Recent content by M-Speezy

I figured it out I think. If the force at t+dt is instead expressed using a first-order approximated taylor series, then the extra dt comes out.

Why does this matter, though? I would think Newton's 2nd law would be used, and then a change in the momentum would simply be given by f(t)dt. I'm not sure what else should be done to lead to anything else.

I have begun studying Ashcroft + Mermin on my own, and am trying to follow the math in the text. They suggest that an electron in a metal with some momentum p(t) and exposed to a force f(t) will at some time later (t+dt) have a contribution to the momentum on the order of f(t)dt plus another...

When normalizing a Wavefunction for a particle on a ring why is the normalization only done as dPhi? It's a particle on a ring, so shouldn't it be r*dPhi? This is my thinking, but I do not find other solutions doing this, just ignoring the r part. I understand that for a ring it's just a...

For center of mass problems, it's possible to use a variable mass distribution. For a half cylinder, I've been looking at different mass distributions (constant, 1/r, 1/r^2, etc.) My teacher pointed out that at some point it runs into problems. I found that this was the case at 1/r^3, as you...

I think I may have answered one of my questions, the one about ignoring portions of solutions. Griffiths discusses the fact that sines or cosines can be used to construct any solution, so it is somehow justifiable. I think to understand it at a deeper level I'd be looking at a lot of math. My...

I am curious how legitimate a solution Separation of Variables tends to give. I've been working problems out of Griffith's book on Electromagnetism, and am often uneasy as to the way things are done. I have two specific issues. The first, is that in spherical it is often necessary to remove...

Oh, now that is an interesting thought. Thanks for your help, you've done wonders to clear this up for me. Have a good day!

How literally should we take Earnshaw's theorem then? What if instead of a cube it were a spherical array of positive charges. Would you still have the same result, of it being mathematically impossible to contain the charge using electrostatic repulsion? I can see why this would be the case...

I was working on a problem out of Griffiths, and have become a bit confused. The problem is regarding to Earnshaw's theorem, which states that a particle cannot be held in stable equilibrium by electrostatic forces. (3.2 for anyone with the text). He suggests a cube with a positive charge on...

The exhaust velocity is considered to be with respect to the rocket, and assumed constant. The faster the rocket, the higher the exhaust speed would be to a rest frame. Also, the derivative of velocity is the reason why it was an issue, because the velocity has such a complex relationship with...

Nevermind, I realize now what this is. M is the variable that's being used. Rather than doing what I did, finding the specific time where it's maximized, it's easier to find the mass where it's maximized. At that point, it's trivial to find the time. Sorry, I should have been more observant of...

Generally, we would say that the there's an equal and opposite force between ejected fuel and the momentary acceleration of a rocket. (This is how they accelerate in space) Specifically, d(m)/dt*velocity of jettisoned gas = -m*dv/dt This is rearranged so that it's integral (dm/m)=integral (dv)...

The concept of a problem is that if rockets continue to jettison fuel, at some point they will get a very small momentum because their mas will be so small. (Bit of a silly problem, there's a lot of mass in the rocket itself) Anyways, the idea is that you would take the derivative of the...