MDJH

If we're to simplify damped and resonant oscillations by assuming that there is some specific pattern with which the oscillation's amplitude either decreases (damped) or increases (resonant) then is it still sinusoidal or does it qualify as something else?

Ok, so supposedly in calculus it's a rule that the limit of a ratio of two functions should be logically equivalent to the ratio of the limits of those two functions. Supposedly even for discrete sequences the same applies to limits at infinity. So what if two functions (or sequences) tend to infinity on their own? Let's say we have f(x) and g(x), both of which tend to infinity as x tends to infinity... however, the limit at infinity of f(x)/g(x) is a finite number, let's say c. If c were greater than 1, would it be logically equivalent to say that lim f(x) > lim g(x) even though both tend to infinity? Similarily, if c were less than 1, would it be logically equivalent to say that lim f(x) < lim g(x) even though both tend to infinity?

So I had a hypothetical idea a while back involving a large rotating wire-mesh (of course, in hindsight, it would be more likely to attract lightning if there were pointy ends distrubuted throughout said wire mesh) turning high in the sky, to attract lightning during thunderstorms, and run it through whatever it leads to. (ie. epsom-salt water for electrolysis, lightning electromagnet, etc...) One idea I had for what it would lead through is a flat sheet of tungsten, immersed in water. As the lightning runs through it, the tungsten heats up; 60 watts of electrical power is enough to light a tungsten bulb significantly; imagine if I were to run hundreds of thousands of amps at millions of volts of electricity (implicitly hundreds of billions of watts) through tungsten; that should heat it up very brightly, flash boiling the water and forcing it out of whatever container to turn whatever turbine and generate electricity in a more controllable, presumably more storable manner. However, thinking about blackbody radiation, I'm also curious as to whether or not heating it up with hundreds of billions of watts of electricity would also cause it to emit UV light, or X-ray light... or even gamma gays. How likely would that be to happen?

I'm not sure what "a large quantity" is myself. I've heard it can be fairly expensive. I was thinking somewhere along the lines of a few ounces... so that I could get a strong bright fire, without spending too much on the magnesium to light. Part of the reason I vaguely said "large quantity" was because I'm not sure how much fog it would cut through on a foggy night, (or whether refraction through the fog would also have an affect) or to reach the clouds if it were overcast, etc... let alone what the implications of it would be. I guess I should check to see what regulations there are on such things too but first I wanted to know a bit more about the chemical reaction in and of itself. Also, the reason I mentioned gasoline was because it was a liquid fuel and would easily distribute the heat to the whole thing rapidly. Would a piece of paper underneath the magnesium suffice?

I thought centrifuges were when the whole container revolved around an external axis, rather than rotating about one that passed through the container...

Do you have to be so condescending? I was not sure if there was any restriction on doing something like this if it was done in an area that would not set fire (such as a flat region of barren dirt... far enough from actual houses that people could only see it from the reflection on the clouds) and I do not know how far the light would reach. That is sort of why I am asking this now, to find out what the implications of this would be, from both a social and directly physical perspective. But hey, if you want to sarcastically berate someone for asking questions that is up to you...

Well, I already mentioned that I had guessed my idea wasn't so new...

I mentioned before about centripetal forces, and the idea that if some closed container were spun about a central point such that one end of the container always pointed to said central point, the pressure would be higher at the end further from the centre than away from it. Now that I've gotten to the part relating to rotational motion I was also supposed to have learned in introductory physics, one equation caught my attention; a = r*(w^2). This means that the centripetal acceleration (which for constant mass is proportional to force) is proportional to radius; a bit strange, when you consider a = (v^2)/r, where r is in the denominator; but then you consider that v=rw, ergo v^2 = (r^2)*(w^2) and it makes a bit more sense. However, this also means that within the same rotating object, centripetal force is a function of distance from the rotation axis; even if the axis passes through the object. This also means that the closer you get to the radius, the closer the centripetal force gets to zero. So basically, unless an inner object within it has a centre of mass lying EXACTLY on the axis, centripetal forces will pull it outward, and they will only get stronger and stronger as it goes further out... that is, so long as it's within the rotating object. So, let's say this container was filled with a fluid, whether liquid like water or gaseous like air, and was spun such that its axis of rotation passed right through it. Wouldn't that mean the implicit pressure gradient from the axis of rotation outward would suck fluid away from the middle and bunch it up at the outer sides?

I'm not very familiar with checkers, and even less so with chess. But after I heard of polar coordinates (has to have been more than half a year ago now) and its nature of being analogous to rectangular ones... I imagined, would you be able to play a game that uses a rectangular-coordinate grid... whether chess, or checkers, or something else... on a polar-coordinate grid?

Let's assume I hypothetically managed to get my hands on a large quantity of magnesium ribbon, and I decided I'd use it to start a bright fire. I'd use something underneath it to ensure the fire was strong, (such as gasoline) but the key component of the show would be the magnesium itself. First off, I assume it'd be dangerous to have the flame viewable directly, so the flame itself would only be recorded by camera. But let's say I had everyone involved facing away from the flame, and instead looking at the buildings, the ground in front of them, and maybe the clouds depending on the conditions. Which brings me to my next question... how would the weather conditions (assuming it was at night) affect this light show?

Named for the arrows from the video game Ocarina of Time, I've imagined a potential means of using arrows to ignite targets from a distance in real life... I'm guessing that someone's thought of this before though. Basically, the idea would involve a burning torch, a gasoline-soaked arrow, and a target, within the same path of estimated trajectory (which should in theory be a parabola, and I'm guessing can even be approximated as a line for fast enough arrows travelling along short and/or horizontal enough paths) such that the arrow, soaked in gasoline, would be shot, from a safe distance, through the torch, setting fire such that it does not leave a sufficient vapor trail to ignite the person firing the arrow, and travelling along the trajectory to its supposed target. (Such as a hydrogen-filled balloon.) Is this realistic?

I've made topics before about water electrolysis... never got around to actually doing said electrolysis though. But I've heard of alternative means of making hydrogen, such as mixing strong acids with metals. I'm guessing that would be more expensive and/or wasteful than electrolysis?

... underground? I'm only speaking hypothetically here. o.o

Hearing about the recent heat wave in southern Ontario... one of the more obvious thoughts to come to mind is, "well, they should have stored a lot of spare energy over time so that people could use their air conditioners without causing a power outage." But then I began to think... what if, hypothetically, energy were so abundant that people could afford to air condition the outdoor air, at least within the city limits of major cities like Toronto, so that people could comfortably go outdoors? Would it be a good idea then? The method I imaged was of super-powered air conditioners distributed every few hundred metres or so, in areas that would be fenced off so that people couldn't get TOO close... strong blasts of very cold air (let's say, which goes through some pipe immersed in liquid nitrogen) are shot high into the sky, forcing strong convection currents. This would decrease temperature and/or condense moisture until humidex values plunge, creating a more comfortable environment. Would it work, in that scenario? And what would be the side-effects?

So I hear that maglev trains are able to go up to hundreds of kilometres an hour. How quickly would they tend to approach such speeds, given the forces acting on the passengers due to acceleration? Would strong force over short time interval, or weak force over long time interval, be the preferred approach? Also, if they were about to round a turn at hundreds of kilometres an hour, would they slow down first, and if so for how long?

Let's say you had a container from which matter could not enter or leave, but energy could enter or leave easily by conduction. This container is filled with warm, humid (but not saturated) air and then its temperature is lowered to far below the dewpoint without being opened. Would the drop in temperature cause condensation, or would the drop in pressure prevent it? Which factor would outweight the other, if either?

Leibniz' rule? I'm not sure if I've heard of that one. Though if you're referring to the product rule, then yeah that's what I assumed applied in the 2nd case. I just wasn't sure if it worked differently when you had the product of a scalar and vector or something...

Ah... sort of like voltage and voltage gradient in that case?

Momentum is a vector quantity, in the same direction as speed, and velocity is the magnitude and direction of said speed, with mass being the scalar coefficient by which velocity is multiplied to yield momentum, right? So let's say we're taking the derivative of momentum with respect to time (seeing as how that's what net force actually is) and mass of a particular object is transferring elsewhere... if we're analyzing the momentum of the object in particular, and both mass and velocity are changing at the same time, would the rate of change in momentum be: (dp/dt) = (dm/dt)*(dv/dt) OR (dp/dt) = m*(dv/dt) + v*(dm/dt) OR would it be something else because of the differing natures of the quantities involved?

... and if it doesn't have a direction, then how do you describe the difference between the pressure on one side of a surface and the pressure on the other side? (ie. Let's say there was a force imbalance from one side of the surface to the other... does that mean the pressure has a direction?)

"Various sources"? From what I recall drag force referred specifically to the force resulting from the vehicle pushing against the air... what other sources are you referring to?

Interesting... so kinetic energy varies, depending on the reference frame one is referring to... so it has "kinetic energy with respect to x reference frame"?

So is it safe to say that generally speaking, the higher the speed, the higher the percentage of the engine's power goes into overcoming drag, and the lower the speed, the higher the percentage of the engine's power goes into propelling the car forward?

Ah, right, centripetal acceleration... ... so basically, because the pen is what keeps the chain accelerating towards the center, the pen pulls on the chain, and by Newton's third law the chain is as a result pulling on the pen?

Ok, so the kinetic energy of an object is supposed to be proportional to the mass of the object, and to the square of the speed of the object, and speed is basically the magnitude of velocity, right? Also, velocity depends on the reference frame in which it is measured, so long as said reference frame is also of a constant velocity, right? So if we were considering a moving object from two reference frames, one that treats the object itself as a reference frame, and an external reference frame, from which the object was moving... would that imply different kinetic energies?