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GeneralRe: hamilton algorithm Pin
soap brain22-Apr-08 1:06
soap brain22-Apr-08 1:06 
GeneralRe: hamilton algorithm Pin
73Zeppelin22-Apr-08 1:33
73Zeppelin22-Apr-08 1:33 
GeneralRe: hamilton algorithm Pin
soap brain22-Apr-08 1:58
soap brain22-Apr-08 1:58 
GeneralRe: hamilton algorithm Pin
73Zeppelin22-Apr-08 2:10
73Zeppelin22-Apr-08 2:10 
GeneralRe: hamilton algorithm Pin
soap brain22-Apr-08 2:49
soap brain22-Apr-08 2:49 
GeneralRe: hamilton algorithm Pin
73Zeppelin22-Apr-08 3:30
73Zeppelin22-Apr-08 3:30 
GeneralRe: hamilton algorithm [modified] Pin
soap brain22-Apr-08 17:23
soap brain22-Apr-08 17:23 
GeneralRe: hamilton algorithm Pin
73Zeppelin22-Apr-08 22:21
73Zeppelin22-Apr-08 22:21 
Ravel H. Joyce wrote:
No acceleration = no forces?


But can I not put a particle in a magnetic field or even a gravitational field and have it exhibit zero velocity? Can I not put a particle in a magnetic field or even a gravitational field and have it exhibit no acceleration? ("At rest" implies zero velocity.)

Let's get a nice, accurate definition of no acceleration:

1. No acceleration = no NET external forces.
2. A net external force acting on a particle produces an acceleration in the direction of the force - the force being equal to the product of the particle's mass times its acceleration. Sound familiar?

Ravel H. Joyce wrote:
Moving in a straight line relative to what? At rest relative to what?
I didn't think that there was a difference...
[Edit #1] Wait...I'm confused about kinetic energy. So...accelerating something gives it kinetic energy? What is kinetic energy? Is it an increase in mass because of an increase of energy? (E=mc2)? Or am I just completely missing the point?
Maybe I'm just making this unnecessarily complicated...
[Edit #3] I don't think I really get the concept of 'at rest'.
Just a thought - would the act of dropping a nuclear bomb (and having it accelerate towards the ground) increase the energy of the explosion a tiny bit? Rather than having it sit motionless? Ignoring, of course, the ground absorbing heaps of the energy of the explosion.


You are over-complicating it. Let's go step by step.
For your edit 1: When a particle is at rest in the presence of external forces, it possesses potential energy. When you climb up a hill and sit on top of that hill (at rest, v=0, a=0 and so no net external forces acting on you) you possess potential energy. If you roll down the hill - you start to accelerate down the hill with acceleration due to gravity, g - then you possess kinetic energy. You have taken the potential energy you gained by climbing that hill and converted it to kinetic energy. As you accelerate down the hill and your velocity increases you gain kinetic energy. Eventually you will stop accelerating and move with constant velocity, v. Your kinetic energy is then proportional to your mass times the square of your velocity. So kinetic energy is very sensitive to velocity!

Kinetic energy is 0.5*m*v^2, where m is the mass of the particle and v is the velocity. Kinetic energy is "energy of motion", hence "kinetic". Any particle with nonzero mass (or with zero mass! but the above equation is no longer valid) and velocity possesses kinetic energy. Since acceleration doesn't appear in the equation, acceleration can be zero and a particle can still possess kinetic energy. Kinetic energy, in the classical sense, isn't an increase in mass, no.


Ravel H. Joyce wrote:
Just a thought - would the act of dropping a nuclear bomb (and having it accelerate towards the ground) increase the energy of the explosion a tiny bit? Rather than having it sit motionless? Ignoring, of course, the ground absorbing heaps of the energy of the explosion.



No. It would certainly increase the kinetic energy of the bomb, but not it's yield. The yield is proportional to the configuration of the bomb, not it's velocity towards the ground.


Ravel H. Joyce wrote:
Ground state.
Lowest energy configuration.
What does that entail? Absolute zero?


No, not absolute zero. That's something different. In the basic hydrogen atom you have a proton for the nucleus circled by an electron. The electron "orbits" the proton and possess a certain quantized energy value. If we "excite" that atom, the electron "jumps" to another energy level by another distinct "quantum" of energy. There are ground state hydrogen atoms all around you! There are ground state atoms of neon gas all around you! An example of neon atoms not in the ground state is a neon store sign! When you add energy to "excite" a neon atom, you cause some electrons in that atom to jump from their ground state to higher energy levels. As they fall back to the ground state they emit light - that light is the light you get from a neon sign.

Ravel H. Joyce wrote:
Question: if you accelerate an atom to a high enough speed can it cause an electron to jump to a higher orbital?
Ground state incorporates both being at rest and having minimum level energy electrons, doesn't it?


Not by accelerating the atom, but by adding energy to it - for example hitting it with another particle. On impact, the impacting particle can impart energy to the target atom. That energy will cause orbital electrons to jump into higher energy orbits. The ground state doesn't imply "at rest" here. The ground state implies the minimum energy configuration for the atom's electrons.



Ravel H. Joyce wrote:
Kinetic energy is a relative measure, isn't it? Ek = 1/2*m*v2, and velocity is relative, so kinetic energy is too?


Ahhhh...now you get into relativistic corrections...to give you a simple answer - yes, there is a relativistic version of the kinetic energy equation. But to talk about that, we have to consider velocities that approach the speed of light.



And when the sunlight hits the olive oil, don't hesitate.

GeneralRe: hamilton algorithm Pin
soap brain22-Apr-08 22:30
soap brain22-Apr-08 22:30 
GeneralRe: hamilton algorithm Pin
soap brain22-Apr-08 22:53
soap brain22-Apr-08 22:53 
GeneralRe: hamilton algorithm Pin
73Zeppelin22-Apr-08 23:56
73Zeppelin22-Apr-08 23:56 
GeneralRe: hamilton algorithm Pin
soap brain23-Apr-08 0:15
soap brain23-Apr-08 0:15 
GeneralRe: hamilton algorithm Pin
73Zeppelin23-Apr-08 0:43
73Zeppelin23-Apr-08 0:43 
GeneralRe: hamilton algorithm Pin
soap brain23-Apr-08 0:57
soap brain23-Apr-08 0:57 
GeneralRe: hamilton algorithm Pin
73Zeppelin23-Apr-08 1:05
73Zeppelin23-Apr-08 1:05 
GeneralRe: hamilton algorithm Pin
soap brain23-Apr-08 1:28
soap brain23-Apr-08 1:28 
GeneralRe: hamilton algorithm Pin
Paul Conrad2-Aug-08 11:04
professionalPaul Conrad2-Aug-08 11:04 
GeneralRe: hamilton algorithm Pin
Paul Conrad2-Aug-08 11:02
professionalPaul Conrad2-Aug-08 11:02 
GeneralProcess time of the Skipjack and RC5 [modified] Pin
Cryptogrpahy6-Apr-08 23:02
Cryptogrpahy6-Apr-08 23:02 
GeneralRe: Process time of the Skipjack and RC5 Pin
cp98767-Apr-08 1:21
cp98767-Apr-08 1:21 
GeneralRe: Process time of the Skipjack and RC5 Pin
Cryptogrpahy7-Apr-08 2:09
Cryptogrpahy7-Apr-08 2:09 
GeneralRe: Process time of the Skipjack and RC5 Pin
cp98767-Apr-08 15:49
cp98767-Apr-08 15:49 
GeneralRe: Process time of the Skipjack and RC5 Pin
Cryptogrpahy8-Apr-08 2:44
Cryptogrpahy8-Apr-08 2:44 
GeneralRe: Process time of the Skipjack and RC5 Pin
cp98768-Apr-08 18:20
cp98768-Apr-08 18:20 
GeneralNumber of answers for complex numbers Pin
MarkB7772-Apr-08 16:45
MarkB7772-Apr-08 16:45 

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