of ...
0
votes
1answer
403 views

Determining $y$ coordinate of charged particle motion [closed]

I've tried several different ways, with a tutor, and with other colleagues. One of my colleagues has even gone to the professor with whom he worked out an equation for the component, and it was later ...
-1
votes
1answer
24 views

Computing power based on weighted averages [closed]

I'm struggling to understand the reason why I'm getting different results with two apparently similar ways to compute the power consumption (over multiple time intervals) of an electrical circuit. ...
0
votes
1answer
44 views

Help with momentum question involving vectors/trig [closed]

The problem: A car with a mass of 1200 kg and speed 10 m/s runs into a traffic barrier at an angle of 45 degrees, and is thrown outwards at an angle of 45 degrees relative to the barrier with a speed ...
0
votes
0answers
35 views

Force exerted by a capacitor on a polar object

I was reading about capacitors and wondered what the force an electrostatic field created by a capacitor would be on an object with a certain charge and mass. If it can exert a force on a polar object ...
-1
votes
1answer
40 views

Finding charge (electromagnetism course) [duplicate]

I'm a maths undergrad taking a course on electromagnetism, I've drawn a diagram to represent this following question, but I'm having a bit of trouble approaching it: "Two tiny balls of mass m = 0:1 g ...
0
votes
1answer
70 views

Power and speed [closed]

I'm asked to calculate how much POWER a 1210kg car needs to drive with a 85 km/s speed up a 655 meter long slope of 4.5°. I can find how much energy and work is required to do this, but isn't ...
1
vote
2answers
42 views

Final position of an object after aplying several horizontal forces [closed]

I'm given an object with a starting position. Several horizontal forces are applied to this object one after the other for different amounts of time. How can I determine the final position $x$?
4
votes
1answer
73 views

How to get a function for the voltage across a capacitor connected to an AC voltage source? [closed]

I am looking for the way of obtaining a solution for $V_{c}$ ,as a function of $t$ depending of $\omega$, of the following differential equation related to an electrical circuit involving a low-pass ...
1
vote
1answer
92 views

How to find the center of mass? [closed]

A massless rod of length $L$ attached to mass $m$ and with axle to cart of mass $M$. The cart has a shape of equilateral triangle (edge $L$). the cart is at rest and its center of mass is above $x=0$ ...
3
votes
0answers
69 views

Vertex for quartic interaction of complex scalar multiplet

Since I'm new to QFT and I tend to do a lot of errors during calculations, I would like you to tell me if I got the four-point vertex of the quartic interaction with a multiplet of complex scalar ...
1
vote
1answer
87 views

Moment of inertia of a system in different cases

A rod of mass $m$ and length $l$ is pivoted at one end to ceiling and free to rotate in the vertical plane. A disc of radius $R$, which is less than $l$, can be fixed at its other end in 2 ways : ...
0
votes
1answer
120 views

Wavefunction Problem wrong in solutions manual? [closed]

Well there is a problem in my book which lists this problem: Calculate the probability that a particle will be found at $0.49L$ and $0.51L$ in a box of length $L$ when it has (a) $n = 1$. Take the ...
0
votes
2answers
261 views

In Which of the following situations would force be exerted on on object and no work be done on the object?

Consider the following question: In which of the following situations would a force be exerted on an object and no work be done on the object? I. a centripetal force is exerted on a moving ...
0
votes
1answer
162 views

Help understanding a potential energy problem [closed]

Apologies if the following problem does not seem to involve potential energy, it is a homework problem that is labeled under the potential energy chapter. Question While a roofer is working on a ...
1
vote
1answer
76 views

Does the 1-D poisson's equation have monotonic potentials if $\rho=\rho(\phi(z))$?

I am solving the 1-D poisson equation: $$\frac{d^2 \phi}{dz^2}=-4\pi\rho(\phi)$$ with the additional requirement that $\rho(\phi(z=0))=0$. If I start by multiplying each side by $\frac{d\phi}{d z}$ ...
0
votes
2answers
176 views

How to choose a location for rocket launching?

What's the relation of earth's magnetic equator with satellite launching? How does the nearness of a rocket launching station to the earth's magnetic equator make it an ideal location for scientists ...
0
votes
0answers
20 views

Radiometric Intensity of Non-Monochromatic LED

So I have a problem with the LED with the spectrum shown below I am asked to find the radiometric intensity in Watts/steradian given that the LED produces $5.6\times 10^{-3}$ mcd. We are also told ...
0
votes
1answer
32 views

Equation of conservation of mass for isotropic fluid considering external forces [closed]

I have trouble doing the following problem: Consider a fluid isotropic in three dimensions such that one can ignore all dissipative forces effect, as would be the viscosity. By analyzing the flow ...
0
votes
1answer
88 views

Two masses attached by a spring [closed]

Suppose there is a system of two masses $M_1$ and $M_2$ connected by a spring with constant $K$ on a frictionless surface. What is the frequency of this system's oscillation? So I have fixed a ...
2
votes
2answers
209 views

What will be the velocity of a comet is falling to the Earth from infinity at the time of impact if Earth had no atmosphere?

What will be the velocity of a comet is falling to the Earth from infinity at the time of impact if Earth had no atmosphere? the comet is falling radially towards the earth. Will this velocity be ...