mezarashi

After a year or so of not having done calculus I hope my fundamentals still hold. If you consider the property of linearity of the integration, then you can always simplify the second equation to: int(b,a) [ f(x) + 5]dx ---> int(b,a) [f(x)]dx + int(b,a) [5]dx I guess the answer from here is obvious. The first term leads to (a + 2b) and the second term leads to 5x, substituting in b and a to get: 5b - 5a.

Interesting. I guess it can't be denied that your brain can stretch psychological time, which suggests an increase in the speed of conscienceness.

Well, that's a very unusual question you have. Work and Momentum are concepts used in physics that can indeed help us to model and predict our world. Their notions to exist as with any other model in physics is because it is a tool for us in problem analysis. Work is the concept of looking at the world in terms of relative energy content and energy exchange (i.e. the concept of conservation of energy) Momenum works on its own concept of conservation of momentum, or more like the conservation of inertia. Your question, Why is work F*d and not F*t... well if they were both the same, we wouldn't have to come up with two words and two concepts for them ^^;. Although the two models are usually not used together in most cases. I don't think there is a general relationship, as it depends on the situation. In simple linear motion however, I think it may be safe to say that generally a loss of momentum also constitutes a loss of kinetic energy. Feel free to ask anything else

Hahaha, this is the funniest thread I've read so far on this forum, and you know what, I'm just going to agree with reverse that yes, darkness is that stuff that creeps out of your closet. FEAR!

It can be possible, however, the natural disturbance must indeed be very very large. Because as far as I understand on the nature of waves is that they transfer energy. While the tsunami is travelling across the ocean, there is little or negligible translation of water. What is actually transferred is actually wave energy and slight water compression at the wave front. The main bulk of the "destructive" action occurs when the propagation reaches its end at the shores of an unfortunate continent. Personally, I would think that you would be better off looking at damages caused to shorelines and such rather than global changes.

Well, let's see. My way of approaching this problem would be assume that all the possibilities take some form of statistical curve. Just suppose anything say a normal curve. The curve extends to infinity in either direction. However, the chances that the outliers will occur are so little. 0.00000000000294 for example. However, with a sample large enough, there is a chance it will occur, and occur pretty often too. With an infinite sample, I don't see why ever thing on the statistical curve of possibility will not occur. So simply said, my answer is that *if* the universe is indeed infinite, yeah, I would imagine a world exactly like ours and many others similar to it. However, I don't believe in infinity so hehe, too bad there.

Sounds interesting, though I don't quite see the picture of what's happening and the definition of "h". I'd understand that the wave propagation here involves waves that are of the pendulum's natural oscillating frequency.

Haha, alright. Glad you're making progress

Ok, so if the yoyo was in space, then we again apply basic Freebody analysis. There is no external force acting on the yoyo other than the Fstring, so the acceleration of its center of pass is indeed a = F/m. It will also gain rotational momentum, with an accelerated rate of alpha = Torque/I. It would be as simple as that. It's also important to note that this may appear to be in violation of the laws of conservation of energy as in, how can you get acceleration and rotation. But consider the yoyo, as you pull the string, the string unwinds. In effect, to pull its center of mass a distance x, you need to pull the string a bit longer than distance x due to the unwinding string. I hope you can visualize all this.

Hmmm, I guess you're not understanding what I'm saying. Maybe it's better off we discuss this somewhere like on the IRC channel. There is no F2 because you are looking at it from the reference of the entire yoyo. In that frame, there is on ly Fgrav and Fstring. If you look at it using yoyo's body as the reference, then there is an F2, which is coincidentally also the Fstring. Sorry, but I don't think I can explain it better than this

Hi again. Yes, that example is not directly relevant to your question. I was merely illustrating the concept of internal/external forces and how they don't affect each other in predicting the motion of objects. If the concept of external forces on a rigid body still isn't clear to you from the yoyo example. I have yet one more. Imagine a rigid ruler. If you push it at its center of mass with force F1, it will accelerate. If you push it with double the force, 2*F1, it will accelerate twice as fast. Now consider if you pushed it with F1 each at both its ends. Would it accelerate at the same rate? The answer would be yes. It doesn't matter where you apply a force to a rigid body as long as what concerns you is the motion of its center of mass. That's atleast one thing easy about dynamics

The law of Newtonian mechanics holds for any reference frame you see. *IF* your reference is the entire yoyo. That is you enclose the yoyo in a box, then the net force will act on the center of mass of the box/yoyo. Regardless of where the force acts on the yoyo, as it is an internal system. This is a relatively fundamental understanding you need in not just dynamics, but statics. For example, imagine firing a canon ball into the air at an angle, the canon ball flies up, and say it explodes in mid air. The center of mass of the exploded particles will continue to travel in a clean particle trajectory because there was no external force. That's just to illustrate the concept of internal/external forces. Back to your yoyo problem. Now imagine that the yoyo is on the table, and you wind two strings around it in opposite directions and pull with the same strength. It will start spinning right? Now take the freebody diagram of the BOXED yoyo. Two forces in opposite directions, the net force is zero, the center of mass of the yoyo won't move, and that is exactly the case. The yoyo will start rotating, but the center of mass will remain the same. The yoyo will remain undisplaced. So reiterating my first statement. It is important to consider your FRAME OF REFERENCE. Physical laws apply equally to all inertial frames, and indeed that is fundamental, even in relativistic mechanics.

I think you're question was generally, what's beyond Calculus. So let me try to fill you in some from my endeavors in Engineering. I know this isn't all the mathematics out there, but "researched mathematics" is beyond my scope. Generally I can say that what is classified now as "advanced mathematics" is searching for general solutions to existing problems. For example, we still have much difficulty solving differential equations. It is still basically impossible for us to analytically solve alot of equations, which we end up using iterative/numerical methods like guessing the answer and checking and reguessing etc (now that we have the power of computers with us hehe ^^). Anyway, for the interesting theories you can explore beyond calculus. They are not necessarily ground-breaking new research, but they are "advanced": Laplacian Mathematics, and the Laplace Transform An interesting mathematics. It transforms our every calculus into a different domain, known as the Laplace domain or the S-domain, and all of a sudden, all the complex calculus jargon because algebraiac equatinos. Pretty neat eh. Fourier Series/Transform It's really hard to mathematically quantize certain signals, like human voices. If you've ever observed one through an oscilloscope. It looks like some crazy wave, but if you do a fourier series/transform on it, then it becomes pretty simple. It turns into a series of clean sine and cosine functions. Also pretty cool. Differential Methods Of course, as much as we still have difficulty solving them, there has been some proven methods to do simple things, like solving standard form differential equations. Ever heard something of the Bernoulli equation or homogeneous differentials? Yup, there are interesting methods that mathematicians have come up in the past to solve scary looking things to a calculus newbie. Vector State-Space and Linear Algebra Ever heard of eigenvectors and eigenspace, or about diagonalization? It's about stability analysis. Did you know that every set of differential equations has a characteristic solution? Yup, we're not putting plain numbers into matrices this time, we're putting differential equations in em. It's pretty interesting, but has a relatively daunting proof. Who would've known that matrix theory you studied in highschool has much more depth to it than you think. How does this apply in engineering? Given any physical system, a sattelite in orbit for example, there is only one particular axis in which it will safe to rotate without disturbing its equilibrium. Thats where this field of mathematics comes in. Complex Analysis So the imaginary numbers were mind-breaking in highschool, but this time you have much more to it. You're not analyzing complex number, but complex function, complex geometry, and complex planes. Gladly brought to you by Cauchy, Mr. Euler, and friends. I'm sure some of these names are familiar to you. Advanced Statistics You've probably heard of standard statistical models like the bell-shaped curve if you've done an introductory statistics class in highschool, but trust me, there are a billion more statistical models. The maxwell distribution used to govern gas molecule motion (like that in an ideal gas used in Thermodynamics), and Einstein came up with his own distribution with the help of Bose, known as Einstein-bose statistics used to govern his own physics governing particles at low temperatures (if I remember right). Guess what, there are many others being researched to accurately model our world, and methods in which to use these models to predict what will happen next, in economics and engineering. Welp, thats all for now that I can remember. I'm glad I don't have to do anymore of that now though. One word for math, HATE! XD

Yeah, alot. You get to see them generally when you're doing programming. It's probably a very intersting topic in computer science. They are more precisely known as psuedo random number generators though, because they are not truly random. A truly random number generator would have to be both unpredictable and unreproducable. This is probably not achievable by us anytime soon until we can get a hold of quantum computers maybe The point being is that we will always know the algorithm we used to generate the numbers so knowing that its obvious that we will know the next generated number. It may let you down to know that most of these random number generators are REproducable, yes. Given any particle seed, you will get the same list of random numbers everytime. They do work however, because the successive numbers will appear to be random, but they distribute themselves evenly over a long range. The "better" a generator is, the longer its period is. That is say, most generators, after 500 billion numbers, will start to look periodic, thus not random anymore. You may be asking, then why use them. That's because if for example your random number generator has a cycle of 500 trillion numbers, and you only need 100 samples for your experiment, then your generator will indeed appear random. Depending on your practical application, you may need to look at different generators. Oops forgot to post a link to some C++ generators: http://www.agner.org/random

My guess would be that if you could find the center of the triangle, then everything would be easy from there. THe radius would be the center to any vertex.

Okay, I see where you are getting confused. Dynamics, I remember this was the horry of my 1st year college course. Anyway, to clarify, this doesn't assume anything. The answer simply lies with proper understanding of how to use FreeBody Diagrams. When you analyze the free body diagram of the entire yoyo, you draw a box around the yoyo. The point being is that you do not care where the forces act on the yoyo. You are dealing with external forces. Draw a box around it, then add the force vectors of any that extrude or intrude the box, in this case you have Fgrav and Fstring. The resultant force, Fnet will act on *the center of mass* of the yoyo. Yes. The rotational analysis is done using the yoyo itself as the reference frame. For obvious reasons, when we do the rotational analysis, we see again that the tangential force is indeed that save force Fstring. There's nothing arcane about that

Well not to say your theory is wrong, but you have to understand that alot of physics is not proportional, so your changing of just that one shrinking rule would mean that ALOT if not ALL physical laws must change in some what will seem to us as a random and chaotic manner. For example, halving the mass/volume (also known as density) may need to have you to increase the speed of light by 1.563 times, reduce the proton/electron charge by 24.298%, and so forth to keep the world as we know it stable. And well lastly, I see no reason to propose something as funny as that. Our theoretical understanding of the universe itself is already tangled up with quantum mechanics, relativity, and string theory. By having everything shrinking at once, we don't particularly achieve any new insight to the workings of the universe, it may be the case, but then again, how much is it going to shrink. If everything keeps shrinking as you say, then there really is no point of disappearance, because even the fabric of space time is shrinking, and what is beyond our universe, we don't know. Maybe it is, but it's pretty much irrelevant from a practical sense or way beyond the scope of our understanding at the present time.

I don't have any links for you, but I say confidently to you that indeed there have been tests on this time dilation effect. Some accidently actually. For example clocks on aircraft have been known to become desynced with those on the ground, and need to be adjusted every so often, but more importantly, I believe that NASA has put some atomic clocks on space shuttles or stations before and they have proved to run slower than the references on Earth, so if that's enough experimental proof for ya. I don't have the numbers though I'm sure you can search the literature from there, goodluck Oh, I reread your question again, and erm... I think that your "reference" should generally be Earth, thus any experiment to time dilation should be with reference to the Earth's surface . What else are we going to do?

Hmm, I'm not sure how the discussion is going here, but to answer you're very first post, I think you are confusing classical mechanics with relativity and such. The only reason that mass increases when you approach high velocities is because the velocity (v) cannot exceed the speed of light ©. So E = 1/2(mv^2) If you E increases, that is you give it more energy by whatever means you'd like, there is no way that v will increase any further. The only way to balance the equation out then is to increase the mass (m). The relationships between how much the mass increases for any given velocity can probably be found from the Lorentz equations? as I seriously don't have them off the top of my head for now. I don't think it has to do with what you were supposing up. Though the question of "what is mass" is another interesting one, but that itself can bet tackled by many many different perspectives, and I don't think its directly relevant to the original post. Anyway, did that answer your question?

It may be true, but you're going to have to come up with a theory to say that the laws of physics actually changes over time. I think its not too farfetched a theory, as there has been some indication that the physics of very very distant galaxies may be different from we know in our locale. However, as we know it on Earth, and for all practical reasons, the speed of light is constant, and as long as that is the case given any reference locale, then there won't be a problem.

I'm no nuclear scientist, but I think to answer to this question, you have to clearly define what you mean by "radioactive". Because as far as I know, radiactive material is simply metastable configurations at the atomic level, as similarly you have metastable chemical substances. In anycase, what makes something radioactive is that it emits "high-energy" atomic particles, the more commonly known ones being alpha-particles (helium nuclei), gamma particles (high frequency photons), beta particles (high velocity electrons), that can penetrate and rip apart other atoms if they come into contact with them. So that is a problem of course if you're around and it starts ripping apart your cell's DNA. So yeah, knowing what these elements are would put you in a better position in classifying what kind of energy makes up this radioactivity. Generally it is in the form of kinetic energy yes. They are released at high enough velocities to cause damage on collision. Thats why nuclear facilities use lead or some kind of boron carbon? if I'm not wrong, in thick layers to stop the penetration of these particles. And of course, the high energy photons like gamma particles and x-rays can literally fry you alive, somehow like your microwave cooks food.

I just wanted to say... you really need that information for something important? I'm pretty sure the US Atomic Energy Dept won't let you get your hands on any Plutonium, nor uranium for that matter. It's been taking foreign scientists years to be able to enrich, and yes, plutonium's even harder to get than uranium XD... so I was just wondering if you indeed had a nuclear facility under your basement and are selling plutonium to others

Hmmm, for this question, I don't think there is any logical reason to actually assume that. It would be safer just to analyze it using the tools you've been taught, a la free body diagrams. If you enclose the falling yoyo in a box and look at the FBD, then there are basically two forces, the string Fstring, and the force of gravity, Fgrav. If you look at it from reference to the yoyo itself, then you have Fgrav acting at its center of mass, and a force Fstring, acting tangentially to the body surface. Though obviously, the yoyo will not fall as fast as it would in complete freefall, because some of the potential energy is not only being converted into translational kinetic energy, but also rotational inertia through Fstring which is a tangential force, thus as we know, causes rotation then using the I*omega formula. I'm not really sure what you're confused or up to, if you could give me more specific calculations or answers you are looking for maybe I could help you better.

It's been sometime since I've tackled highschool physics problems (doing Engineering in college atm), and I'm just working on these off the top of my head, so give me a good smack someone if I get them wrong. 1) For wave propagation, the energy associated with the wave front is directly proportional to the area covered by the wave front (energy conservation rules). In the case of a water wave, a 2 dimension wave that is, then Energy1/(2*pi*R1) = Energy2/(2*pi*R2) In the case of 3 dimensional waves, then you use 4*pi*r^2 instead, as that is the formala for the surface area of a sphere instead of the circumference of a circle. 2) If the spring has a frequency of 2.81 rad/sec then in 1.42 seconds, it will be at the location of 3.9902 radians, or 228.63 degrees. Doing a sin(228.63), you get -0.7505 of unity. Since the max displacement is 0.232 meters, then this is when the spring is displaced at x1 = 0.232*0.7505 = 0.1741 meters. The associated potential energy is calculated using PE = 1/2(k)(x^2), probably in your equations list. Derivable from fundamentals using calculus. You can try, it's not too hard. I hope those are right^^ Goodluck!

third year student in a school of electrical and electronics engineering. Interests in control theory and doing a little research in photodiodes at the moment. I had much interest in physics back in highschool, and hope to be contributing to the liveliness of this community cya around