Sour grapes, eh? Looks like you think an olive branch is a whipping switch. OK, we'll use it that way. Bend over and let's go back to sophomoric level......
I state above: KEmax=power*mass/resistance. (1) This is not wrong as you imply.
KEmax = 1/2 M vfinal^2 - 1/2 M vinitial^2 (2) where M = mass and v = RMS velocity Starting from zero velocity, the the last term = zero
KEmax then can be written starting from zero velocity as KEmax = M v^2 (3) Assign values for M and v and try it, noting vfinal = vRMS * 1.414
re-arranging eq. (1) KEmax = M (P/R) (4) where P=power R= equivilant resistance Therefore M v^2 = M (P/R) (5) divide both sides by M
v^2 = P/R (6)
from which
P = v^2 R (7)
Which is basic.
Is it time to clip and throw up a smoke screen, i.e. a barrage of non-pertinent theory?
KE = 1/2 M v^2 But v is not 'RMS velocity', it is vfinal.
vfinal is *not* vRMS*1.414 unless you think that your velocity is varying sinusoidally. The 1.414 (sqrt(2)) only works for particular waveform of acceleration and is not always true.
Why would your acceleration be varying, don't you want to accelerate from vinitial to vfinal in a smooth, linear manner? If you do that, your velocity profile is most decidedly *not* sinusoid.
Now you've *jumped* from mechanical system to electrical system? The 'resistance' of a moving body in the atmosphere is completely different from 'resistance' in electrical circuits.
a)rms velocity- are you assuming a varying speed velocity and as it appears from your later 1.414 factor, a sinusoidal velocity? What if you want to simply increase velocity at a constant rate, rather than just wobble back and forth?
b)Your expression (2) is fine if you simply say the "change in" KE = ... and eliminate the rms factor. For an initial velocity of 0 then the final or max KE is given by 1/2Mv^2 where v is the final velocity. This has nothing to do with rms. It simply means that at a given velocity there is a given KE. I suggest that you actually try to find out how this expression for KE is obtained. It should be explained in all but the most elementary texts. If not, I can show it to you.
c)Your equation (4) is made up out of whole cloth. YOU have decided to call power =v^2R without defining R or giving its units. From this point on, you are simply re-arranging the equation.
d)If you are defining mechanical resistance as force/velocity (which you have not said) then Eq.7 simply says that mechanical power =force*velocity and that at a given specific velocity, one can assign a "resistance" Rmec and replace force with (velocity^2) *Rmec. Fair enough and useful in those cases where this is reasonably true One problem is that the mechanical resistance is a non-linear function of velocity so that your approach actually complicates the calculations (disregarding the factor of 1/2). Another and more important problem with this is that you are then assuming an energy dissipating mechanical resistance in place of the undissipated stored kinetic energy of the mass and trying to relate the two is incorrect- it would be like treating an inductance or capacitance as a resistance in circuits- it doesn't represent what is going on.
The value of a model or equation is related to how well it reflects reality. Since you have not presented any reality here, I guess it doesn't matter.
Have fun, but please do attempt to understand what the equation really says in terms of the physical situation it describes. So far there is little sign of that as otherwise you would not be spouting this nonsense.
Agreed. So then I shall accelerate in a sinusoidal manner, starting from zero velocity with acceleration stopping (propulsion energy flow terminated) at the mid point of the sinewave. Overshoot neglected.
R is mechanical ohms. So now what do you make of it, restated here for convenience? TIA
KEmax=power*mass/resistance (1)
KEmax = 1/2 M vfinal^2 - 1/2 M vinitial^2 (2) Starting from zero velocity: KEmax = 1/2 M vfinal^2 Starting from zero velocity, KEmax then can be written as KEmax = M v^2 (3) With v as RMS, and noting v = vfinal * 0.707 re-arranging eq.1 KEmax = M (P/R) (4) where P=power R= equivilant mech. resistance Therefore M v^2 = M (P/R) (5) divide both sides by M v^2 = P/R (6) from which P = v^2 R (7)
rms is meaningful only for periodic signals- i.e, signals such that v(t) =V(t+T) where T is the period. Hence it is meaningless to use "rms" in the situation you postulated as you do not have a periodic signal (part of a sine wave by itself is not a periodic function) nor do you have steady state. Rms "anything" is a convenient mathematical fiction. Certainly it is useful and measuring instruments are calibrated in rms. What you have in actuality is a velocity, force, voltage, etc which exists at a given instant of time. If it varies periodically, then the rms values are useful, otherwise not.
Note that if you stop at the "mid point" of the sine wave (whatever that is) then motion past that point is not sinusoidal. In any case, constant acceleration is more practical than trying to accelerate "sinusoidally" just to complicate the math. You have two equations:
KE max =1/2(m)v^2 (3)
which gives the of a mass at velocity v (actual) This can be recovered.
p (instantaneous)=v^2 R (7 modified) which is the power dissipated at velocity v (actual)in a mechanical resistance such as friction, wind resistance etc. This is lost -eventually as heat. (7 as written with v as rms, is quite correct for the average power over a cycle of a steady state periodic signal but is useless for anything else. In a sinusoidal situation -one or more cycles, then...Pave =Vrms^2 R but this doesn't apply here and even if it did, you would find that the average KE would be 0)
Both equations are correct but they are dealing with two entirely different and unrelated things. This is why your Eq.4 is meaningless.
In writing your equation 4, you have implicitly used equation 7 so the "development" in between is, in fact simply going around in circles because you have used P=R*v^2 in Eq 4 and then found that it led back to P=R*v^2 which means you can divide by m.
Equation 4 simply says that m(R*v^2)/R =(mv^2)*R/R =mv^2 for any value of R. You don't know R, and don't know the power without R so you have introduced two completely unnecessary and meaningless factors. If you knew R, then the equation won't help you as the power calculated has nothing to do with the KE.
I could say that KE =0.5m*(gas)/beans where gas=beans*v^2 and the mathematical reasoning would be exactly the same as that behind your Eq.4.
--And--
just as wrong- for exactly the same reasons.
This is a form of mathematical m*********on because while it may give one pleasure, it does nothing to add to the gene pool of knowledge or understanding.
This and the following was in reply to daestrom, and ask of him. Why did you answer?
OK, you can have the first round, although I have qualms about your m*********on comment. :-)
Now suppose the above applys to the sinusoidal motion of a dynamic PM loudspeaker in a closed box. I believe all equations are valid. Any comments? P.S. Note the third equation was not numbered - I labeled it 2a.
JC: "For my part, anyone is welcome to weigh in on this." DK: "Fine by me."
Now ain't that cute. You clip my analysis and invite comment. IOW, if you can't rewrite history, burn the history book... A *cheap* shot.
My analysis reinstated verbatim:
JC: KEmax=power*mass/resistance (1) KEmax = 1/2 M vfinal^2 - 1/2 M vinitial^2 (2) Starting from zero velocity: KEmax = 1/2 M vfinal^2 (2a) Starting from zero velocity, KEmax then can be written as KEmax = M v^2 (3) With v as RMS, and noting v = vfinal * 0.707 re-arranging eq.1 KEmax = M (P/R) (4) where P=power R= equivilant mech. resistance Therefore M v^2 = M (P/R) (5) divide both sides by M v^2 = P/R (6) from which P = v^2 R (7)
DK: "Eq.2a is valid if v final is the v max. and so is (3) Eq (7) is valid for the P=average power and v as rms velocity. The merging of the KE and power equations (4) is valid for the case of the sinusoidal motion of a PM loudpeaker (or an (electro)dynamic speaker). In fact it is not valid in any case."
JC: "You made a fundamental error: You say equation 3 is valid KEmax = M v^2 (3) You say equation 4 is not valid in any case KEmax = M (P/R) (4) but they are equivilant, since (P/R) = v^2 as shown by equation 7, which you note is correct P = v^2 R (7)
DK: "Eq 4 reduces to KE=KE*(R/R) which is trivially true and an example with differently named variables was given to you."
JC: "Thanks for proving yourself wrong when you said equation 4 was not valid." In view of the above, your smoke screens and obfuscations are for naught. You are caught with your pants down, as it were.
---------- You are repeating your previous statements but not including my answer to the above canard. You have also managed to ignore, rather than try to counter, the points that I raised and the questions that I asked (both repeated below signature).
In summary:
Eq7 describes the power dissipated in a mechanical resistance. Eq. 2, 2a describe the energy stored in a moving mass. How is the power dissipated related in any real and physical way to the energy stored in the mass. KE exists independently of the power dissipated. You haven't even tried to address this (and Eq4 certainly doesn't). Can you?
I had thought that you might be Northstar under a different alias but that is not fair to him.
From the tenor of this thread and others, I simply have to come to one of two conclusions-
Either:
a) You really don't know what you are talking about and don't really want to know.
b) You are a troll and I was slow to realise that.
Don Kelly @shawcross.ca remove the X to answer
P.S. what you ignored.
"It works algebraically (as I said ) but it doesn't work in terms of physical relationships. Hence the substitution of the power equation in the KE equation means nothing.
Given any R you can calculate a power. However, this power has no physical relationship to the KE so it is meaningless (*** Eq.4,not the power of Eq7
***). All you have done is calculate KE =KE*(something/something) The KE is independent of the "something"- whatever you want to call it." ......
********** "My basic point is that the power as given in the valid Eq7. has no physical relationship to the KE given in the valid (for steady state sinusoids) Eq.3 so that Eq4 gives no meaningful information.
******** This is a fundamental point that you haven't attempted to address. Please do so. To help you:
a) what is R and what is its relationship to the KE?
How do you find it? If you don't know it, how do you find the power in Eq.4?
b) The energy into a resistive element such as R is energy that is dissipated ending up as heat. The energy used to accelerate a mass is stored energy and as such can be recovered. How is this related to the dissipated energy which cannot be recovered?
c) If a mass is moving at a steady state velocity v then its KE is constant but there is no acceleration force and hence the input power (force)*(velocity) is zero. There is KE but no power?
d) define the relationship between energy and power."
You clipped out my analysis, invited comment on what you chose not to clip, and now whine about me repeating my previous statements when I repost my analysis. In short, you deceive. Then as an out to your error, you claim that although my equation works algebraically, it means nothing re physical relationships. Of course it doesn't until you understand it, and I have better things to do than educate rude and deceitful people.
--------------- Your "analysis" (that was finally clipped on your invitation) had been repeated ad nauseum. I went over it in detail and saw exactly what you have done- and told you. You have two equations which are dealing with two different things. Combining them doesn't give you anything not said in the original pair (7 and 2). NO new physical insight results in Eq.4.
You certainly have said nothing to counter my points and nothing at all to indicate any physical validity or usefulness of your EQ.4, nor have you made any attempt to answer my simple questions. That's simply not good enough.
A reasoned argument would have been interesting but it is apparent that I won't get that. Too bad.
I'm not deceiving- I called your bluff. You haven't responded except to call me names. Wouldn't it have been better if you had been able to say something that indicated that you actually know the subject?
More deception with a canard, otherwise show where I invited you to clip my analysis.
except to call me names.
There's a difference in calling names and labeling someone a deceiver after the facts. You stoop rather low to "look good". Clearly a self defeating approach, and likely why you get very little to no response to your posting here. Too bad.
So... you are willing to back up your comment, but don't do so. Then you say tough. Ahhahahaahahaaaaa.................... Really, this is so damned ridiculous it's funny. You made my day.
Here's the bottom line, Cowboy: You clipped out the basis of my argument, then invited comment on what you did not clip. Not professional behavior, thusly you are a fake.
---------------- Quote: "JC: "Maybe time to clip?"
I took you at your word and what was clipped (both what you said and my response), I considered as covered and there was no point in continually repeating it, particularly as you really do think that you have accomplished something with your Eq.4 (which you haven't, for reasons that were given to you).
Also, please note that all my past posts as well as yours are available- Nothing hidden, even your earlier inanities.
You actually have not presented an argument -even if your algebra is right because you not shown a meaningful physical relationship between power and KE in Eq.4. You haven't addressed this- or made even an attempt to challenge what I have said.
You have a problem beyond simply not knowing basics- at least the latter can be fixed.
Yet another example of your ongoing coniving. You have pulled my question "Maybe time to clip?" out of context. Clearly my question related to me destroying this false statement by you: "In the light of that supposition I did NOT make an error re equation 3 as you clearly indicate"
My reply was: "I did not indicate you made an error re equation 3, as shown above. Smoke screen rising."
My question meant "time to destroy the evidence?", which you did by clipping the evidence debunking your false statement, along with the basis of my argument, i.e. my *entire* analysis. Like I said earlier, a cheap shot. Now you attempt to cover your shifty deed with yet more conniving. Quite suckful.
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