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4
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1answer
455 views

Finding Stagnation Points from the complex potential

I am trying to find the stagnation point of a fluid flow from a complex potential. The complex potential is given by $$\Omega(z) = Uz + \cfrac{m}{2\pi}\ln z.$$ From this I found the streamfunction to ...
4
votes
1answer
289 views

Wick Order and Radial Ordering in CFT

I am not so much familiar with the computations tools of conformal field theory, and I just run into an exercise asking to demonstrate the following formula (related to the bosonic field case): ...
3
votes
2answers
548 views

A block on a wedge

The system is as follows - Friction exists only between the 2 blocks. I am trying to find out the accelerations of $m_1$ and $m_2$. Let $a_2$ be acceleration of $m_2$, and $a_x$ and $a_y$ be the ...
2
votes
2answers
116 views

CPT invariance of Dirac equation

We know that Dirac equation is \begin{equation} ( i \partial _\mu \gamma ^\mu - m ) \psi ~=~0. \end{equation} How can we show that Dirac equation is invariant under CPT transformation?
2
votes
3answers
94 views

Instantaneous angular momentum of a disc

Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity $v$. I want to calculate the instantaneous angular momentum with axis through the edge of the disc (on the circumference). ...
2
votes
1answer
988 views

Elastic collision in two dimensions

Suppose a particle with mass $m_1$ and speed $v_{1i}$ undergoes an elastic collision with stationary particle of mass $m_2$. After the collision, particle of mass $m_1$ moves with speed $v_{1f}$ in a ...
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vote
4answers
3k views

Capacitor Charging and Discharging when connected to the ground

When we charge a capacitor using a battery and then remove the battery, the plates of capacitor becomes charged. One holds positive charge and the other one gets equal negative charge. o. k. ? Now ...
1
vote
1answer
543 views

Finding the electric field for a shell of charge

Suppose we have charge density defined $$ \rho(x,y,z) = \begin{cases} 0 & 0 \leq r < a \\ K & a \leq r\leq b\\ 0 & b< r \end{cases} $$ For some constants $K,a,b$ How would ...
1
vote
2answers
5k views

Preventing a block from sliding on a frictionless inclined plane

I want to demonstrate what force $F$ you would have to exert on an inclined plane of angle $t$, mass $M$ to prevent a block on top of it with mass $m$ from sliding up or down the ramp. I worked out ...
1
vote
2answers
403 views

Motion of a rod struck at one end

Imagine a strong metal rod of uniform density and thickness floating in a weightless environment. Imagine it lies on an X-Y plane, with one end (A) lying at 0,0, and the other end (B) at 0,1. Then it ...
1
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2answers
275 views

Doubt concerning centripetal acceleration

What is the centripetal acceleration and angular velocity of a child located 8.2 m the center of a carousel? The speed (size of the tangential velocity) of the child is 2.1 m / s A train moves in a ...
0
votes
1answer
756 views

How to find constant of motion for Hamiltonian system?

I have to find a constant of motion associated to this Hamiltonian but I don't know how to proceed. $$H=\frac{\mathbf{p_0}^2}{2m}+\frac{\mathbf{p_1}^2}{2m}+\frac{\mathbf{p_2}^2}{2m}-2V(\mathbf{r_1}- ...
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votes
4answers
1k views

4th equation of motion

Ive been given the 4 equations of motions The fourth being: $$s=ut+\frac{1}{2}at^2$$ If rearranged it forms the quadratic equation $$at^2+2ut-2s=0$$ But that means that t has 2 values. Will ...
-1
votes
1answer
529 views

What's the electric field with a point charge not in the center of the sphere? [closed]

That's a hollow conducting sphere link My charge is at P (10uC). R = 0.15m. PS = 0.05m. DS = 0.35m. What's the electric field at point D?
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votes
3answers
232 views

Can you lift a basket up while standing inside it? [closed]

Suppose you stand in a basket and you try to pull the handles of the basket. Will you be able to lift the basket from ground? Similarly, Baron Münchhausen allegedly pulled himself and the horse on ...
7
votes
3answers
2k views

Charge density in concentric spheres

Question: If there are two conducting spherical shells and the inner shell is grounded, what will be >the charge density in the inner shell if there is a charge Q placed on the outer shell? ...
4
votes
5answers
440 views

The approximate uncertainty in $r$

The volume of a cylinder is given by the expression $V=\pi r^2 h$ The uncertainties for $V$ and $h$ are as shown below $\begin{align} V&\pm 7\%\\ h&\pm 3\% \end{align}$ What is the ...
3
votes
1answer
59 views

Moments of vibrating string

I have to calculate first 10 moments for vibrating string with damping, but I don't know how to do it. I read about moments and in definition they mention linear system $$x'=Ax+Bu, \qquad y=Cx$$ with ...
3
votes
3answers
138 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 ...
3
votes
1answer
53 views

How to find the force of the compression at the core of a planet?

For example the core of the planet Jupiter, how to find out the magnitude of the force that compresses its core? and can that be thought of as the total force that holds the planet together?
3
votes
2answers
349 views

Newton's third law does not apply to the kinetic energy formula?

Here is a classic problem: A 60kg boy and a 40kg girl are sitting in front of each other on skateboards on a frictionless horizontal surface. The boy pushes the girl and the girl gains a velocity ...
3
votes
2answers
4k views

Does Earth's Rotation Affect Its Shape?

The question I am working on is, "Consider the following. (a) Find the angular speed of Earth's rotation about its axis. rad/s (b) How does this rotation affect the shape of Earth?" I am fully ...
3
votes
1answer
550 views

Transmission and reflection

What is the transmission amplitude of a wavefunction $\phi(x)=e^{ikx}(\tanh x -ik)$? I would have thought that it is $\tanh x -ik$ since this is the factor associated with the forward travelling ...
2
votes
1answer
137 views

Add air resistance to projectile motion

I am given an initial x and y position and initial velocity and I was asked to graph the trajectory in 1 second intervals. This is what I have so far: If $x_0 = 1, v_{0x} = 70, y_0 = 0, v_{0y} = 80, ...
2
votes
2answers
157 views

What is the relative speed of two near-light speed particles headed towards each other?

I understand that nothing can move faster than light due to time dilation. I want to build upon my understanding of Einstein's theory of Special Relativity, so I came up with this hypothetical problem ...
2
votes
1answer
159 views

An Electric Potential Glued to a Cube-Shaped Insulator to Replicate a Point Charge: Charge Distribution

I have been going back over this problem with a friend for the better part of a day: A potential is glued to a cube-shaped insulator so that outside of the insulator the field is the same as a point ...
2
votes
2answers
226 views

Velocity of an object undergoing homogenous acceleration

So I was considering the following problem within the context of Special Relativity: Given an object O, with initial velocity v, undergoing constant acceleration at a rate of a, I want to express the ...
2
votes
1answer
1k views

Uncertainty Principle and Energy range for an electron in an atom

I have the following exercise: Use Heisenberg's uncertainty principle and the relation $\Delta u = \sqrt{\langle u^2 \rangle - \langle u \rangle^2}$ to find the range of energy an electron has in an ...
2
votes
1answer
890 views

Kinematics with non constant acceleration

A particle experiences an acceleration described by $$ a=kx^{-2} $$ where x is the displacement from the origin and k is an arbitrary constant. To what value does the velocity v of the particle ...
2
votes
3answers
223 views

Condition for closed orbit [closed]

I'd like to know when an orbit is closed. I know that, to have a closed orbit, there is a ratio that must be a rational number, but I don't know other things..
2
votes
2answers
481 views

Homework about spinning top [closed]

I have a top of unknown mass that has a moment of inertia $I=4\times 10^{-7} kg \cdot m^2$. A string is wrapped around the top and pulls it so that its tension is kept at 5.57 N for a distance of .8 ...
1
vote
1answer
67 views

Resistors in para and series circuit, finding volt [closed]

How anyone know how to do the question? I know how to reduce it to a window pane of 6/6/6/6 with a 3 in series but i have no idea how to do it. Well i did manage to reduce the right side of the ...
1
vote
1answer
69 views

Tension in an Atwoods machine conceptual?

Assuming $T_1$ is the force that acts on box $1$ and $T_2$ is the force that acts on box $2$. Exactly what causes the Tension? Why does $T_1 = T_2$? The problem is we are told to memorize that ...
1
vote
1answer
92 views

Man on a rope task

Some time ago I came across this simple task. Instead of describing it a lot I will just post a picture and try to explain like that. So the man and the weight on the other side of the rope have ...
1
vote
3answers
248 views

Commutators involving functions

I am looking for the commutator: $$[e^{aq},p]$$ My approach is to Taylor expand the function: $$[\sum_n \frac{1}{n!}(aq)^n,p]$$ I know that $[q^n,p]=ni\hbar q^{n-1}$ So how do I account for $n$ ...
1
vote
1answer
157 views

Finding the Schwarzchild radius of a star of solar mass 30

I am currently trying to determine the Schwarzchild radius of a star with solar mass 30. I am calculating it both with respect to solar mass, and w.r.t kilograms, however I am getting conflicting ...
1
vote
0answers
83 views

Derivation of equations of motion in Nordstrom's theory of scalar gravity?

Nordstrom's theory of a particle moving in the presence of a scalar field $\varphi (x)$ is given by $$ S = -m\int e^{\varphi (x)}\sqrt{\eta_{\alpha \beta}\frac{dx^{\alpha}}{d ...
1
vote
1answer
1k views

Commutator of Momentum with a Position dependent function

I heard from my GSI that the commutator of momentum with a position dependent quantity is always $-i\hbar$ times the derivative of the position dependent quantity. Can someone point me towards a ...
1
vote
3answers
425 views

Simple Quantum Mechanics Question about The Commutator of Translation Operators

Say there is $\hat{J} = \exp[-i \hat{p} l/ \hbar]$ and $\hat{U}= \exp[-i\hat{H}t/ \hbar]$, where $\hat{H}$ is time-independent. Can we say anything about $[\hat{J},\hat{U}]$? Is it zero? How do we ...
1
vote
3answers
2k views

Magnitude of magnetic field at the center of circular wire

I'm preparing for an exam by solving the sample questions , here is the one I'm having difficulty with : Following is the given circuit. Which contains two resistance $R_1$ and $R_2$ in form of ...
1
vote
0answers
62 views

How to absorb a characteristic line in a spectrum

I have an x-ray tube. When I see the spectrum, I notice the characteristic lines of the anode. What do I have to do if I want to absorb a characteristic line? I have thought that I can add a filter. ...
1
vote
0answers
40 views

Calculate the acceleration of the trailing muon bunch

Two separate suitably short but intense bunches of muons, "A" and "B", are both supposed to be constantly accelerating (in an otherwise sufficiently flat region) with constant proper acceleration ...
1
vote
2answers
1k views

The potential and the intensity of the gravitational field in the axis of a circular plate

Calculate the potential and the intensity of the gravitational field at a distance $x> 0$ in the axis of thin homogeneous circular plate of radius $a$ and mass $M$. Could anybody describe how to ...
1
vote
2answers
135 views

Does the sign of $\Delta x$ matter in this time dilation calculation?

I cannot for the life of me figure out what I am doing wrong with this problem: If a high speed particle travels a distance of 39 Km with a half life of 1 micro sec, what must its speed be to travel ...
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2answers
1k views

Why does the light bulb's brightness decrease?

The book said that the brightness of R1 would increase and R2 would decrease. I don't understand this at all. Why does adding a wire from b to c change anything to R1? Shouldn't charge still flow ...
1
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1answer
2k views

Trajectory of projectile thrown downhill

I'm teaching myself mechanics, and set out to solve a problem determining the optimum angle to throw a projectile when standing on a hill, for maximum range. My answer seems almost plausible, except ...
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vote
3answers
1k views

Flying a toy helicopter inside an accelerating train [duplicate]

Scenario: You ride in a train, you have this helicopter toy. The train is not yet running when you flew your helicopter on a constant altitude (say 1 meter above the train's floor). Question: What ...
1
vote
1answer
120 views

How to find the value of the parameter $a$ in this transfer function?

I am given a transfer function of a second-order system as: $$G(s)=\frac{a}{s^{2}+4s+a}$$ and I need to find the value of the parameter $a$ that will make the damping coefficient $\zeta=.7$. I am not ...
1
vote
2answers
729 views

What is a Free Body Diagram?

I have this problem: A 10 kg box is resting on a frictionless table and someone drags it by a string at a 30 degree angle to the horizontal with a force of 40 Newtons. Find the acceleration of the ...
1
vote
3answers
2k views

Maxiumum weight a buoy can float [closed]

I have a buoy that can hold 2943.02 cubic millimeters of non-pressurized air, I need and equation to work out the maximum weight that the buoy can float.