Motion
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From: Randy Poe on 24 Sep 2005 19:27 TomGee wrote: > No it's not. We are trying to establish which are those many P-M > systems you claim exist, for one. What do you mean by "P-M systems" and my claim that "many P-M systems", whatever those are, exist? I don't recall ever saying anything about a P-M system. > For another, we are trying to > establish what the relevance is of your statement that F=dp/dt to my > claim of the equivalence of energy, force, and momentum. It says that the relationship of force and momentum is not one of equivalence, but one of time derivative. Because F and p are related in this way, and two things that are related in this way are not equivalent, therefore F and p are not equivalent. I haven't even brought energy into this, but there are other equations involving energy. For instance, the work done by a force is the integral of F over distance. If that work gives the object kinetic energy, then that tells you that the KE given to the object is the distance integral of force. Two things related in this integral relationship are not equivalent or interchangeable. So that's my answer: What is the relevance of this to your claim of the equivalence of force, energy, and momentum? The relevance is that it tells you the relationship of force and momentum, and that relationship is not "equivalence". It is "time derivative". > > So momentum and force are > > not the same thing. So momentum and force are related > > by the differential relationship, F = dp/dt. > > > > > I agree, You do? Then why are you arguing with me? > but that is not the only relationship of the two, Yes it is. It is the only relationship there is between force and momentum. > simply > because momentum is not only a quantity but also a force. No, it's not. If momentum is defined in the usual way, and force is defined in the usual way, there is no way to interpret momentum as a force. They have different properties. When you have a force, you have a time changing momentum. So you're saying momentum is its own time derivative, which is in general impossible. (You're also saying that any object with momentum accelerates itself). - Randy
From: Randy Poe on 24 Sep 2005 20:46 Don1 wrote: > stephen(a)nomail.com wrote: > SNIP< > > The article seems to be written for a totally untechnical > > audience. It does not include any equations, so it is > > likely TomGee will be unable to understand dp/dt. > > > > Stephen > > What is this with the d in front of everything? It's calculus, Don. Go back to sleep. dp/dt means the slope of the tangent line on a plot of p vs. t. > Why is dp/dt any different than p/t? Because for a general curve of p vs. t, the slope of the tangent line is not the same as p/t. A line with slope p/t won't be tangent. > Do you mean its just a short piece of a sloped line? No. - Randy
From: Randy Poe on 24 Sep 2005 21:02 TomGee wrote: > Randy Poe wrote: > > So actually > > working out dp/dt for some specific examples illustrates > > how very different momentum and force are for any > > given situation. > > > > > Of course, for some specific examples. The law F = dp/dt is always true. The examples were just specific examples of p as a function of time, and what dp/dt looks like. No matter what p is as a function of time, the relationship F = dp/dt holds. > But for some other specific > examples, they mean the same thing; No, there are no examples in which they mean the same thing. > we use them interchangably in well-accepted ways. No, "we" don't use them interchangeably, and any way in which they are used interchangeably is not accepted, certainly not "well-accepted". > Now let's have some of them P-Ms you spoke of earlier in our > discussion. No idea what I might have said that you are reading as "P-Ms". - Randy
From: TomGee on 24 Sep 2005 21:38 Randy Poe wrote: > TomGee wrote: > > Randy Poe wrote: > > > So actually > > > working out dp/dt for some specific examples illustrates > > > how very different momentum and force are for any > > > given situation. > > > > > > > > Of course, for some specific examples. > > The law F = dp/dt is always true. The examples were just specific > examples > of p as a function of time, and what dp/dt looks like. No matter what > p is as a function of time, the relationship F = dp/dt holds. > > I did not say it was ever untrue or that it ever does not hold. You are reading more into my statements than what they say. Whether it's just to be contrary or for your lack of comprehension, it's hard to tell from here. > > > > But for some other specific > > examples, they mean the same thing; > > No, there are no examples in which they mean the same thing. > > > we use them interchangably in well-accepted ways. > > No, "we" don't use them interchangeably, and any way in which they > are used interchangeably is not accepted, certainly not > "well-accepted". > > Sure "we" do, just read a physics book. It is rare where we don't use terms like force and momentum nterchangably. > > > > Now let's have some of them P-Ms you spoke of earlier in our > > discussion. > > No idea what I might have said that you are reading as "P-Ms". > > Um, we discussed "perpetual motion machines"? Remember?
From: TomGee on 24 Sep 2005 21:47
Now, PD, how does calling your teachers stupid mean I'm talking to you in the 3rd person? When I call you stupid, I always say it directly to your face, like in this missive to you: I had a whimsical moment when I thought you might respond exactly the way you did, but I shrugged it off: "Naaah, Pd's not that stupid." Dammit, I was wrong again! |