Momentum Definition and 1000 Threads

To get the dynamics of particles in a box. You are supposed to get the Hamiltonian which is potential energy plus kinetic energy. But does the potential energy take into account the momentum of the particles in the box? What happens if you change the momentum of the particles.. do the potential...

For a divergent paraxial field like $$E = E_0 e^{-\frac{r^{2}}{w(z)^{2}}} e^{-i(kz - tan^{-1}(\frac{z}{z_{0}}))}$$ What is the direction of the momentum density of the E-field. I have two competing feelings about it. 1) The momentum density should be parallel to the Poynting vector, and since...

Homework Statement A rocket starts from rest in deep space. The rocket structure and systems weigh a total of 500kg and it has 500kg of fuel initially. When the engines are fired, fuel is ejected from the end of the rocket at a speed of 100m/s relative to the rocket. How fast will the rocket...

In non-relativistic QM, wave functions are represented as a superposition of complex exponentials in which the energy/frequency is a function only of momentum/wave number (dispersion relation). This seems to imply that under the HUP, precise momentum guarantees precise energy. Are there any...

Hi, Consider a spherical planet of mass m and radius rp orbiting a star with a circular orbit of radius ro (distance from axis of orbit to the planet's center of mass). The planet has an angular velocity ω. Say we wanted to find the magnitude of the angular momentum of the planet. Going about...

In the proton chain, a deuteron and proton fuse to make a nucleus of helium 3, releasing 5.493 MeV by E=mc^2. To have the same total momentum before and after fusion, at least two particles must be emitted, right? That way they can "cancel out" some momentum by having roughly opposite...

Homework Statement A 0,15kg frame, when suspended from a coil spring, stretches the spring 0,070m. A 0,200kg lump of putty is dropped from rest onto the frame from a height of 30,0cm. Find the Maximum distance the frame moves downward from its initial position. Homework Equations I tried to...

Is momentum in the atoms part of the potential energy of the system? I read the momentum is a Hamiltonian.. and the potential is also a Hamiltonian.. so are the momentum the potential itself? In the atoms, the potential could be the electromagnetic attraction between electrons and nucleus.. how...

Hello everybody! I'm layman in physics, but recently I have very strong interest. Now I am struggling to obtain some knowledge all by myself. That's so complex, probably impossible for me... that's why i decided to sign up in the forum and I hope to get help from people who are versed and...

We have two cylindrical shells (with radii a and b and charges +Q and -Q) along the z-axis. There is a uniform magnetic field (in the positive z-direction) out to radius r from the z-axis. Because of the symmetry, the total field momentum is zero. Suppose we now connect the shells using a wire...

Kind of the basic question of atomic physics is momentum distribution of single electron of ground state hydrogen atom - especially the power in its high-energy tail (HTMD: high-tail momentum distribution), which should have strong impact especially on various scattering experiments. Fock's 1935...

Homework Statement Homework Equations I have thought about using the momentum formulas here. The Attempt at a Solution As the momentum is a conservative quantity, I have thought that p (before collision) = p(after collision). Since p (before collision) = 12, I wanted to use that result to...

Homework Statement Q1. A ball is rolling on a flat surface and another ball rolling on an inclined surface. When do both the balls have same velocity? Q2. When two people throw a ball and catch for a period of time, will the distance between them increase, decrease, or remain the same...

Homework Statement Does the speed of a ball increase, decrease or remain the same once it leaves the hand as it being thrown horizontally? Homework Equations Law of conservation of momentum[/B] The Attempt at a Solution According to my calculations, it increases as momentum is transferred...

Homework Statement I am trying to fill in the steps between equations in the derivation of the coordinate representation of the Darwin term of the Dirac Hamiltonian in the Hydrogen Fine Structure section in Shankar's Principles of Quantum Mechanics. $$ H_D=\frac{1}{8 m^2...

Homework Statement Two blocks move along a horizontal frictionless surface and collide head-on with each other. The mass of the first block, moving to the right with speed v is m, and the mass of the second block moving towards the left with speed 3v is 2m. After the collision, the block of...

This is the problem I'm trying to understand: Consider two particles with spin 1 without orbital angular momentum. If they are distinguishable, from the rule of addition of angular momentum applied to spin, we'll have states of total spin j=0,1,2. If we have, however, identical particles which...

For an inelastic impact situation where two bodies traveling in opposite directions (vehicles say) collide and coalesce (perfectly inelastic collision) , one can derive the following expression for equal and opposite transfer of momentum. On the basis that if impact forces are equal and...

Homework Statement I have the following problem to solve: A 1.8m board is placed in a truck with one end resting against a block secured to the floor and the other one leaning against a vertical partition. The angle the Determine the maximum allowable acceleration of die truck if the board...

Homework Statement Picture looks like this: ----------------------- ○ (empty space) ● (Cue) (White ball) (Black Ball) Mass: Cue (595g), White Ball (170g), Black Ball (155g) Question: On the given pool table, the white ball bounces off of the black ball and moves in the direction...

I'm trying to understand the rotations of rigid diatomic molecules such as HCl. My understanding of the orbital angular momentum is that it is quantized with a total value equal to $$E=\frac{\hbar^2}{2I}J(J+1)$$ where I is the rotational moment of inertia and J is the quantum number. Also, J...

Homework Statement Small object A (mass: [m][/A]) is traveling in a linear path on a horizontal surface and collides elastically with small object B ([m][/B]), at rest on the same line, with a speed of v. Friction between the objects and the horizontal surface is negligible. What is the...

Why are impulse and momentum treated as different quantites?

Homework Statement A high-energy photon collides with a proton at rest. A neutral pi meson is produced according to the reaction ##\gamma + p \to p + \pi^{0}##. What is the minimum energy the photon must have for this reaction to occur? (The rest mass of a proton is ##938\ \text{MeV/c}^{2}##...

Why ain't momentum conserved when external force acts on the system? Please explain with an example.

If a pendulum swings in a given arc, because of gravity acting on it in the vertical direction, does the linear and angular momentums change since it is picking up velocity because of gravity?

Homework Statement Multiple choice question: The momentum of a body has increased by 25%, then its kenitic energy will roughly increase by... 1. 25% 2. 5% 3. 38% 4. 56% 5. 65% Homework Equations Pl = mv (Pl is the momentum, m is mass and v is velocity) K.E = 0.5 mv^2 The...

If there is a ball falling from a height due to gravity, and you keep your hand still and let the ball fall onto it, it stops suddenly and makes a loud noise. However, if you lower your hand as you catch the ball, like when a cricketer catches a fast moving ball, the catch is almost silent. I...

Hello everyone, I'm needing help understanding how to take the conservation of momentum equation and substitute moment of inertia inplace of mass in the equation. I understand this is a linear equation and I'm trying to incorporate angular momentum. I just want to determine the speed of the ball...

Homework Statement Homework Equations Radiation pressure i.e.R.P is the instantaneous pressure exerted by radiation on a perfectly absorbing surface perpendicular to the propagation vector of the radiation. Maxwell has shown that R.P = u , (1) where u is energy density R.P = F/A, (2) F...

Homework Statement In a particle physics lab, an electron e− and a positron e+ collide, annihilate, and produce a W+ boson and a W− boson. Just before the collision, the electron and positron have a total energy of E = 100 GeV each, with velocities pointing along the +x-axis and -x-axis...

In my experiment I am performing a collision with two carts with magnets attached with photogates and a labquest on an air track. I pushed the carts together and made sure that the carts did not come into contact. Based on my knowledge of collisions, I believed that the collision would have been...

Homework Statement A particle of mass m is moving along the positive x direction with momentum p and energy E It collides with a particle of the same mass at rest to form a new particle of mass M. Show that M^2 = 2m/c^2 * (E + mc^2) 2. Homework Equations E^2= p^2c^2 + m^2c^4 The Attempt...

Homework Statement Show that ##|l, m\rangle## for ##l=1## vanishes for the commutator ##[l_i^2, l_j^2]##. Homework Equations ##L^2 = l_1^2 + l_2^2 + l_3^2## and ##[l_i^2,L^2]=0## The Attempt at a Solution I managed to so far prove that ##[l_1^2, l_2^2] = [l_2^2, l_3^2] = [l_3^2, l_1^2]##. I...

How do you account for the conservation of momentum for a photon? Specifically, if you have light traveling in a medium where the refractive index is not constant. For example, a graded index multi mode fiber optic. So here is another diagram to help articulate my question. Inside this graded...

Homework Statement Please see the attached photo. (down) Hminitial= 1.5R M = 2/3m Perfectly elastic collision What is the velocity of object m immidiatly after the collision? (by m,g,R) Homework Equations Conservation of energy Conservation of momentum The Attempt at a Solution I assumed...

Hi, Homework Statement A free falling object of mass "m" falling from some height, collides the floor in speed of 20 m/s (perfectly elastic collision). In his 1/2 height back up he splits into 2 pieces- ¼m which going downward and ¾m keeping upward. The ¼m reaching the floor after ½ second. 1)...

Homework Statement Hi all, I'm given an electron with momentum 2.0*10-20kgm/s and was asked to convert the momentum into units of Mev/c then calculate the total energy of the electron, the lorentz factor and the speed of the electron, I did this successfully but then the question got confusing...

A pretty straightforward question because right now I can't think how it works: The missing transverse momentum azimuthial angle (φ) is calculated by measuring the x- and y- components of the missing transverse momentum E_x,E_y and taking: \phi^{miss} = arctan(E_y/E_x)...

Homework Statement This is my 'carrying out a practical investigation' assignment for Maths. I've attached the coursework (what I've wrote up to now) and my main concern is whether I've got the right differential equation to find 3 new velocity values throughout the pendulum trajectory...

1. Homework Statement Determine the total magnitude of angular momentum Ho of the particle about point O. The velocity of the particle is 5.5 m/s.Homework Equations Ho= r x mv The Attempt at a Solution The answer is 43.04. My question is, isn't the graph wrong? If you take the magnitude of the...

This is not coursework, it is from a past paper (which we don’t have solutions for) and am doing preparation for this years exam. 1. Homework Statement Particle ##A## with energy ##E_A## hits particle ##B## (at rest), producing particles ##C## and ##D## in the reaction A+B \longrightarrow C...

Homework Statement A body X moving with a velocity v makes an elastic collision with a stationary body Y of equal mass on a smooth horizontal surface. Which statement gives the velocities of the two bodies after the collision? (multiple choice question)The Attempt at a Solution The answer...

Hi everybody, I apologize if something like this has been asked before but I have been unable to find an answer through searching. If a weight is carefully added to a moving cart then the cart should slow down due to conservation of momentum. How is it that the cart has accelerated without a...

I've managed to derive the form of Reynolds transport theorem as a bilance of linear momentum of the system: \left (\frac{\vec{\mathrm{d} p}}{\mathrm{d} \tau} \right )_{system}=\frac{\mathrm{d} }{\mathrm{d} x}(\int_{V}^{ }\vec{v}\cdot \rho dV)+\int_{A}^{ }\vec{a}dm+\int_{A}^{ }\vec{v}\cdot \rho...

I am reading a proof of why \left[ \hat{L}_x, \hat{L}_y \right ] = i \hbar \hat{L}_z Given a wavefunction \psi, \hat{L}_x, \hat{L}_y \psi = \left( -i\hbar \right)^2 \left( y \frac{\partial}{\partial z} - z \frac {\partial}{\partial y} \right ) \left (z \frac{\partial \psi}{\partial x} -...

This is a problem for a fluid dynamics class I'm in. My current approach is to use a conservation of mass approach and say that the d/dt(momentum in the cart) = momentum into the cart. This leads to (u is speed of the cart, V is volume J is jet velocity, A is cross sectional area of the jet)...

Hello I need help to explain the affect of the cross product without the its current symbolism, but for angular momentum. I can explain angular momentum in terms of the cross product of 3D space formulated like this: |r| |v| * sin(angler.v) e-perp to r and v Eq.1 (I can explain this to...

In a closed system, I know the rider wouldn't be able to change the combined center of gravity of the system by moving his weight around. If he pushes the bike to lean to the right, he would go to the left by the amount that would keep the combined cog the same. But a bike with tires and a road...

Homework Statement The red box only Homework EquationsThe Attempt at a Solution I suppose we have to show L_3 (Π_1) | E,m> = λ (Π_1) | E,m> and H (Π_1) | E,m> = μ (Π_1) | E,m> And I guess there is something to do with the formula given? But they are in x_1 direction so what did they have...