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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Selection of system in Conservation of momentum

I came across a question in which a cart is moving and having sand. Suddenly the sand valve malfunctioned and the sand starts falling from the cart. So momentum of which system will remain conserved. ...
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64 views

Diffracted electron - where does it gain additional momentum?

When an electron is diffracted, the momentum after the diffraction has different direction than before. Where does the electron gain this momentum? This is related to this question, but it's ...
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56 views

Is there a general formula to translate from *canonical* to *physical* momentum?

In Peskin and Schroeder, after having derived a conserved tensor $T^{\mu \nu}$ associated with translations in space-time (the stress-energy tensor), it is said that the charges $\int d^3 x T^{0i}$: ...
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Obtaining momentum operator $P^\mu$ from Lagrangian and energy-momentum tensor $T^{\mu\nu}$

I am pretty new to quantum field theory. Given the Lagrangian density, $$ \mathcal{L} = \frac{1}{2} ( \partial_\mu \phi ) ( \partial^\mu \phi ) - \frac{1}{2} m^2 \phi^2 $$ and its energy-momentum ...
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246 views

Isolated and non-isolated systems: Momentum?

I'm having a difficult time understanding why two billiard balls colliding is an isolated system, yet a car crashing into a wall is a non-isolated system. Does it really only have to deal with the ...
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5answers
364 views

The elusive difference between force and impulse

Impulse is defined as the product of a force $F$ acting for a (short) time $t$, $J = F*t$, and that is very clear. What I find difficult to understand is how a force can exist that doesn't act for a ...
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584 views

Relation between linear momentum and translational kinetic energy

The momentum $m v$ of a particle is formally the same as the derivative its translational kinetic energy $\frac{1}{2} m v^2$ with respect to $v$. Similarly the angular momentum $I \omega$ is the ...
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66 views

What does the relation between mass and energy of a free particle mean?

What does the Hamiltonian for a free particle mean? Does it mean that the kinetic energy of the particle is in reverse relation with mass? $H$ or $E=\hbar^{2}k^{2}/2m$. Or better to ask: what's the ...
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49 views

Mass of photon, is it possible? [duplicate]

$P=E/C$ In relativistic mechanics a Photon is defined as. $P=hf/C$ Replacing "P" $ mc=hf/C$ $M=h/CT$ What does it mean, did they have mass?
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28 views

Conservation of generalized energies in Newtonian and Relativistic Systems

I was considering the following problem: In a closed system, it is assumed that mass, momentum and energy is conserved. If we label the total mass of the System $M(i)$ at a time i, the total Momentum ...
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170 views

Force of a Train

Imagine that there are two trains and the first train is twice as long as the second train. They have the same mass per unit length and they are traveling at exactly the same speed. If the first ...
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Does a force really act on a body during a collision?

Consider two bodies A(black) and B(red) having equal mass. A is moving at a constant speed towards B, which is stationary. At certain point of time, they collide elastically, $\therefore u_{A}=v_{B}$ ...
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Does Newton's third law apply to momentum or to forces?

I read all the previous answers concerning the 3rd law and I have seen that it is definitely not universal, (Edit: but conservation of momentum is. If it is not universal it should be not a problem to ...
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Conservation of momentum when rain pours into a wagon

Suppose a wagon is moving at constant velocity on a friction-less surface, and rain begins to fill the wagon. The net force on the wagon is zero, so momentum is conserved; as the mass of the wagon ...
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1answer
118 views

Total divergence term and corresponding Feynman Diagram

A total divergence term added to the Lagrangian doesn’t affect the action because the integral of a total divergence vanishes. But if one attempts to derive the Feynman rules from the Lagrangian with ...
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3answers
72 views

Why doesn't an object that collides with one that is at rest just do a 180?

Newton's third law says "for every action, there's an equal and opposite reaction." So why is it, say, that when a pool/billiards ball hits the wall of the table, the ball doesn't just turn around?
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1answer
74 views

What is the motion of a balloon with a person climbing on a ladder?

Suppose you had a balloon of mass $M$ in the atmosphere at rest relative to the ground, with a ladder attached reaching towards the ground. A person (of mass less than $M$) begins climbing up the ...
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47 views

How are momentum and position operators dependent on the chosen inertial frame?

How are momentum and position operators in quantum mechanics dependent on the chosen inertial frame of reference?
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65 views

Does constant velocity of center of mass imply linear momentum is conserved?

I know that if momentum is conserved for a system, you can derive that the velocity of the center of mass of that system is constant. I was wondering if the second condition also implies the first: if ...
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1answer
58 views

Relationship between momentum and energy for rocket-powered aircraft

I'm trying to write a problem for my students in an algebra-based physics class. We have a flight simulator and I've got a glider in the simulator that has a couple rocket boosters attached. Students ...
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2answers
78 views

Interpretation of the four-vector $k$ in scalar QFT

I'm studying the canonical quantization of the Klein-Gordon real scalar quantum field theory, given by the classical Lagrangian density $$\mathscr L = {1\over ...
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3answers
151 views

Is the kinetic energy of an electron always $1.6 \cdot 10^{-19}~\text{J}$?

I was doing the following problem. For $d$. They bizarrely added an extra step. They calculated the momentum of the electron to find the De Broglie wavelength using the kinetic energy relationship. ...
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2answers
93 views

Playing catch in space?

I was thinking about this on the bus (exam this week :P). What would happen if two people played catch in outer space? Lets say person A and B are in space at rest, A throws a mass m at B, what ...
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Ball flying towards me or me flying towards ball

Suppose a ball is flying towards me at a speed of 10m/s and that, on impact, I feel "x" amount of pain. If, instead, it was me flying towards the ball at the same speed, with all other conditions ...
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88 views

Origin of momentum. Noether's theorem

My professor talked about Noether's theorem and how translation is the origin of momentum conservation. But why is it not velocity that is conserved but mass times velocity. And on the same note why ...
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Low-momentum behaviour of a short-range potential

I've read the follow sentence in a journal article (arXiv preprint) which constitutes part of my coursework. As discussed in the previous section, the low-momentum behavior of any short-range ...
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281 views

Total Momentum From a Standing Electromagnetic Wave

How does one show the momentum imparted to a perfect conducting resonance cavity (boundary) of any shape by a classical standing electromagnetic wave inside is zero? It should be by conservation of ...
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2answers
98 views

Why do these two derivations of the formula for impulse contradict?

I was trying to derive $I = F\Delta T$ from $p = mv$. First I converted $v = at$: $$\begin{align} p &= mv \\ p &= m \times at \\ p &= ma \times t \\ p &= Ft \\ \Delta p &= F ...
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4answers
170 views

Why is $M\frac{dv}{dt} = v_{rel} .\frac{dm}{dt}$ correct and $(M - dm)\frac{dv}{dt} = v_{rel} .\frac{dm}{dt}$ wrong?

Newton's 2nd law of motion can't be applied for mass-varying systems. Another force, known as Thrust must come to play. It can be measured using law of conservation of linear momentum. ...
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24 views

How does momentum effect velocity? [duplicate]

I'm in AP physics and we haven't even covered this yet so sorry if my question seems strange... I know $p = m v$, However right now I am writing a 2D physics engine and I am having some trouble with ...
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1answer
299 views

What is the time dependent expectation value for momentum

For an electron in an equal linear superposition of two eigenstates in a one-dimensional infinitely deep square potential well of width L, how do you isolate the time dependent part of the expectation ...
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2answers
183 views

A student of mine wants to build a Gyroscopic Inertial Thruster

I work as a tutor with students in their first three semesters. One of my more eager students is obsessed with this thing: A Gyroscopic Inertial Thruster Here is a Wikipedia Article on that. I was ...
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3answers
480 views

Impulse and force in a karate chop, can we maximize force minimizing the time of impact?

I have heard that we can maximize the force by minimizing the time of impact in a punch. If that is true, the paradox is if we increase the time of contact with the same amount of force still we ...
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71 views

Throwing a baseball against the back of a car [closed]

We, some fellow students and I, are trying to figure out what to. But we simply do not know which formula to use at question a. We found the following: $\Delta P=(2mv_{ball,i}M)/(m+M)$ Could someone ...
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2answers
79 views

Mathematical subtlety in a physics problem

A wagon of initial mass $M$ is moving with an initial velocity $V_o$. Now sand starts accumulating on this wagon, increasing the total mass from $M$ to $M+s$. We have to find the final velocity of ...
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1answer
67 views

Why does accounting for direction give the wrong result for a bouncing ball?

This a conservation of momentum problem, gathered from an old textbook. I thought it would be simple, but I seem to be goofing up somewhere in my basic conceptual understanding. PROBLEM: A 1.0 kg ...
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3answers
101 views

Work done after explosion of chemical bomb

Question: Suppose, a chemical bomb is stationary. Then it explodes into n parts in all direction. What is work done? My Efforts The bomb is stationary, so momentum and and kinetic energy is 0. ...
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1answer
150 views

Can Hooke's law go along with Newton's 3rd law & how is momentum conserved in case of spring?

Let there be a spring in its relaxed state- that is neither compressed nor extended. One end is fixed on the left and other end is free in the right. Now, I stretch the spring by pulling the free-end ...
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510 views

Question of Conservation of Momentum

I think I understand the concept of conservation of momentum in an inelastic collision. However, what if two objects, one being more massive than the other, started out together and then separated ...
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1k views

Elastic Collision And Momentum

The question I am working on is, "Two blocks are free to slide along the friction-less wooden track shown below. The block of mass $m_1 = 4.98~kg$ is released from the position shown, at height $h = ...
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Calculate the distance travelled by hot air before it looses its momentum

Hot air is released from a nozzle with certain velocity into the atmosphere. As the stream travels, it looses momentum and after some time mixes with air.How can we calculate the distance the stream ...
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2answers
123 views

Penetration of a bullet into a wall

In which of the following situation will the bullet of the pistol penetrate deeper in the wall? Why? Alternatively will the penetration in both cases be the same? Can you explain the concepts behind ...
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3answers
356 views

Quantum explanation of Newton's Third Law of Motion

Newton's law states that for every action there is equal and opposite reaction. This law explains how rockets fly in space and accounts for the the majority of the lift action generated by a ...
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1answer
59 views

Calculating speed of spheres in an asymmetric Newton's cradle?

If we assume there is an asymmetric Newton's cradle with 3 spheres of different masses and the first one is initialized with some certain speed can we calculate the outcome speed of the all the three ...
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1answer
97 views

Conservation of momentum 1-D problem: track is not level

This problem is a standard kind of 1-D problem. You have 2 equal carts approaching each other and collide on linear air track. BUT the person setting up the track did NOT do a good job at making the ...
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2answers
174 views

Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?

I'm curious where the de Broglie relation $p=\frac{h}{\lambda}$ comes from? I know that for light (which has no rest mass), the following is true: $E=pc$ and $E=hf$ so, $$pc=hf \Rightarrow ...
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Newton's cradle

Why, when one releases 2 balls in Newton's cradle, two balls on the opposite side bounce out at approximately the same speed as the 1st pair, rather than one ball at higher speed, or 3 balls at lower ...
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What matters more in the strength tester game at a carnival, momentum or force?

A buddy and I were arguing over which matters more in the strength tester game (assuming the same accuracy of the hit): 1) momentum or 2) force. He was arguing that if you swing the hammer directly ...
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245 views

Is it possible for photon to run in circle by its own gravity?

I have heard that gravity came from energy and momentum so photon has gravity too. Then there are theory state that photon has energy tied to frequency. So if a photon has very very high frequency ...