DQW

Thanks for that link Erlen. The last time I needed a little bit of Ga in a hurry, I paid twice as much for the shipping as the price of the gallium itself ! I bought from one of either Alpha Aesar or ESPI.

Incidentally, the point system for crackpot rating (see above) was developed by John Baez (not Carl Sagan). http://math.ucr.edu/home/baez/crackpot.html

If you are an engineering student, I highly recommend you get a copy of a good Materials Science text. Callister is excellent - worth buying, if you can.

Not in the sense that I think you are asking. If they come to this forum to learn, and I can help them do so repeatedly, then maybe I am their teacher, eh ? In any case, I don't see what that has to do with : (i) Giving (what I consider) good advice to students, (Heck, it's an internet forum! I can give any kind of advice - not that I intend to give "bad" advice - as long as I do not violate forum rules.) (ii) Keeping with the spirit of Homework Help in this forum - that it is meant not for others to do your homework for you, but to help you along in your effort whenever you are stuck. IMO, you are doing a disservice (both to the OP, as well as to other classmates of the OP who have put in their time and effort into solving their own homework problems) by simply posting solutions to homework problems/projects.

With aerogel, that shouldn't be hard.

True, (for some reason) I thought the OP wanted particles that weren't directly observed.

But don't these alloys (also the Cu and Ni ferrites) oxidize in water (releasing hydrogen, of course) ? But they don't evolve gaseous oxygen, do they ? Or is it easy to recover the oxygen by heating the oxide or somesuch ?

What I was trying to highlight is that the algebra of velocity addition (which seems to be the crux of the discussion) does not change only when you consider light - you start to see deviations from Newtonian behavior as the velocities get closer and closer to c. No doubt, it is - I should have worded my previous post differently. In theory though, if I considered a massive particle (a neutrino, say) traveling at a speed that's arbitrarily close to c in some inertial frame S, its speed will remain arbitrarily close to c in any other frame S'.

Known or proven: All kinds of quarks, leptons, mesons, hadrons, baryons , ... Theoretical: gluons, virtual photons, Higgs' Bosons, gravitons,... http://hyperphysics.phy-astr.gsu.edu/hbase/particles/parcon.html Fictional: chronitons, anyons, chronometric particles, dechyons, delta rays, kedions, metrions, nadions, polaric ions, tetryons, ...all from Star Trek http://www.midwinter.com/~koreth/particles/

<non-rigorous argument follows> This can be explained in terms of the wavefunction of a pair of particles. Consider a pair of identical particles with the distance from particle 1 to particle 2 being 'x'. The square of the wavefunction is the probability density, and this should not chage for the particles by swapping their positions - since they are identical, swapping them should make no difference. Mathematically, you could write this as [math]|\psi (-x)|^2=|\psi (x)|^2[/math] [math]\implies \psi (-x) = -\psi (x) ~or~\psi (-x) = + \psi (x) [/math] Of these two possibilities, the first case is satisfied by particles known as fermions - which include electrons and protons. In this case, let's see what happens when we set x=0 (ie:at zero separation). [math]\psi(-0) = -\psi(0)~but~-0=0,~so~\psi(0) = -\psi(0) [/math] [math]but~k=-k ~ \implies k=0,~so~here,~\psi(0)=0 [/math] What this is saying is that there is zero probability that the two particles can be at zero separation (making contact). In other words, fermions can not make contact. Since all the atoms in our bodies and other objects are essentially swarms of elecrons (which are fermions) around a nucleus, no electron from my large collection of swarms may make contact with any of the electrons in the chair's collection of swarms. Notice that the second case (the one I left out) does not impose this "no contact" rule. That case is satisfied by bosons - such as photons, which we know have no such qualms about "touching each other". :biggrin:

It's not that light behaves differently, as the understanding that the approximation we use at low speeds (compared to c) does not work at all at speeds near c.

It is statements like this that demonstrate where your method fails. You first must understand metric spaces and manifolds before you go about constructing them. You've thrown together a general binary function, a 3-dimensional object, a dimensionless object, a temperature, and several different curves, and called them dimensions in some space.

No, they won't. The speed of the bullet from the gun mounted on the moving vehicle will be faster (relative to the stationary target) than the other bullet, by the speed of the vehicle. Consequently the time taken will be less. PS : The speeds here are low enough that relativistic corrections are meaningless, so this thread should be moved to classical physics (not that SR isn't a classical theory).

Not really ! The person who wrote down that first equation with Ca+ was just plain WRONG ! End of discussion.

Just looking into phase diagrams I find that the density of helium gas at 10 atm, 80 K is much bigger than that of liquid nitrogen (at same conditions, of course). What phenomenon will you observe ? Buoyancy, I guess. The liquid will stay at the top of the container.

To paraphrase : You need to make up questions and you need to answer them.

Which part of this is the question, and which part (if any) is your attempt ? Where do these cellular concentrations come from, and what relevance do they have to the described galvanic cell ? And where on earth did the 61 come from ? The solution to this problem (if the question ends at the word "positive") is a direct application of the Nernst Equation. All you have to do is plug in the given numbers and you are through. But I have no idea what all the stuff in the second half of the post is about.

And you got this revelation how ? I have a suggestion. Take your geometry classes and then go to college, and then grad school, and now you may be ready to give it a reasonable shot. Until that time, let's trust the experts. Anyway, I believe this is in the wrong forum.

<continuation> 6. PARTICLE DYNAMICS - II : In this chapter, there's more of the same stuff that went into the previous chapter, but in addition, you learn about friction and centripetal forces. No new math here. 7. WORK AND ENERGY - Here's where you will first need integral calculus - to deal with the work done by a variable force. You will also learn how to use the work energy theorem and how to understand power. Math prep : integral calculus. 8. THE CONSERVATION OF ENERGY : Here you are taught important concepts of conservative and non-conservative forces and potential energy, and the powerful technique of energy conservation. There's also a little section on relativistic mass which you could easily skip and not hurt yourself. It's best to learn relativity separately, as a coherent package. 9. CONSERVATION OF LINEAR MOMENTUM : First you will learn about the center of mass and its frame of reference. Then you will learn to apply momentum conservation to open and closed systems. No new math here.

I partially agree with Tom. When you learn calculus, you want to learn it right - from first principles and definitions up to applications. But I do think that (with a focused effort) you can learn this from a good text, by yourself, in no more than a couple of weeks. The test of your understanding is simply your ability to solve problems. If you can work the exercises at the end of each chapter (of a calculus text), you are good to go. I'm not sure about your grandfather's introuductory text though (no insult here, and I speak from no knowledge of what he's written, but you are certainly not a judge of that either) - I would get a good book from a library. We can recommend a few perhaps.

The Chapters : 1. MEASUREMENT : Reference frames, and units. R&H does not have a section on dimensional analysis, which I consider essential to this part of your learning. Find another source for this (or ask me). Math required : basic arithmetic. 2. VECTORS : This chapter teaches you basic vector algebra, and is a pre-requisite to everything that follows in the book (and in physics, in general). Do not go to the next chapter until you can solve all the problems in this one (at least all but the last few, which are exercises in mathematical muscle-building). Math prep : very basic trig (the definitions of sin, cos, tan and the knowledge that sin2(x) + cos2(x) = 1 is minimum), a prior knowledge of vector algebra will make this chapter a breeze, but that only means you can get to the problems sooner ! 3. MOTION IN ONE DIMENSION : This chapter teaches you how to use the equations of (linear) motion, under constant acceleration (and otherwise). An important special case is the free-fall problem. It rigorously teaches you what velocity and acceleration are, and in the process, develops the concept of a derivative and its application to finding rates or slopes of functions. Learn how to draw the graphs - that's essential. Math prep : You will need know how to find derivatives of (or to differentiate) polynomials. While you're at it, learn how to do this for other functions as well : trig functions, logs and exponentials should do. 4. MOTION IN A PLANE : Here, the concepts taught in the previous chapter are extended to motion in 2-dimensions, by means of the previously developed tachniques of vector algebra. Important special cases are projectile motion and circular motion. You will also learn the valuable technique of using relative velocities and accelerations. Math prep : nothing new - more vector resolution, addition and subtraction. Also, you must understand how a 2D vector equation is nothing but a pair of scalar equations. 5. PARTICLE DYNAMICS - I : Here, you learn how forces affect dynamics (motion), through the framework of Newton's Laws. Be perfectly clear about what the Third Law teaches. You will also learn the vital (and I can not stress this too much) technique of drawing free-body diagrams, and using them to solve static and dynamic problems. No new math here (but you get more practice writing vactor equations as pairs of scalar equations in the x- and y-directions). <more follows>

The First Golden Rule of Forum Life : Make no apology for asking honest questions. There is no shame in wanting to know more. (and do remind me of this if I err the same way) Since you're persistent (which I respect) I shall put in more effort than I did the first time. <digs through the rubble for dust-covered tome titled : "Physics, Part I; Robert Resnick, David Halliday"> Okay, here goes : My copy is a 1960 edition !! These are the first 9 chapters according to my book (make sure they roughly agree with yours) 1. Measurement, 2. Vectors, 3. Motion in One Dimension, 4. Motion in a Plane, 5. Particle Dynamics - I, 6. Particle Dynamics - II, 7. Work and Energy, 8. The Conservation of Energy, 9. Conservation of Linear Momentum Next, I shall list what are the important things to be gained from each chapter, and the math preparation required (of course, going by what's in my book). The pre-requisite for any chapter is all of the preceeding chapters. Do not skip a chapter, ever !

Yes, I didn't imply that you should charge him for it.

I speak from knowledge of an old edition, but I don't think it's changed very much since. Just very basic differentiation and integration (definite and indefinite). No knowledge of differential equations, special functions, etc. is required. The only functions you will encounter are polynomials, exponents/logarithms, and trigonometric functions.

Warning : Personal crackpot theory follows ... (At the risk of sounding quackish) I think a parallel can be drawn between the green spot (actually the absence of a pink spot) and hole conduction (movement of the absence of an electron). As we well know, transport of an electron vacancy can be pictured as the motion of a unit positive charge (or the negative of the electron charge). Likewise, the movement of a pink vacancy appears like it were in fact the motion of a spot whose color is the negative of pink - which is green.