Bignose

You probably want to look up "Why Does the Wronskian Work?" by Mark Krusemeyer. The American Mathematical Monthly Vol 95, pp. 46-49, 1988.

I have tried several times now to stop, but I just keep laughing at this statement. You can't be serious, can you? Absolute proof about anything is exceptionally hard to find (that's why there is still a "theory of gravity") but a preponderance of evidence, i.e. statistics, is how science makes its best guess about things. And statistics are pretty much the entire basis of sciences like psychology, sociology, etc. Never mind that in almost every single physical situation it is impossible to get exactly the same data no matter how closely you try to replicate the experiment at hand. The answer... statistics of course. So, I still keep laughing at that statement. Here's hoping it really was just a joke.

ParanoiA, please forgive me if this was answered before. I read this thread quickly, and concede I may have missed some of the details. But, do you have a viable solution for crime? One where crime can be reduced to zero or close to zero while still retaining our personal rights and freedom and free will? The reason I ask, is that it is easy to want change and complain about the current state of affairs; however it is a lot harder but much, much more meaningful to come up with real changes that can be made to remedy the situation.

If the only force on this object is gravity (since it is in a vacuum, I assume that you wanted to neglect all drag), you have to remember gravity is a force that pulls on all objects to the center of mass. If we assume that the only two obejcts in existance are this object and the earth, yes, the earth's gravity pulls on the object, but the object's gravity also pulls on the earth. It is just that the force of gravity, which is small, does not move a large mass like the earth very far at all. Like 10^-20 or 10^-30 m. But, the force of gravity is equal in both directions. and p.s. your signature at the moment is very obnoxious.

Again, the stone sitting on the ground has two forces on it: gravity and the force of the ground on the stone. If gravity is 200 N, and the stone is not moving (not sinking onto the ground, not sliding around, etc.), the force of the ground on the stone is also 200 N. Now, you come along and try to lift the stone with 100 N of force. Now there are three forces: 200N of gravity downward, 100N of lifting by you upward, and the the force of the ground on the stone still. Your lifting force was insufficient to lift the stone off the ground, so the ground supplies the remaining force, in this case 100N. Again, the forces sum to zero and there is no movement. No net force, no acceleration. Just to run the gamut of all examples here, say instead lifting the force, you pushed down on the block. Now there is a total of 300 N of downward force, gravity plus your force. In this case, the force supplied by ground to the block becomes 300 N. Again, the net forces sum to zero, which corresponds with the no movement. Finally, if the stone was being held up by someone or something else and you are handed it, but you can only lift 100 N, there is still 100 N of force acting downward. That some is going to move toward the ground, with you in the way, probably hurting you. I am sure you have experienced this when someone has tried to pass you something too heavy for you. Look, I need to state this again, and it is not a personal attack, I am not trying to insult you, I am trying to help make these ideas clearer. But, have you studied physics from a textbook at all? These are pretty basic issues and are covered in the first chapters of any physics text. There will be lots of discussion about this, and the course of study is probably more coherent and collected and directed than questions bouncing back and forth on an Internet forum. I would strongly urge you to go to your local library and check out an Introduction of Physics book and read the first few chapters. This forum will be happy to answer questions you have about the material. But, if you are trying to build this all up on your own, please sit up on the shoulders of the giants who have already done all that building up. Take advantage of the fact that you do not have to start from scratch. Learn from the people who have studied physics thouroughly, who have written some very good texts on the subject, learn from the masters. Like I said above, the system in place today is extremely successful. If you study it, I think you will find that a lot this confusion you have will be cleared up. Like I said, this forum will help answer any questions you have on the material. I'll even extend this offer: you can PM me personally and I will answer any questions you have. But you shouldn't have to struggle to recreate the entire system when the system in place is really good and there are many really good texts that describe this system. So, do yourself the favor of finding a good book, preferably on with a study guide or answer guide or answers printed in the back so you can try some of the problems and see if you understand the material, and read it.

thank you.

If Hercules overcomes the static friction, then in case two, you will help him, even if it is a little tiny bit. Again, you can accelerate this 10 ton block in space. It may not be by a lot, just like your help compared to Hercules' will not be a lot, but it will help. Let me create a small example then. Let's say the maximum friction force is 1 million N. You can push with a force of 50 N. Hercules can push with a force of 1.5 million N. You push the block yourself. 50 is not greater than the maximum friction force, so the friction force in this case is 50 N back. Zero net force. Hercules pushs the block himself. 1.5 million is greater than the maximum friction, friction can only counteract with 1 million N. The net result? 0.5 million N in the direction Hercules is pushing. You both push together at the same time. 1,500,050 N is greater than the maximum friction. The net result? 500,050 N in the direction you both are pushing. Your meager contribution compared to Hercules is small, but it is there. And the net force that results is different than just Hercules himself.

At rest, the block sitting on the ground has two forces acting on it. The gravitional force pulling the block to the middle of the ground. And the force of the ground pushing back up on the block. These two forces are equal and opposite and sum to zero net force, that is why the block has no movement. What happens if you start pushing on it? You apply a force to the side, but then static friction resists that force. Static friction is not always there -- you don't see block just slide about on their own. Friction is a resistance when a force is applied. So, the instant you apply a sideways force, friction attempts to neutralize that force. Friction can neutralize any sideways force up to a certain amount -- that amount is determined by the normal force and the coefficient of gravity. If you apply more sideways force than the maximum frictional force, then you will not have the forces balance to zero, and some net movement. But, if you do not apply more sideways pushing force than the frictional force, then the net forces again sum to zero. Zero force = zero acceleration. However, a block in uniform motion in the absence of any other force, will continue indefinately. Again, we go all the way back to some of the first examples in this thread. A comet flying through deep space is assumed to have no forces acting on it. We assume no gravity, no drag from the few particles in space, etc. There is no force on that comet to ever slow it down -- it will have the same velocity forever. The same velocity, means the time derivative of velocity is zero, or in other words the acceleration is zero. No acceleration, no force. The equation works both ways. Finally, back to the example of the car on a straight flat peice of highway with its cruise control on. This case is exactly like the comet. The only difference is that the comet has no forces on it at all, but this car example has the sum of the forces on it sum to zero. The drag from the air and the force the engine applies to keep the car moving and the friction in the tires and all the other forces sum to zero. That is what the cruise control is designed to do -- keep a constant speed indefinately. Again, constant velocity means that acceleration is zero. No acceleration, no net force. Maybe the misunderstanding here is that nature is completely indifferent between the two situations. The first where there are no force or the second where forces are present, but they sum to zero. Nature does not differentiate between these two scenarios. They are the same, and the equations reflect that. p.s. I am little tired of the "please try to understand" and "understand it (if you can)" I have tried not to insult your intelligence (and if I have I apologize) and would greatly appreciate it if you would stop insulting mine.

Static friction resists whatever pushing force you apply. If you do not push with more than the static friction force, the total force on the block will be zero. You pushing + static friction = zero. No net force, no acceleration.

spunnery, regarding the 10 ton block: There has to be some force resisting you. Static friction immediately comes to mind. If there is no force resisting you at all, then you will move it. You or I can move a 10 ton block in deep space (where I assume no other forces act on the block). You may not move it very fast, but you will move it. Edit: In case spunnery didn't put it back with his edits, he asked what if I pushed against a 10 ton block sitting on the ground. and I don't move it, didn't I apply a force? But, if the 10 ton block is sitting on the ground on earth, there will be a static friction force resisting any force you put on it. The static friction force will be proportional to the normal force. The normal force is the force the block applies on the ground, in this case due to gravity. The gravitational force on a 10 ton block is obviously huge. The coefficient of friction would have to be measured but it would be a percentage of the normal force. Even a tiny percent of the normal force of a 10 ton block is huge. Unless the force you apply is larger than that frictional force, the net forces will sum to zero, hence, zero force, zero acceleration, zero work. Here is the best example of this: You toss a ball in the air, and watch as it falls to the ground. The earth's gravity has applied a force to the ball, and moved the ball towards the earth. But, forces have to be equal and opposite. That ball has moved the earth closer to the ball. You can calculate this using Newton's law of gravity. It is going to be a very, very, very tiny amount. Like 10^-20 m. But, it has done it. This is a case of a small force -- the gravitational force of a ball -- moving a very large object, albiet an extraordinarily small amount. Also, I don't think that the whole world is supporting me, but I do know the current state of Newtonian physics today. I am talking about the phsyics that has been developed for quite some time -- since before it was readily accepted that the world is round. And I know that anyone else who knows Newtonian physics is going to give you the same answers the other people who posted in this thread, and I, have given you. So, I am very comfortable speaking for everyone who knows how to do Newtonian physics properly.

It looks like a pain for multiple !'s, but you can use Sterling's formula as a pretty good approximation for n! for n>10. Sterling's forumla is: [math]n! \sim \sqrt{2 \pi n}n^{n}e^{-n}[/math]

spunnery, are you trying to tell me that your "revelation" that force and momentum are the same thing is akin to the revelation that the earth is not flat? Or, are you trying to tell me that my saying that the members of this board want to help you is wrong, and that my ignorance is comparable to the people who once thought that the earth was flat? Either way, I can prove you wrong. For the first, read a basic introduction to physics book. Force and momentum are different quantities. They are defined differently, and they describe different behavior. The onus is on you to prove to us that force and momentum are the same (best of luck). For the second, when I started writing this, this thread is up to 37 posts, with 9 different forum members helping you. Please don't take this as condescending, it is not how I mean it, but this is a pretty basic physics topic. This probably goes back to the first part -- read a basic physics book -- but this thread's question was answered in post #2. over the next several posts, we gave several examples how the question was answered in post #2. If you don't want our help -- if we are the human beings who have not changed our fundamental thinking -- then, frankly, you are free to leave. Or you are free to create your own entire system of physics where force and momentum are the same thing. But don't expect people to start converting over and shouting your praises unless your system of physics proves to be as easy and clear and consistent and as good at predicting phenomena as the current system is. In fact, it better be a lot better than the current system, because the current system does an awfully darn good job. I suspect it is almost incalculable how often the current system is used to make predictions today -- from lauching satellites to transmitting TV signals to building bridges -- and an almost innumerable number of other successful applications of the current system of physics -- quite a system you wish to buck here. Also, don't expect me to spend my time trying to poke holes in your system by pointing out the inconsistencies (like making force and momentum the same.) So, whatever you choose to do, Good luck. Perhaps the biggest point here is, every other person that replied in your thread has tried to show you one point of view, and you either don't understand it or just rejected it. Perhaps you are on to something new and grand here, or perhaps you should accept ours and the many thousands of exceptionally intelligent people who developed the system as we have it today expertise. And learn why the system is as it is today. Learn why momentum and force are defined the way they are. Learn why force and momentum as separate quantities. At the very least, you need to learn the current system so you can show all of us non-thinking humans specifically why your system is better. So, you need to know all the details in-and-out of the current state, so you can give us loads of examples why your system is soooooo much better. Either you learn the current system to understand the replies you got in this thread or you learn the current system so you can demonstrate exactly where your system is going to be better. You have to study and learn the current system in both scenarios -- so pick up a introduction to physics book and start reading.

spunnery, may I just ask in the search for common ground. What year of school are you in? How much math and physics study have you had? Has it been in a formal setting at school with homeowrk and exams or has it been self-taught? The reason I ask -- and please don't take this as an insult because I and I suspect most of the rest of us on the forum want to help you as much as we can -- is that there seem to be some very fundamental issues that are not being understood or expressed correctly. The definition of force is pretty much the very first thing taught in a physics class. The independence of vector components is rather fundamental also. So, answer those questions about your background and experience, and I think that we could probably provide much more informative and helpful answers. Thanks.

spunnery, sorry if this seems like piling on, but the exact usage of terms that are defined unambigously demand preciseness. It is not like the regular English language (or other spoken word), where there are subtleties, and slight changes of meaning, and words that mean one thing in one context and mean another thing in another context. Physics and mathematics demand very precise and correct use of the terms. You want to talk with other physicists and people who understand this material, right? It is just like learning a language, but a language with very little use for ambiguity. A force is defined exactly how it is, you cannot just change what it means. So, defining F1 as you have, and calling it a force is, quite simply, meaningless. [math]Force \ne mv[/math]. So, in order to convey your ideas with other people who are knowledgeable, you need to learn the correct terminology. Yes, force is a vector quantity, but so is momentum. Just because two quantities are both vector quantities does not imply anything special, like equality. Why not use the position vector then? By that same logic, position and force should be equal. As should acceleration, and rotation, and the derivative of acceleration, etc. To respond to your "logic behind my explanation," quite simply in light of what I and the others have said above, there is no logic at all. What you have written is pretty close to having zero meaning. Since the very first equation your attempt to redefine force, is flawed, everything you dervied from that equation is wrong. It's like building a home on a sinkhole. It doesn't matter how well-built the first floor is, the ground the house is sitting on is sinking and everything will fall down. p.s. As an aside, even mathematics and physcs aren't immune from some language-ambiguity creeping in, there are two different meanings of the word homogeneous in mathematics, for example. I am sure there are others. That said, both definitions of homogeneous are very exactly defined, and it is unlikely to confuse one with the other. Unlike your attempt to redefine force and then use the correct formula later, where confusion is rampant.

Ummmm, true? Dennis, do you have some thoughts on this, or something you'd like to discuss?

OK, to space then where we will just assume all gravity is zero. A comet passes by. Assume also that the comet is not losing any mass. It is definately moving, but it's movement is due entirely to inertia. Lots of displacement, but no forces, no change in kinetic energy, ergo no work. If you stop the comet, or the comet hits a rock or something like that, then a force will be applied and then work. But, an object in motion tends to stay in motion, and unless some force is applied to the comet, it will continue to move at a constant speed forever. Look at the work equation again. dW=F*dl. It is a product on the righthand side. If either F or dl equals zero, the prodcut will be zero. If there is no net forces, F=0, then work equals zero.

If you are just looking for the relationship between temperture, pressure and density, then the Ideal Gas Law is the place to start. P=(n/V)RT P=pressure (n/V)=moles per volume (which is a density) R=gas law constant (very dependent upon which units you use for all the other variables) T=temperature While only a very few gases really follow this rule exactly, and only over a limited temperture/pressure range, it is also a pretty reasonable approximation for a large range of gases over a large range of T & P. To improve the accuracy, you can use different gas laws, like the van der Waals gas law, or Reidlich-Kwong, but the ideal gas law is a very good starting place. It is possible to derive that going all the way back through kinetic theory of gases, but it is unlikely to be a useful exercise. It does have several hundred years of observation behind it. I really doubt that you would get accurate estimates using what you described in post #4. The energy is probably going to be very far from equal, since there are so many energy loses in the system. Heat and noise and the fact that some gas will escape around the projectile are all significant loses.

Here is the problem, you need to look at Gibbs' Phase Rule: F = C - P + 2 F= degrees of freedom in the system C = number of chemical species P = number of phases in the system Let's take a single component gas, like pure Argon. C=1, only Argon, P =1, it is assumed to be only a gas. F = 1-1+2 = 2 So, there are two degrees of freedom. That means, in order to describe the system, you have to know at least two variables, like temperature, pressure, or density (which is directly related to volume). So, if you only know pressure, for example, you cannot know exactly what the temperature or density is. You know how they are related, so the temperature and density can be graphed as a line, but you have no knowledge whatsoever of where on that line the state of the system is at. If you know exactly what the pressure and density is, there is only one temperature a pure gas system can be at.

This is a good example. Maybe an oppostie example would help too: Consider driving in a car along a flat, straight stretch of highway. You want to drive at exactly the speed limit, say 70 mph, and set the cruise control for that speed. Are there forces on the car? Sure, friction between the road and tires, air resistance, and of course, the engine applying a force to keep the car going. But, if the cruise control is working properly, speed will be maintained at exactly 70 mph. No change in velocity means no change in acceleration, means no net forces on the the car. But, there are definately forces acting on the car.

Here's my advice, and I'll even give it to you for free. Use Google, Wikipedia, and some of the many other resources the web has to offer. Just whatever you do, don't copy and paste the info, teachers look for that all the time, besides being illegal. Do cite whatever sources you use properly, however. And maybe the biggest one, go to the library and do some research on your subject. It is funny since you didn't even tell us what the crud your paper is on (I'm lmfao too, hot!), but with 99.999999% certainty I can tell you that a lot more than 10 pages have been written about your subject already. Get as wide a variety of sources as you can find, and have time to read and understand before you have to start writing. Try to make sure that you get perspectives from as many different viewpoints as possible, i.e. both the conservative and liberal or both the pro- and anti- positions. Triple check your grammar and spelling when you've finished. Make sure both the intro and conclusion are concise and sum up the issues quickly without running on. Stay on topic. Follow a lot of that and you should have yourself a pretty good paper.

Please try the dropping balls experiment on your own. You will be able to achieve much more consistent results. Gravity will accelerate the objects much more consistently than your hand will be able to. All you have to do is time it so that you drop both objects at the same time. While not easy, it is far easier than pushing two objects at the same time with exactly the same force. In fact, you can probably very quickly improvise a device that would allow you to drop two objects at exactly the same time. You are right in that the theoretic calculations are not perfect. Even the dropping balls example is not perfect, since two different balls will have two different drags. However, the difference is drags is very, very small, you should see both balls hit the ground very closely to the same time. To really show this using the experiment you were trying to perform, you need to build some device that will push your two objects at exactly the same speed. You must also have some method of verifiying that the two initial speeds were exactly the same, like a high speed camera or something. It can be done, but under more exacting and rigorous standards, your hand is not going to cut it. Athiest brought up a good point, that just because your intuition doesn't like the result, certianly does not mean it is wrong. Your intuition has not been tuned towards solving physics problems, and, at least regarding solving physics problems, your intuition is unreliable.

swansont's last sentence there got me thinking and so I gathered some numbers together: Given that it costs around $15,000 US to place one pound of mass in orbit (http://answers.google.com/answers/threadview?id=431680) and that the 2005 US GDP was $12,455,070,000,000 (http://devdata.worldbank.org/query/default.htm) It would take the US over 10 million years (at steady 2005 production) to place one one-thousandth of one percent of the earth's mass into orbit, and I am not sure that a change of 0.001% would affect the orbit of the earth too much. Now, obviously, that is a little farcical since the entire US economy is not based on just putting mass into orbit, and if it was, I suspect that it would not take too long before significantly cheaper way of getting mass into orbit would be designed. Nevertheless, it just shows how large of a mass the earth really is, and at the rate of payloads of only a few thousand pounds at a time... well, your scoffing was very well justifed. Edited to put the last three zeros on the GDP (good eyes entwined)

But, this is exactly the same problem as dropping two objects weighing different weights in a vacuum. And that experiment was done in one of the few places it could be done on the moon. A feather and a hammer dropped from the same height on the moon fell at identical speed. And a feather and a hammer do not weight the same! The experiment is the same as yours with only a few modifications. The initial velocities are the same, the initial energies are potential instead of kinetic, and the force is the same, g. The frictional force is modified by a frictional coefficient, but otherwise, they are exactly the same. Your experiment with a paper and two weights is definitely flawed. 1) Using your hand it is impossible to give the objects the exact same initial conditions 2) Were both the objects the same in every way except mass? Different sized objects would behave differently. Heck, if they were different objects they would behave differently. You should be able to try this out at home: Open your window and drop a basketball and a baseball. They should impact the ground as very similar times. You can use most any ball, golf ball, tennis ball, etc. While you are doing it, think of the story of Galileo doing pretty much that exact same experiment from the top of the leaning tower of Pisa. Then, try other objects. Think about why the astronauts could use a feather on the moon, but why that would not work here on Earth.

This forum does not do your homework for you. This forum will help you along the way, and show you what mistakes you may have made and/or confirm the correct answer. With that, please show what work you have done thus far, and where in that work you have done you are having problems.

Any fluid will have some surface tension, even gases will-- though it is several order of magnitudes smaller than a liquid's. And while noble gases are very non-interactive, none are exactly perfect. Obviously, it is a much more important phenomenon for fluids. For that matter, solids have a surface tension-like quantity sometimes called spall strength. Both surface tension and spall strength have units of energy per unit surface area. One professor I know if working on a self-cleaning windshield using surface tension. From the bottom to the top of the windshield is a gradient of a chemical on the surface. The drop of water is more attracted to the top of the water than the bottom -- and this attraction force is greater than gravity. Hence the drop rolls up the windshield and over the top -- no wiping needed. Right now, he's demonstrated this effect on an opaque windshield; he needs to find a chemical that will remain clear and retain its attraction when dry.