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From: Don1 on 24 Sep 2005 17:19 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? Why is dp/dt any different than p/t? Do you mean its just a short piece of a sloped line?
From: TomGee on 24 Sep 2005 17:25 stephen(a)nomail.com wrote: > In sci.math Randy Poe <poespam-trap(a)yahoo.com> wrote: > > > TomGee wrote: > >> Herman Trivilino wrote: > >> > "TomGee" <lvlus(a)hotmail.com> wrote ... > >> > > >> > >> Where did I say that? I would have snipped more, but I wanted > >> > >> to leave all the stuff you quoted from me so you can point > >> > >> me to the passage where you think I said F = p. > >> > >> > >> > > If you think you did not say it. then just what do you mean by F=dp/dt? > >> > > >> > Wow! Don't you know the difference between a quantity and its time rate of > >> > change? > >> > > >> > We can write v=dx/dt, where v is velocity and x is position. Do you think > >> > this means that velocity and position are equal? And that we can write > >> > v=x?! > >> > > >> So you don't know what he means by that either, eh? > > > He just told you what I meant. I didn't say F = p, I said F is the > > time rate of change of p. > > Even TomGee's Oracle agrees with you. > > Agrees with what? He hasn't said anything to agree with or disagree. He doesn't know what his equation means else he would have seen it's not relevant to what he's arguing against. > > > From the Allmight Encarta > > "Almighty" (one l plus a y)- -learn to spell before you deign to criticize a source, it will help strengthen your arguments even when they're wrong. > > > According to Newton's second law of motion, named after the > English astronomer, mathematician, and physicist Sir Isaac Newton, > the force acting on a body in motion must be equal to its time > rate of change of momentum. > > Equal for it to do what? You don't even know what you're reading, do you? > > > Another way of stating Newton's second > law is that the impulse, that is, the product of the force multiplied > by the time over which it acts on a body, equals the change of > momentum of the body. > The restating of Newton's laws is what caused you all that confusion in the first place. Anyway, you must think that the change of momentum is relevant to our discussion. If so, show us where. > > > This is the last paragraph of > http://encarta.msn.com/encyclopedia_761554136/Momentum.html > 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. > > Right, like your unsupported opinion of a source means anything. Look at your Wiki wiki how the mad scientist keeps rewriting in it. If you understood dp/dt you would know it is not relevant to our discussion. Since you believe it is but can't explain how, that shows you don't understand dp/dt, our discussion, or both.
From: TomGee on 24 Sep 2005 17:54 Randy Poe wrote: > TomGee wrote: > > Randy Poe wrote: > > > TomGee wrote: > > > > Randy Poe wrote: > > > > > TomGee wrote: > > > > > > It would be a pity if you were right, but you contradict yourself > > > > > > immediately by saying above that force and momentum are equivalent. > > > > > > > > > > Where did I say that? I would have snipped more, but I wanted > > > > > to leave all the stuff you quoted from me so you can point > > > > > me to the passage where you think I said F = p. > > > > > > > > > If you think you did not say it. then just what do you mean by F=dp/dt? > > > > > > That force is the derivative of momentum with respect to time. > > > > > I see. And the relevance of that to our topic is ...? > > That force and momentum are not the same thing. That the > equation F = dp/dt does not say that they are the > same thing. That the discussion was whether I had said > they were the same thing. > > Isn't the topic of discussion "momentum and force are the > same thing"? > > No it's not. We are trying to establish which are those many P-M systems you claim exist, for one. 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. > > > > For instance suppose p is a constant in time, say p = 5. > > > The F = dp/dt = 0. Five and zero are not the same. > > > > > > Suppose p is increasing linearly in time, p = p_0 + b*t > > > > > > Then F = dp/dt = b, a constant. The constant b and the > > > linearly increasing function p_0 + b*t are not the same. > > > > > > > > Okay, so what? > > So p and dp/dt are not the same thing. So when I say > F = dp/dt, I'm not saying F = p. > > I did not say you were. > > > So momentum and force are > not the same thing. So momentum and force are related > by the differential relationship, F = dp/dt. > > I agree, but that is not the only relationship of the two, simply because momentum is not only a quantity but also a force. You cannot show the "relatedness" of your equation to my claim of force and momentum equivalence because your specific example is a calculation of the force in a given mass. There validly exists a difference between the force and its measurement. Thus, in the case of a measurement of force via the momentum of a mass, momentum and force are not the same thing. In other cases, however, the two are validly thought of as being equivalent. > > > 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. But for some other specific examples, they mean the same thing; we use them interchangably in well-accepted ways. > > Now let's have some of them P-Ms you spoke of earlier in our discussion.
From: Randy Poe on 24 Sep 2005 18:39 TomGee wrote: > stephen(a)nomail.com wrote: > > In sci.math Randy Poe <poespam-trap(a)yahoo.com> wrote: > > > He just told you what I meant. I didn't say F = p, I said F is the > > > time rate of change of p. > > > > Even TomGee's Oracle agrees with you. > > > > > Agrees with what? He hasn't said anything to agree with or disagree. Except this: "I didn't say F = p, I said F is the time rate of change of p." > He doesn't know what his equation means else he would have seen it's > not relevant to what he's arguing against. So what is your claim. I'm really curious. 1. That I didn't write that. or 2. That that is not a statement about the meaning of F = dp/dt, or 3. That I don't know what F = dp/dt means, even after you agreed that it means F = the time derivative of p, or 4. That when I told you that F is the time derivative of p, that is "not relevant" to our discussion of the meaning of F = dp/dt and whether it's the same thing as F = p. - Randy
From: Randy Poe on 24 Sep 2005 19:18
TomGee wrote: > Randy Poe wrote: > > So the topic is still "Tom informed me I said force and momentum > > are equivalent", and you amplified it to say that "F = dp/dt > > is a statement that force and momentum are equivalent". > > > > > I did not amplify it. OK. > You're the one who said it "relates" force and > momentum. Yes, I did. > I simply asked you to explain how you think it relates to them. Well, "relates force and momentum" and "relates TO force and momentum" aren't quite the same thing, but I'll tell you how it does both. The equation F = dp/dt relates to force and momentum because it is an equation in terms of force F, and momentum p. It relates force and momentum, i.e., tells you how force and momentum are related, by telling you that force is the time rate of change of momentum. > I did not ask you for that. And you have not yet answered my question > of what you meant by the statement. By the statement F = dp/dt, I mean that force is the time rate of change of momentum. In what way is that not an answer to the question? It is an equation that tells you, given an expression for momentum, how to find out the corresponding force. It tells you, given a force, how to find out its effect on momentum. > Why, if you cannot decipher the very very very simple question? It's a very simple equation. There are only three things to explain in it. It contains force F, momentum p, and the time rate of change operation d/dt. So when I tell you that this equation says that force is the time rate of change of momentum, I have explained every single symbol in the equation. Furthermore, I gave a couple of examples of momentum vs time and the force that would give rise to that behavior, using this equation. What, in your opinion, have I not explained about this equation? - Randy |