A problem with KE = ½mv². Help.

[arkain101]

Has anyone heard of ring theory?

 

I just realised it contains the same equation I have been working with to describe motion and interaciton. I think this is what I was striving for when writing the equations. M> = motion relationship. M> = I (M*V)

M> = -M>

-I (M*V) = I (-M*V)

 

 

Ring Theory Definition:

http://en.wikipedia.org/wiki/Ring_theory

 

a * (b * c) = (a * :) * c

a * (b + c) = (a * :cup: + (a * c)

(a + B) * c = (a * c) + (b * c)

and such that there exists a multiplicative identity, or unity, that is, an element 1 so that for all a in R,

 

a * 1 = 1 * a = a

[CraigD]

Has anyone heard of ring theory?

As has nearly anyone under 75 years old with an undergraduate or higher Math degree, I studied rings as part of the standard “abstract algebra” curriculum.

 

My advice would be to study them in their usual context, as part of a systematic treatment of number and set theory. Though this can be done independently, it is for most people much easier to learn in an traditional, instructor and peer assisted setting – that is, in school.

 

Classical Newtonian mechanics are defined for the Real numbers, which are a group, but not quite a ring, under all the required operations. I don’t think an effort to map ring theory onto classical mechanics will prove very useful, though the effort, especially the necessary background-acquiring preparation, could be very fun and rewarding :)

[arkain101]

hehe.. I guess that was my bad to not really read what ring theory was all about..

 

I assumed it was something a little different I suppose.

[Qfwfq]

that all the energy goes into moving the craft, then it will be as I said. Four times the fuel for twice the speed.

If the propulsion system is pushing against the ground, with no slipping, OK, but not with jet propulsion.

 

Suppose your sled weighs a tonne, and you shoot a little pebble to the rear, which of the two will recieve most of the availale kinetic energy?

[Farsight]

Qfwfq: the pebble. If I can summarise what I think I've learnt from this thread. I'd like to use the sled and puck, which is like jet propulsion and your pebble but we know all the numbers:

 

I fire the spring gun, and there's a force acting on the 0.2kg puck, and an equal force reacting against the 100kg sled. Work is defined as Force x Distance and is measured in Joules, as is Kinetic Energy. The puck moves further than the sled so there's more Force x Distance (or Work or Kinetic Energy) going into the puck, by definition.

 

If the system starts from a rest position, it takes 1 puck fired at 50m/s to accelerate the sled to 0.1m/s. A second puck will accelerate the sled to 0.2m/s, so the sled has now has four times the kinetic energy for twice the "fuel". The fuel here is the spring power, and by definition most of its kinetic energy went into the exhaust, which is the puck.

 

But if the system starts from a 50m/s motion in the sled direction, firing the puck at 50m/s means the puck is now travelling at 0m/s, so all the energy went into the sled.

This difference in the distribution means kinetic energy is a relative quantity, and not a fundamental property. It is relative to motion. A sled of mass M has kinetic energy KE relative to an observer moving with a velocity difference V.

 

Because energy is relative rather than fundamental, it cannot exist on its own. Something is not made out of energy, something has energy. Energy cannot be created or destroyed because it was never there in the first place, and all it ever was, was a shorthand mathematical measure of some combination of fundamental properties which do exist. Like Mass and Velocity.

[sebbysteiny]

It all sounds good to me, except this idea that

Energy cannot be created or destroyed because it was never there in the first place

 

Although you qualify this by saying that energy is

a shorthand mathematical measure of some combination of fundamental properties which do exist.

I think this is going too far.

 

I think energy does exist as a real and meaningful concept in a frame, it's just it's exact measurement varies depending on which frame you are it. However, with special relativity, Einstein found an equation that holds for all frames.

 

For example, if you are travelling at 50000 ms^-1 (ie at a non relativistic speed) in space, and come accross the earth for a few minutes and take LOADS of measurements, you will still conclude the Earth's energy resourses will run out and both you and the Earth will agree on the time.

 

Also, this only happens for kenetic energy. Potential energy and other forms all remain constant regardless of the frame.

 

Badly explained perhaps, but I'm sure sombody might be able to get what I'm talking about and explain it better, even if just to refute it.

[arkain101]

I've found that energy is also not a thing in of itself. It is a term that covers the workings of the unified balance between all things.

 

For example, If we point at a flowing water and say look its a river (like saying energy). It is not just a river as simple as that, it is only a river because it is water, on a sloap. It has waves because of rocks. It has swirls because of curves and bends.

 

Energy is what we call everything when we see it working as a unit or whole. However it is not a thing itself which we can look for as a particle or wave. It is the use we can make out of these particles and waves that energy describes.

[sebbysteiny]

Energy is what we call everything when we see it working as a unit or whole. However it is not a thing itself which we can look for as a particle or wave.

 

Photons?? Gluons?? Gravitons (granted, not yet discovered)?? These are all particles for the fundamental forces and their number and / or frequency can tell exactly how much energy there is.

 

Further, ignoring kenetic energy, from E = MC^2, all energy (potential, electric, heat etc) will increase the mass of the object by a small but theoretically measurable amount. And even kinetic energy increases the measured mass in a frame.

 

Surely, this suggests it must be some kind of 'thing'.

[arkain101]

Thats the point. Everything is energy, if you so choose to look at how it can never be created or destroyed but can only change form. So its not a thing of itself. Its the name we give to everything, because everything changes form but is not lost.

 

It isnt energy untill we bother to measure it.

[Farsight]

If I can back arkain up here, sebby: I think energy is a property of something else, not a thing in its own right. It's rather like red. Red can only exist because something has the property of being red. You can't say "hey look, it's a piece of pure raw red".

[Qfwfq]

Is red a conserved quantity?

[Farsight]

I guess not. But you could say "color" is a conserved property. Or "colour".

[Qfwfq]

Hmmm, yeah, according to quark confinement, I suppose it must be conserved!

 

;)

[arkain101]

Is red a conserved property?

 

There is no red. There is no colour period in space-time. It requires none of it to function. There is frequencies or discrete energy values of EMR.

 

Color is seperate, and in order for it to be experienced in space-time is needs to be created in the moment from somewhere outside. The input of EMR's details dictates what it is to 'look' like.

 

I am probably going to cover this in the unified theory model thread I recently started. It of course fits into the theory beautifully.

[Farsight]

That was an analogy, arkain.