3
votes
1answer
127 views

Directional derivatives in the multivariable Taylor expansion of the translation operator

Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$. Where $P=-i\hbar \nabla$. Here's what I've gotten: ...
4
votes
3answers
110 views

Different results to a basic question ( Newton's law and perservation of momentum)

Trolley with mass of $m_0=1 \ kg$ is moving without friction on the railway track. It is raining so there is a constant mass flow of water $\Phi_m=0.1\ kg/s$. Constant force $F=0.1 \ N$ is ...
-2
votes
1answer
39 views

What formula connects the moment of inertia and angular velocity? [duplicate]

I need to determine angular velocity of a disc when a man with given mass and speed whacks on the edge of it. I calculated the total moment of inertia of disc and body, how do I calculate the ...
0
votes
1answer
49 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 ...
3
votes
1answer
58 views

Why do safety helmets have a softer inner layer nearer the head?

I know that when an object collides onto the helmet, it causes an inelastic collision so that energy is absorbed by the structure of the helmet, so what exactly does the softer inner layer do? Does it ...
0
votes
1answer
40 views

I need to know how many pounds of force a 3 million pound object has moving at 1 mph [closed]

How many pounds of force does a 3 million pound object have moving at 0.1, 0.5, and 1 mph?
0
votes
3answers
47 views

Kinetic energy relationships with momentum and mass [closed]

If I have some arbitrary particle, we will call particle 1 and another particle 2 that have the same momentum, yet particle 1 has half the mass of particle 2, how does the kinetic energy compare ...
0
votes
2answers
67 views

Calculating velocity change after impact?

Let's say there is no gravity here and objects won't crush. We have 2 rocks with $m=10\text{ kg}$. First rock has velocity $v_1=0\text{ m/s}$ and second $v_2=10\text{ m/s}$ (flying in leftward ...
0
votes
2answers
85 views

Ballistic Pendulum Demo Problem

I have a question about the following problem: I got the solution $v=\frac{M+m}{m} \sqrt{2gh}$. But my real question is in the following picture: In the above slide, how can you derive ...
3
votes
1answer
39 views

Probability of measuring momentum [closed]

Suppose we have this wavefunction: $$ \psi = A \left( cos(kx) + cos (2kx) \right) $$ I have to find the possible results of measurement of momentum and their probabilities. Attempt For a momentum ...
0
votes
1answer
40 views

Spacecraft momentum question [closed]

Assume you're sitting in your spacecraft. The mass of you and the spacecraft is 2000 kg. You're traveling at 200km/h through the vacuum of space. You have a thruster pointing in the direction you're ...
2
votes
3answers
84 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 ...
1
vote
0answers
33 views

Calculating a spacecraft's deflection angle [closed]

There is a spacecraft with mass $M_1$ moving in a certain trajectory with a constant speed $V_r$. To modify its trajectory, a engine is turned on and starts ejecting gas at a speed $V_g$, which is ...
2
votes
1answer
76 views

Does the average momentum vanish for an eigenstate of the simple harmonic oscillator?

Suppose we have a simple harmonic oscillator, let's consider the ground state, $|0\rangle$ and the first excited state $|1\rangle$. $\langle 0|\hat p|0 \rangle$ is zero right? Since the particle can ...
1
vote
0answers
72 views

Particle In a Box and momentum, velocity

So on a homework assignment, we are give the width of a well, $a$, and the mass of the particle $m$ and we want to find the average velocity of the particle at the n=1 state. So here is my attempt at ...
0
votes
1answer
84 views

Quantum Mechanics - Finding momentum probability density [closed]

everyone. I got a bit stuck on 2(iii), this is supposed to be a easy question, but i don't know how you get the square term? I thought you just do the Fourier transform, but then I got some ...
-1
votes
1answer
87 views

How does $p_x$ commute with $p_y$, i.e. $[p_x,p_y]=0$? [closed]

I know it's a simple and basic question but would someone show me how to evaluate $[\hat{p}_x,\hat{p}_y]$?
0
votes
1answer
59 views

Recoil from a shotgun

First of all I'd like to point out that I'm a complete layman when it comes to physics and I apologise if this isn't the correct forum for this. If I were to sit on an office chair on a laminated ...
0
votes
2answers
41 views

Calculating the Probability Current of a Travelling Wave

Calculate the probability current density vector $\vec{j}$ for the wave function : $$\psi = Ae^{-i(wt-kx)}.$$ From my very poor and beginner's understanding of probability density current it is : ...
1
vote
1answer
63 views

Colliding particles at speeds aproaching c [closed]

(In natural units where $\hbar=c=1$.) Two particles are to be collided. Each of these particles has a rest mass of 0.9 GeV and they will be collided at equal but opposite speeds. What is the minimum ...
1
vote
0answers
19 views

Calculating rate of change of momentum for a package [closed]

A helicopter is flying to the right (in the $+x$ direction) with a constant speed $v$, carrying a package of mass $M$ suspended below it using a cable as shown in the figure. (You can assume that $H$ ...
1
vote
1answer
145 views

Spring Damper System : Recoil Reduction

I am designing a man-"portable" 30mm sniper rifle. Although it may be classified as a anti-materiel cannon. I have the mass of the round in total, and the mass of the projectile leaving the barrel, ...
0
votes
2answers
78 views

Conservation of Mass, Momentum and Energy - Airburst Rounds

I have a airburst round with set amount of fragments with a certain shape inside my bullet. After a certain distance has travelled, a charge explodes in the back of the round disintegrating the shell ...
0
votes
1answer
84 views

Relative Velocities and Conservation of Kinetic Energy

An object of mass m moves with velocity $v$ towards a stationary object of same mass. Impact is an elastic collision. $v_1$ is the velocity after impact of the mass originally moving $v_2$ is the ...
1
vote
1answer
98 views

How do I calculate stopping power?

Malcolm Gladwell made a claim in a recent talk that a sling with a stone going at 30m/s has the same stopping power as a .45 calibre handgun. How would I verify whether or not this claim is true - ...
0
votes
3answers
69 views

Confused about Impulse

Encountered a problem that involves impulse while studying for my exam and I'm not sure how to even approach it. I know that momentum is conserved, but I'm not sure how to relate that to avg force. ...
0
votes
2answers
54 views

Homework Question involving Momentum [closed]

I'm trying to solve a homework problem as review for an exam I have tomorrow and I was wondering if someone could help explain it to me. It is as follows: You are at Lowe’s shopping for bricks ...
3
votes
0answers
157 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 ...
0
votes
1answer
45 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 ...
1
vote
2answers
45 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 $x$?
1
vote
2answers
116 views

A question about canonical momentum and arbitrariness for potential in magnetism

The following question confuses me: There exists magnetic field $B_z =- \beta x$ where $x > 0$, and a particle is incident from origin point $(0,0)$ with pisitive charge $q$, mass $m$, and ...
0
votes
2answers
220 views

Energy transfer in elastic collision [duplicate]

In a given reference frame where object 1 (with known mass and velocity) collides elastically with object 2 (with known mass and velocity), can we identify which object loses kinetic energy? Is it ...
1
vote
3answers
666 views

When is energy conserved in a collision and not momentum?

Consider the following example: A bullet of mass 45g is fired at a speed of 220 m/s into a 5.0 kg sandbag hanging from a string from the ceiling. The sandbag absorbs the bullet and begins to ...
1
vote
0answers
61 views

Collision Between Two Particles: Writing the Mass As A Function of The Angle [duplicate]

Suppose we have two masses, $m_1$ and $m_2$, where $m_2$ is at rest, and $m_1$ is headed directly towards $m_2$. I would like to write the ratio of the masses as a function of the angle. Using ...
2
votes
2answers
210 views

How to calculate velocities after collision?

I'm currently writing a program for a particle simulator. One of the requirements is that the particles collide in a realistic way. However, I don't know how to calculate the final velocities. For ...
-1
votes
2answers
52 views

A block in motion explodes [closed]

A 9.5 kg block (A) is traveling in the positive x-direction with a speed of 3.0 m/s. At some point, it explodes and breaks into two pieces. After the explosion, block C, which is 6.0 kg, moves off ...
2
votes
2answers
865 views

Calculating angular velocity after collision

Suppose I have a disc which doesn't move, just rotate around the axis going through its centre of mass perpendicular to its surface. The disk has a stick perpendicular to its surface at the edge. I ...
1
vote
3answers
216 views

Effect of incoming force on linear vs. angular velocity

First of all, I should note that I'm a programmer and have only an extremely basic understanding of physics; I only know how to explain my question in layman's terms and I apologize if I'm unclear or ...
8
votes
5answers
814 views

How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
1
vote
1answer
101 views

Confused about elasticity and collisions

I was solving the following problem and the explanation to it confused me. There are two objects with mass $m$ and $M$, respectively. The object with mass $m$ has a velocity of $\sqrt{2gl}$ and ...
0
votes
2answers
164 views

Not so simple problem using momentum, energy and angular velocity…?

I have an object in free space (no gravity) with angular momentum $ = \omega_i $, and some velocity vector $=\vec{V_i}$. To simplify we will say it has a mass-less rigid rod length $ = \ell $, ...
-2
votes
1answer
53 views

momentum conservation related to varying mass . please help? [closed]

a heap of chain is lying on a horizontal table a small part of the chain is released through the hole in the table . Calculate the velocity of the chain as a function of length of the vertically ...
0
votes
1answer
302 views

Harmonic Oscillator Energy to Momentum Expectation Value

If we are given a wave function written in terms of harmonic oscillator energy eigenfunctions how can we determine the maximum possible momentum expectation value? It's a combination of the first two ...
1
vote
1answer
113 views

Changing Momentum

Okay, so I am having a hard time wrapping my head around this. Before looking at the answer, I worked the example and got the answer only because I used dimensional analysis to get me to the right ...
0
votes
1answer
204 views

Muon 3 Body Decay

I'm trying to calculate the maximum energy of the electron in the decay muon >electron + electronantineutrino +muonneutrino in the reference frame of the muon having no kinetic energy. $m_m$=mass of ...
2
votes
2answers
3k views

How to find the compression of a spring attached to an object [closed]

I am having some trouble figuring out the equation needed to solve this problem. A 3.0-kg block slides along a frictionless tabletop at 8.0 m/s toward a second block (at rest) of mass 4.5 kg. A ...
1
vote
0answers
362 views

projectile that splits into two fragments of equal mass

I am studying for an exam, and this is part of a problem in my book. A projectile is launch from level ground and is intended to hit a target 100m away. Instead, it explodes into two fragments of ...
1
vote
0answers
31 views

Trouble evaluating an integral arising from particle collision

Assume we have two charged particles colliding. He have particle 1 with mass $m_1$, charge $Z_1 \cdot e$ which travels in $x$-Direction passing by a STATIONARY particle 2 (mass $m_2$, charge $Z_2 ...
1
vote
1answer
3k views

Proof that the momentum operator is Hermitian

I am trying to prove that the momentum $p_x$ operator is Hermitian, my approach is the following $$<p_x>~=~\int \Psi^*(\vec{r},t)[-ih\frac{\partial}{\partial x}]\Psi(\vec{r},t)\, d^3r.$$ I try ...
0
votes
2answers
163 views

How to work out momentum when there are velocity and mass changes

I have a pretty simple homework question, but I can't rap my head around it. In the question a swimmer of $55 \mbox{ } \mathrm{kg}$, jumps off a stationary raft of $210\mbox{ }\mathrm{kg} $. The ...