In introductory mechanics, the momentum of a particle is its mass times its velocity. In electrodynamics, the momentum of a field is proportional to the cross-product of the electric field with the magnetic field. In special relativity, momentum is generalized to four-momentum.

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937 views

What are the general solutions to a hard sphere collision?

Surely someone has found the solutions to the hard sphere collisions (in $n$ dimensions) of two bodies of mass $m_1$ and $m_2$, respectively--that is the resultant velocities (or momenta) of the two ...
0
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2answers
231 views

Changing momentum of moving trolley

Consider a trolley of mass $m$ moving at a velocity $v$ along a smooth horizontal plane. It is full of water, and water is leaking at a constant rate out of the bottom of the trolley, i.e ...
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0answers
21 views

Momentum equation in a Lagrangian configuration

When writing the momentum equation in a lagrangian configuration is the the stress tensor used the first Piola-Kirchhoff stress tensor or the nominal stress tensor (which is the transpose of the 1st ...
13
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6answers
9k views

What is canonical momentum?

What does the canonical momentum $\textbf{p}=m\textbf{v}+e\textbf{A}$ mean? Is it just momentum accounting for electromagnetic effects?
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0answers
12 views

How could you slow down or change direction with photonic propulsion?

So you have a laser shooting at a sort of solar sail to transfer momentum in the forward direction but could you have an onboard laser and turn the laser around to hit another sail? How could you turn ...
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0answers
13 views

Invariant amplitude in QED in terms of Mandelstam variables [on hold]

So I'm having a little trouble with this question: These are my workings thus far: I just can't seem to get certain terms to vanish. I have the 1/4 factor for going between $8e^4$ to $2e^4$. Is ...
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1answer
32 views

Momentum equation of a beam hitting a stationary target to create antiprotons

I'm struggling with the solution of a physics exercise which is to calculate the minimum energy needed to create antiprotons when a proton beam scatters on a stationary proton target: $$p + p ...
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1answer
25 views

How to calculate impulse required to move an object vertically upward by given distance [on hold]

Suppose I have a stationary object of mass $m$ and I want to apply a momentary force in the vertical direction so that it just reaches the height $h$. So how do I calculate the impulse required in ...
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0answers
58 views

Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
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1answer
31 views

Variation of Veritasium bullet block experiment

I'm new here. this is in reference to the video posted by veritasium on the bullet block experiment. i realise there is already a thread on this but i want to ask a variation of the question. so ...
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2answers
231 views

Why do particles of equal mass (with one at rest) undergoing elastic collisions scatter at only right angles?

This is from the Section 9.6, page 351 of "Classical Dynamics of Particles and Systems" by Thornton and Marion. By setting a up a system where mass 1 has initial momentum $m_1 u_1$ and mass 2 is at ...
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0answers
14 views

Momentum conservation problem, elastic collision [duplicate]

This question has got me thinking for a while now and I haven't been able to come up with any answer at all. I've done the basic conservation of momentum, kinetic energy but I have no idea how to ...
0
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2answers
31 views

Momentum of a rack and pinion gear system excited by a time variant force

Background I have a rack and pinion gear system as shown in the image below The pinion gear is attached to a flywheel at the back. The first state of the system, none of the gears or the ...
20
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5answers
3k views

How can there be net linear momentum in a static electromagnetic field (not propagating)?

I understand from basic conservation of energy and momentum considerations, it is clear in classical electrodynamics that the fields should be able to have energy and momentum. This leads to the usual ...
0
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0answers
20 views

Relating Initial velocity and acceleration to distance traveled up a ramp

This is the situation: I am conducting research on the ability of fin-fish to scale short wetted ramps for use alongside sea-lamprey barriers to allow non-target species to pass these barriers. We ...
0
votes
1answer
31 views

Common property of equal momentum of different masses [closed]

Two bodies of unlike masses are possessing the same momentum, now what phenomenon does these two bodies can perform likely. I'll use an example: assume a truck and a car of masses 5000 kg and 1000 ...
0
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1answer
26 views

Why is the acceleration of the center of mass is equal to 0 in this problem?

I don't understand why the center of mass' acceleration is equal to 0 when the center of mass should be moving as an external force is exerted on the cue ? Billiard Balls. Now we can go back and ...
3
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3answers
161 views

Center of mass motion and variation of mass

Here are the proofs regarding the center of mass motion as reported on my book. $$\vec{r_{cm}}=\frac{\sum\vec{r_i} m_i}{\sum m_i}$$ $$\vec{v_{cm}}=\frac{d{\vec{r_{cm}}}}{dt}=\frac{1}{M}\sum ...
3
votes
1answer
369 views

Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: $$\phi(\vec{k}) = \left( \frac{1}{\sqrt{2 \pi}} \right)^3 \int_{r\text{ space}} \psi(\vec{r}) e^{-i \mathbf{k} \cdot \mathbf{r}} d^3r$$ for momentum space and ...
0
votes
1answer
109 views

What will happen to the center of mass of the human body when a person carries a weight with one hand?

What will happen to the center of mass of the human body when a person carries a weight with one hand a briefcase for example. Wouldn't the center of mass move horizontally towards the side carrying ...
3
votes
1answer
170 views

Hidden momentum

I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting ...
4
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2answers
101 views

Is the eigenvalue of Hamiltonian invariant under linear transformation of momentum operator?

It is given The dynamics of a particle moving one-dimensionally in a potential V(x) is governed by the Hamiltonian $H_0 = p^2 /2m + V(x) $, where $p = -i\hbar d/dx$ is the momentum operator. ...
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2answers
178 views

In a CMCS 2-body system, why does the speed of the particles after collision stay the same?

A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
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1answer
33 views

Question about Thrust; am I correct?

Basically, here's what I understand about Thrust: Thrust is a force. You get it by doing $v\times\frac{dM}{dT}$. Pretty basic, because that's the formula you're given. However, because I'm trying to ...
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1answer
23 views

What is the minimal G-force curve in 2-dimensional space?

Given two parallel roads, which need to be connected, what shape of curve would produce the minimum overall horizontal G-force(s) on travelers? Is it a $sin$ or $cos$ wave? Is it a basic cubic ...
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1answer
44 views

The ratio of masses in an elastic collision [closed]

Two blocks of mass $M_1$ and $M_2$ moving along a 1-dimensional straight line with velocities $V_1$ and $V_2$, respectively, collide elastically. After the collision they move with respective ...
0
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1answer
18 views

When to consider friction as an impulsive force?

Suppose a ball obliquely strikes a rough horizontal surface then it experiences a frictional impulse and conservation of linear momentum cannot be done on the horizontal direction. Now consider ...
4
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1answer
416 views

Derivation of force law in special relativity

I've seen force defined in special relativity as the rate of change of 4-momentum $$ {\bf{F}} = \frac{d {\bf{p}}}{dt} $$ Can anyone comment on the following derivation of that relation? Take one ...
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1answer
26 views

Is it possible to measure the spin of an electron without moving it?

I know that the position and spin operators commute, so it is theoretically possible. What I want to know is, what experiments currently exist that achieve this?
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2answers
349 views

Ball flying towards me - Newton's third law is violated?

I was trying to answer the question of the flying ball here on the basis of Newton's third law and momentum conservation. Here is what I have tried. Lets take a ball mass of $m_1$ (index 1 is the ...
0
votes
1answer
18 views

Spheres collide with merry-go-round [closed]

Four spheres, with uniform densities $\rho_1, \rho_2, \rho_3, \rho_4$ and radii $r_1, r_2, r_3, r_4$, respectively, roll without slipping with constant velocities $v_1, v_2, v_3, v_4$ along tracks ...
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4answers
4k views

Does conservation of momentum really imply Newton's third law?

I often heard that conservation of momentum is nothing else than Newton's third law. Ok, If you have only two interacting particles in the universe, this seems to be quite obvious. However if you ...
4
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3answers
102 views

Same quantum states represented in different basis

In literature on an introduction to quantum mechanics which I am working through, there is a section which explains that a vector has different representations based on the basis you choose and then ...
3
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2answers
142 views

Schrödinger equation in momentum space

In literature on an introduction to quantum mechanics which I am working through, there is a section which explains that a vector has different representations based on the basis you choose. It then ...
5
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2answers
825 views

Why is the “canonical momentum” for the Dirac equation not defined in terms of the “gauge covariant derivative”?

The canonical momentum is always used to add an EM field to the Schrödinger/Pauli/Dirac equations. Why does one not use the gauge covariant derivative? As far as I can see, the difference is a factor ...
0
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1answer
38 views

Is Momentum conserved in this block-wedge system?

There's a block slides downward along a frictionless wedge which sits on a frictionless horizontal surface, when the block leaves the wedge, both of the wedge and the block have a horizontal velocity ...
3
votes
2answers
54 views

Does inelastic collision say the ball bounces back to you when thrown at an angle on ground?

I created a bounce simulation using exactly the formula from Wikipedia. The behavior I observe is not what I would expect in two cases: When two balls hit off-centre, they act the same as if the ...
1
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0answers
49 views

Heisenberg theory of uncertainty

I was watching a video on YouTube about uncertainty theory of Heisenberg it said that there is a relation between momentum (multiple of mass and speed) and wave length. And the relation is that if ...
0
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1answer
23 views

A person on a concrete slab on a frozen lake starts walking $ 2 m/s$, what is the speed of the concrete slab? [closed]

Full question: My attempt: Let the M be the mass of the person. Let x be the length of the slab. The original center of mass is $\frac{5M\frac{x}{2}}{M + 5M}$. Let's say the person walks a ...
1
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2answers
168 views

Problem on electromagnetic induction and Newtonian physics

Please imagine a solenoidal toroid (i.e. a donut shaped inductor) powered by an AC voltage source. It creates a changing magnetic field which is confined to the interior of the toroid (i.e. within the ...
0
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4answers
43 views

Why are some system defined with the name “variable mass”?

I do not get why system such as the rocket in space are defined as "variable mass" since the mass of the system is not varying. The equation used for such systems $$\sum F^{(E)}=\frac{d\vec{P}}{dt} ...
2
votes
2answers
5k views

Inelastic collision and conservation of linear and angular momentum

Is it possible for two spheres (a & b) to have an inelastic collision with BOTH the total linear and angular momentum preserved? I'm doing some physics simulation of some spheres attracting each ...
1
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1answer
38 views

How to write the velocity of gas in rocket motion

Consider the motion of a rocket of mass $m$ in space with gas expelled at relative velocity $u$. I found two different version of writing the momentum of the system on Klepper Kolenkow and Morin book. ...
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votes
2answers
61 views

How can work be done during collisions? [closed]

Consider a collision between two material points, with no external forces acting on the system. Linear and angular momentum of the system are always conserved, while the kinetic energy of the system ...
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1answer
27 views

why laser beams don't get reflected (or knocked away) when they intersect with each other?

laser beams are photons with the same frequency and the same direction, but according to the wave-particle duality, photons have mass. but if we shoot two masses and they intersect at some point ...
0
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1answer
46 views

2D Momentum question

I am working through some questions in practice for a mechanics exam and I cant seem to find a solution to the following problem; Two objects, one of which is initially at rest, undergo a perfectly ...
3
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7answers
493 views

Why isn't momentum conserved in this pulley problem?

I have some conceptual doubt about method of solving this problem. 24. A block of mass $m$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown in figure ...
2
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0answers
62 views

What happens to Newton's Third Law during the reflection of a pulse from a free end?

Well, it is known that a pulse gets inverted when it gets reflected from a fixed support while the polarity of the pulse remains same when the incident pulse gets reflected from a free end. However, ...
0
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1answer
117 views

Pressure, Momentum and Energy: A 'Peculiar' Relation

Is the following possible? $$ P = \frac{p^2}{3E} $$ where $P$ is pressure, $p$ is momentum and $E$ is energy. In what convention is the above relation acceptable? EDIT: The source paper can be found ...
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0answers
35 views

Can a collision of 2 objects result in one object having a higher velocity than either object had before they collided?

Assume I had 2 perfectly elastic billiards balls of the same size and mass, that can roll on an endless billiards table losing no kinetic energy to friction. Is there a set of 2 velocities v1 and ...