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From: Randy Poe on 30 Sep 2005 09:47 Robert Low wrote: > Randy Poe wrote: > > I was wondering if Tom would muddy the waters with that one, > > though I already thought through my response. It's > > mathematically possible, but not physically possible for > > p to be equal to k*exp(t) on the basis of units. > > I tend to try not to think about this, because I get > all confused, but if I'm forced to think about it, > I think that the 't' there is just a number, which > we interpret as the number of seconds (hours, fortnights, > whatever) which have elapsed. Nope. Can't work unless there's a time constant in there which makes the argument of exp() unitless. However... see below. > Clearly, in this case, > 'k' would have to have units of momentum. Right. It's the momentum at time t=0. > > You don't see things like exp(t) in physics. > > Used to see it all the time when I did damped > harmonic motion. (OK, it was usually exp(-t) then. It's really exp(a*t) where a is a rate constant, or exp(t/Tau) where Tau is a time constant, and you could have a situation where Tau is 1. But Tau would only be 1 for a particular choice of units of t. Then you could say something like "p = p0*exp(-t) if t is in fortnights." But the preferred expression, in my opinion, is one that doesn't depend on a particular choice of units: p = p0*exp(-t/Tau) where Tau = 1 fortnight or the equivalent in the units of t. > But I suspect that I'm jumping in on a discussion > and adding even more cross-purposes than were already > there. Sorry about that. Naah, Tom is getting boring and repetitive. And now it's getting weird since he's telling me that my positions are the ones he's been insisting on all along. So I welcome a new voice, and Tom can't get any more confused than he is already. - Randy
From: Robert Low on 30 Sep 2005 09:56 Randy Poe wrote: > Robert Low wrote: >>Randy Poe wrote: >> It's >>>mathematically possible, but not physically possible for >>>p to be equal to k*exp(t) on the basis of units. >>I tend to try not to think about this, because I get >>all confused, but if I'm forced to think about it, >>I think that the 't' there is just a number, which >>we interpret as the number of seconds (hours, fortnights, >>whatever) which have elapsed. > Nope. Can't work unless there's a time constant in there > which makes the argument of exp() unitless. However... > see below. Well, OK: you can say it's exp(at) where a has inverse units of time and converts the elapsed time to the number of temporal units. And if t is measured in seconds (or whatever) in the first place, then a has numerical value 1, so I just don't write it in, and remember that t is now a number, not an amount of time. Oops, you wrote that just below anyway. Looks like I agree with you except for the degree to which I like to make the notation explicit. > So I welcome a new voice, and Tom > can't get any more confused than he is already. In my experience of Usenet, that is always a dangerous claim to make.
From: jesper pedersen on 30 Sep 2005 10:53 "Randy Poe" <poespam-trap(a)yahoo.com> wrote in message news:1128088054.216428.265380(a)o13g2000cwo.googlegroups.com... > Naah, Tom is getting boring and repetitive. And now it's getting > weird since he's telling me that my positions are the ones he's > been insisting on all along. So I welcome a new voice, and Tom > can't get any more confused than he is already. > > - Randy As a silent observer I can only hope that you continue the debate. It rates very highly on pure entertainment value. / Jesper P
From: TomGee on 2 Oct 2005 04:33 Randy Poe wrote: > TomGee wrote: > > Randy Poe wrote: > > > I really can't figure out what the distinction between deriving > > > stuff mathematically from F = dp/dt, and "inferring it from > > > the math-deduced something". > > > > > Indeed. How unfortunate. But it's really very simple. We all agree > > that the math construct 2+2=4 is correct, right? > > Correct. > > > But you say it also > > means 2 apples + 2 Oranges = 4 fruits, and that statement on its own > > can be correct, right? > > Correct. It's a consequence of 2+2 = 4. I know this to be true > because of 2+2 = 4. The equation 2+2 = 4 forces this to be > true. > > > But since you are basing your claim on the math > > construct and it does not state apples or oranges, you inferred from it > > that it meant apples and oranges. > > No, I didn't infer from it that it meant apples and oranges. > > You are so funny. Yes you inferred that! Can't you grasp the meaning of the term "infer"? It's a simple concept that no one but you has any problem with it! > > > I don't look at 2+2 = 4 and see apples and oranges. I look > at what the symbols mean when I write "2+2 = 4". The symbols > "2" and "4" are abstractions. This equation isn't just a "math > construct", it's a description of how objects behave in the > real world. > > No. Numbers are not objects in the real world. They are imaginary symbols that do not behave any which way. > > > It's a model. The first symbol "2" means "two of > some object" and the second symbol "2" means "two more of > the same kind of object", in which case the symbol "4" means > "four of the same kind of object". > > So no, I can't see how it is that 2+2=4 does NOT tell me > two fruits plus two fruits equals four oranges. > > Correct. It does not tell the 2s are, so if you say 2 apples + 2 oranges = four fruits, you have inferred from the math that the 2s are apples and oranges and thus the 4 would be fruits. When you talk about numbers telling you all that stuff you hear them say, they ain't, and if you keep that up they'll be coming for you soon to see if you can be helped or if you just need discarding. > > > Remember, > your claim is that the "math construct" F = dp/dt, where > F = force and p = momentum, does not allow me to conclude > anything about force and momentum. > > No, that's just another one of your inferences. > > > By that logic, 2+2 = 4 would not allow me to conclude anything > about two fruits and four fruits. > > Oh, you can conclude what you will from it, but if it is not what it applies to, your conclusion was based on a false inference. If it applies to two dogs and two cats, e.g., your four fruits hypotheses is wrong then. > > > > That's why everything you have added on to F=dp/dt, i.e., everything > > you claim it tells you, > > F is force. p is momentum. dp/dt is the time derivative of > momentum. What did I add? > > You added all those things you hear it telling you. > > > > are mere inferences from the math construct. > > You say that those things are math-deduced, and deductions are as valid > > as logical conclusions (which is still not saying much), > > I know logic means little to you, which is one more reason why > you shouldn't be discussing physics. > > You know no such thing. It means no more than math to me because both have the same limitations wrt the real world. > > > > but they are > > not deduced from the math construct, > > Um, yes they are. When I say that F = 0 means dp/dt = 0, and > dp/dt = 0 means F = 0, then this is deduced from the "math > construct". Do you think F = dp/dt can be true with F = 1 > and dp/dt = 0? > > Wrong. When you say F=0, you are merely saying force equals zero. That is a simple statement. You said, however, that F=dp/dt, which is an equation derived from the general case, momentum. Thus, it is a special case of the general case.
From: TomGee on 2 Oct 2005 04:54
Randy Poe wrote: > TomGee wrote: > > Randy Poe wrote: > > > Because dp/dt is not equal to p. > > > > > > > > Hey, that's my position, not yours! A derivative cannot be equal to > > the function from which it is derived! > > If that's your position, then can you explain this comment of > yours? > > "False logic. dp/dt is a derivative of p so if force is a derivative > of > p, it must by definition also be p." > > http://groups.google.com/group/alt.sci.physics/msg/c61fe7149a24099a > > It sure looks to me like you're saying the derivative of p > is also "by definition" p. > > Yes, it is, but it is not equal to p. We can measure momentum as p=mv without knowing it's rate of change, then we can derive F=dp/dt from it, but we cannot derive it unless we know the mass and velocity first. They cannot be equal to the same thing but they can be the same thing because one is a quantity and the other is the force of that quantity. > > > Now as to this: > > > > >> Sure "we" do, just read a physics book. It is rare where we don't > > > >> use terms like force and momentum nterchangably. > > > > > > So I read this as saying that you believe if I pick up any > > > physics textbook, I will find that force and momentum are > > > used interchangeably. It is rare that they do not. Therefore > > > it should be easy to find such a passage in any physics book. > > > > You show a real problem in comprehension of the written word. I know > > that is your position - did not say it was mine! > > Did you say > "just read a physics book. It is rare where we don't > use terms like force and momentum nterchangably."? > > Is your position that you did not say that? > > > > Finding such a passage in a physics textbook would prove > > > me wrong, because my claim is that such a passage doesn't > > > exist. Yours (do try to remember this) is that it does, and > > > such passages are common. > > > > > Proved you wrong, didn't I? > > By the Tipler quote that says force is the time rate of change > of momentum? > > Again, how does that prove that F = dp/dt is wrong? > > Another one of your bad inferences. I could just as easily infer that you said p=mv is wrong. > > > > Gave you one but you still claim it does > > not prove you wrong. > > Yes, I really can't see how "force is the time rate of change > of momentum" proves F = dp/dt is wrong. > > Never said that. Another one of your false inferences. > > > Nor can I see how "work done on an object equals change in > KE of the object" contradicts "force and momentum are not > interchangeable". > > Aren't you the one who said KE is not changed by an external force? |