Motion
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From: TomGee on 27 Sep 2005 21:26 Randy Poe wrote: > TomGee wrote: > > Randy Poe wrote: > > > Well since I don't recall seeing anything like that, I guess > > > it will have to remain an eternal mystery. Such is life. > > > > > > > > Your memory is quite short then. > > Alas, I suppose so. So since you choose not to refresh my > memory of this alleged statement, I will blithely assume you > never made it. End of that discussion. > > > > > > Something I deduce mathematically from the equation F = dp/dt, > > > > > something that can be derived in clear, unambiguous, deductive > > > > > steps, is not what we normally term a "guess". > > > > > When it tells you that, okay. But when it tells you all the other > > stuff you have claimed it tells you, that is only what you infer from > > what the math-deduced something tells you. > > 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?. But you say it also means 2 apples + 2 Oranges = 4 fruits, and that statement on its own can be correct, right? 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. That's why everything you have added on to F=dp/dt, i.e., everything you claim it tells 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), but they are not deduced from the math construct, they are inductions which you infer from the math construct. > > SNIP irrelevant stuff > > > > > > > > > No, thanks. > > > > > > OK, then you agree that this equation suffices to tell me > > > all I want to know about how forces affect momentum. > > > > > No it does not. You only infer that from what it really tells you. > > What does it not tell me? > > Everything you claim it is telling you which are mere inductions of the general case which is the math construct. > > > Ask me a question about how force affects momentum, which you think > it does not answer, or stop claiming that such things exist. > > You stop claiming you hear math constructs talking to you. > > > > > > And don't the common usage of terms which are distinct at certain > > > > levels of research but can be used as equivalent terms at other levels > > > > of notation. > > > > > > What are "levels of notation"? > > > > > > That sentence seems to be missing something. It starts out as > > > if it was going to ask a question, but I can't fathom what > > > the question was going to be. > > > > > > > > Why did you ask it then? > > Ask what? This: "And don't the common usage of terms which are > distinct at certain levels of research but can be used as equivalent > terms at other levels of notation." > > Even with my woefully failing memory, I seem to remember > seeing YOU ask that. If it's a question. I still can't fathom > what the question might be, if it is one. > > Are you falling asleep? Get your momma to read your own posts and tell you what you asked! > > > > Now that you know what it means > > What WHAT means? Is something there supposed to have explained > "levels of notation" or something else? > > > > > Newton formed the equation F=ma > > > > > > No, he did not. F = ma is a special case of F = dp/dt when mass > > > is constant and p = mv. The time derivative of mv is ma when > > > mass is constant. > > > > > > > > Isn't that in his Law 2? > > No. I quote Law 2 below, in the original 1726 latin. > > > > "Lex II: Mutationem motus proportionalem esse vi motrici impressae, > > > et fieri secundum lineam rectam qua vis illa imprimitur." > > > > > > "The CHANGE IN MOTION is proportional to the impressed force, > > > and is made along the straight line along which it is impressed." > > > > > > As I said earlier in the thread, Newton makes it clear in the > > > discussion which follows that "motus" is the product of > > > mass and velocity, i.e. what we now call momentum. > > > > > > So Newton here is saying that vector force is proportional > > > to vector change in momentum. > > > Here, let me quote from your dearly beloved WikiWiki, Newton's 2nd law: "The acceleration of an object equals the total force acting on it, divided by its (constant) mass, [F=ma], where m is the mass of the object in question, F is the total force acting on the object and a is the object's acceleration, i.e., the rate of change of its velocity with respect to time" Now, if you cannot trust own beloved encyclopedia, who can you trust? > > > > > > which is consistent with Galileo's work > > > > and in contrast to Aristotle's F=mv . He invented calculus where he > > > > obtained derivatives of functions one which is the equation you use > > > > above. Derivatives relate to velocity and speed in obtaining average > > > > velocity. > > > > > > I see. That's the only place derivatives are ever used. > > > > > > You are incorrect. > > > > > No, you're the one who inferred that silly claim, so you're incorrect. > > Again, the words about "derivatives relating to velocity and > speed in obtaining average velocity" I could swear were yours. > At any rate, it isn't true. Derivatives are used in many places, > most notably for purposes of this discussion in the equation > F = dp/dt. > > Are you going to say F = dp/dt doesn't use a derivative? > > It is a derivative of the force of momentum at a given moment, and it can have derivatives of its own too. Anyway, you have sidetracked us enough. You have failed to argue convincingly or logically against my ideas about motion, so let's hear some of your ideas, if you have any, and let me show you where you're right or wrong. As PD claims, "What's good for the goose is good for the panderer".
From: PD on 27 Sep 2005 22:10 TomGee wrote: > Herman Trivilino wrote: > > "TomGee" <lvlus(a)hotmail.com> wrote ... > > > > > There are no bodies at rest in our universe except wrt to other > > > objects. > > > > What is it that keeps bodies at rest (with respect to other objects)? > > > > > Fair question. When we sit at our desk we are "at rest" wrt the > surface of the earth because we are moving through space at the same > velocity (speed and direction) as the planet. Therefore, it can be > said that we are at rest wrt to the Earth. > > > > > > >> Is a state of rest is equivalent to a state of uniform motion? > > > > > No. > > > > Is a state of rest (with respect to another object) equivalent to a state of > > uniform motion (with respect to another object)? > > > > > Not necessarily, but in the case above, I guess we can say we are at > rest with the planet due to being in a state of uniform motion with it > when we sit on a chair. When we get up and then move away from the > chair we are no longer at rest with it or the planet. And so what is physically different between the two cases, one where we are at rest with respect to the Earth (though certainly not at rest with respect to the moon or the sun) and one where we are not. You say a force is required with one and not the other. > > > > > > If your worldview requires a cause for a state of uniform motion (with > > respect to another object), why does it not also require the SAME cause for > > a state of rest (with respect to another object)? > > > > > I think I understand your question, so I will try to answer it. My > worldview requires a cause for an object at constant velocity (CV) with > itself or wrt another object. Give an example of an object that is at constant velocity alone. Give an example of an object that is at rest alone. > CV can be obtained by objects alone or > wrt other objects. Uniform motion in a straight line is CV wrt a sole > object but more than one object can be said to be at CV wrt to each > other. > > The cause when CV exists wrt other objects is the fact that they are > all moving at the same speed and in the same direction. Whatever > causes them to be in such a state can vary, but in our case above, the > fact that we are at rest wrt to the Earth is the cause of our CV wrt > the Earth. So what is the cause of our being at rest wrt to the Earth? You say there is a *cause* for uniform motion that is *not* present when the object is at rest. So is there a physical different cause at work between something that is at rest wrt to the Earth and something that is not at rest wrt to the Earth? > > For a sole object free of any external forces, CV is caused by the > inherent force which I claim exists in every body and which is the > total of the momentum of the mass and the energy it has due to its > motion. Give an example.
From: TomGee on 28 Sep 2005 03:12 PD wrote: > TomGee wrote: > > Herman Trivilino wrote: > > > "TomGee" <lvlus(a)hotmail.com> wrote ... > > > > > > > There are no bodies at rest in our universe except wrt to other > > > > objects. > > > > > > What is it that keeps bodies at rest (with respect to other objects)? > > > > > > > > Fair question. When we sit at our desk we are "at rest" wrt the > > surface of the earth because we are moving through space at the same > > velocity (speed and direction) as the planet. Therefore, it can be > > said that we are at rest wrt to the Earth. > > > > > > > > > >> Is a state of rest is equivalent to a state of uniform motion? > > > > > > > No. > > > > > > Is a state of rest (with respect to another object) equivalent to a state of > > > uniform motion (with respect to another object)? > > > > > > > > Not necessarily, but in the case above, I guess we can say we are at > > rest with the planet due to being in a state of uniform motion with it > > when we sit on a chair. When we get up and then move away from the > > chair we are no longer at rest with it or the planet. > > And so what is physically different between the two cases, one where we > are at rest with respect to the Earth (though certainly not at rest > with respect to the moon or the sun) and one where we are not. You say > a force is required with one and not the other. > > I cannot find where I said in my post above that in one case a force is required but not in the other. Unless you refer to something I say below? > > > > > > > > > If your worldview requires a cause for a state of uniform motion (with > > > respect to another object), why does it not also require the SAME cause for > > > a state of rest (with respect to another object)? > > > > > > > > I think I understand your question, so I will try to answer it. My > > worldview requires a cause for an object at constant velocity (CV) with > > itself or wrt another object. > > Give an example of an object that is at constant velocity alone. Give > an example of an object that is at rest alone. > > There are no objects in this universe which can be at rest alone simply because every visible thing in the universe is in motion due at the least to the universal expansion process. An object which is moving at constant velocity alone is an object or system which is free of any external forces, such as the body noted in Newton's law 1. It is moving at uniform motion and in a straight line, and that constitutes constant velocity because it fits the definition of velocity which is the rate of change in position of something with respect to time, involving speed and direction. > > > > CV can be obtained by objects alone or > > wrt other objects. Uniform motion in a straight line is CV wrt a sole > > object but more than one object can be said to be at CV wrt to each > > other. > > > > The cause when CV exists wrt other objects is the fact that they are > > all moving at the same speed and in the same direction. Whatever > > causes them to be in such a state can vary, but in our case above, the > > fact that we are at rest wrt to the Earth is the cause of our CV wrt > > the Earth. > > So what is the cause of our being at rest wrt to the Earth? > > The "cause" of that is the fact that we are moving at the same speed in the same direction as is the Earth. > > > You say > there is a *cause* for uniform motion that is *not* present when the > object is at rest. > > No, I did not make such a claim. Others make that claim and they support it by saying that Newton said that. I disagree that Newton said that in view of his claim that a body moves at CV due to its inherent force. In another post in this thread another poster has quoted Newton as saying that a sole object moving at CV does so forever, but Newton had no reason to believe otherwise. > > > So is there a physical different cause at work > between something that is at rest wrt to the Earth and something that > is not at rest wrt to the Earth? > > Whatever is the reason for something moving at a different speed and/or in a different direction than the Earth at anytime is the cause for that something not being at rest wrt the Earth. And of course whatever is the reason for something to be at rest wrt to the Earth is the cause of that situation. We know there can be almost any number of situations that work to cause those two conditions. However, someone said that it takes a force to change either one of those conditions, so that would narrow it down to a situation where a force works to cause a change to occur, and so we could probably say that a force also causes a change which initiates one of the two conditions to which you refer above. That is to say, a change from sitting to walking breaks the symmetry of CV wrt the surface of the Earth, and a change from walking to sitting makes the symmetry of CV wrt the chair and the Earth, so whatever forces cause either one of those two conditions could be similar but I would think that there must be some difference in them to cause such different situations. > > > > > For a sole object free of any external forces, CV is caused by the > > inherent force which I claim exists in every body and which is the > > total of the momentum of the mass and the energy it has due to its > > motion. > > Give an example. > > Let's take the example Newton gives in the GreenLion translation where he states that a body becomes free to move in a uniform motion and in a straight line due to its inherent force. I refer of course to the 1st law of motion as well, where a body moves free of any external forces acting upon it. The body appears to us to be moving without a source of energy, but we know that a moving mass has momentum and that momentum is a quantity expressing motion and a body's resistance to positional change. We know it also as the speed or force of forward movement of an object. Those two definitions complement each other and thus are valid in their usage. A force is a physical influence that works to change the position of an object, and is equal to the rate of change in momentum of the object. Thus, momentum as an influence is a force which offers resistance to positional change. A "quantity" alone cannot offer such resistance. Some argue that a force is not needed to provide the CV of the moving object, and indeed we have been taught that Newton said that. I don't think Newton said that as it contradicts his "inherent force" claim. I think it was inferred from what Newton actually stated and no one bothered to notice its nakedness. And now we must make up the loss of knowledge which such negligence has caused. And if someone did notice it and remained silent for fear of ridicule or punishment, we must work to change that situation to one of encouragement of and reward for the many ideas which the human mind is capable of inventing. If Newton did in fact say that, he was wrong, as is anyone who makes that same claim, IMO. An object moving without a net force is impossible in our universe because motion is by definition positional change and a change in position requires a force. An object in motion has velocity, and velocity is the time rate of positional change.
From: Randy Poe on 28 Sep 2005 09:53 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. 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. 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. 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. By that logic, 2+2 = 4 would not allow me to conclude anything about two fruits and four fruits. > 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? > 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. > 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? - Randy
From: Randy Poe on 28 Sep 2005 10:13
TomGee wrote: > Randy Poe wrote: > > Are you going to say F = dp/dt doesn't use a derivative? > > > > > It is a derivative of the force of momentum at a given moment, We call p the "momentum", not the "force of momentum". There's a good reason for that (below). > and it can have derivatives of its own too. Yes it can. So? > Anyway, you have sidetracked us > enough. You have failed to argue convincingly or logically Well, I did argue LOGICALLY, pointing out that F can't simultaneously be equal to p and dp/dt. But as you said above, LOGIC is not, for you, CONVINCING. You don't like logic. You don't believe in it. So I concede all arguments to your impervious irrationality. My puny logic is no match. > against my > ideas about motion, so let's hear some of your ideas, if you have any, > and let me show you where you're right or wrong. OK, here's one. A moving object with a given momentum p might cause either a lot of force or very little force in coming to a halt and reducing its momentum to 0. That's why it makes no sense to say "momentum is force". Example 1: I'm in a car, moving at 60 mph. I hit a brick wall. My momentum goes to 0 in a few milliseconds. The forces on me are huge. I'm dead. Example 2: I'm in a car, moving at 60 mph. I hit a pile of snow. My momentum goes to 0 over the course of perhaps half a second. The forces on me are small. I'm unharmed. Even easier to analyze: something coming to me. A baseball is pitched to me at 40 m/sec (90 mph). It has a given momentum. How much is the "force of that momentum"? Example 3a: I catch the baseball in my glove. My hand might sting a little, but no damage. Example 3b: The baseball hits me in the chest. It breaks ribs. The correct analysis of these situations is to calculate dp/dt. The very same momentum will exert very little force if the time derivative can be kept low, which is done by having soft materials which stretch out the deceleration time. Even the difference between hitting sand or snow (say 100 msec) and hitting brick (on the order of 1 msec) is enough to make a difference of a factor of 100 in the "force of the momentum", the difference between life and death. The amount of momentum doesn't tell you the force. How fast it changes tells you the force. A bullet might only weigh 4 gm. A .004 kg bullet going 1000 m/sec has a momentum of 4 kg-m/sec. A baseball weighs 0.145 kg and goes 40 m/sec when thrown by a good pitcher, so it has a momentum of 5.8 kg-m/sec. If the momentum is a force, then the baseball carries more force than the bullet. Which one would you rather have hit you in the chest? What do I claim? I claim the baseball is better, because by the dynamics of the situation dp/dt is much smaller even though p is almost 50% larger than the bullet. Reference for my stats: Mass of baseball: http://hypertextbook.com/facts/1999/ChristinaLee.shtml Mass and velocity of bullet: http://hypertextbook.com/facts/2000/ShantayArmstrong.shtml - Randy |