Recent content by Meithan

You do realize that 10^20 years is orders of magnitude longer than the current age of the Universe, right?

I am a TA in a class covering an introduction to fluid mechanics, thermodynamics and wave motion. We just finished the thermodynamics part of the class, but out of all the problems we solved, there is still one both me and my students are not comfortable with. Here it is: Problem A metal rod...

Fantastic! I'm ashamed I did not realize a trig substitution would handle that integral! Thanks for the enlightenment. I suppose, as the Wikipedia suggests, that this result is not invertible in terms of elementary functions. So that would be as far as one can go in this problem. Now I'll try...

I've done some advances towards solving this problem (though not the kind I wanted). 1) I used Mathematica to calculate the integral that I can't solve. The solution is ugly, but it's a solution. However, this gives time as a function of position, but we want the other way around. Since the...

I was writing it in cartesian coordinates! I just chose to call the linear distance, measured from the center of mass of the Earth, r. I could've used y or any other letter, it's entirely arbitrary. Regardless, if you choose to write it in spherical coordinates, it would still be correct...

I've been trying to derive the full solution to the problem of free fall when the distances considered are large (and hence, the acceleration is no constant, but a function of height). This isn't homework, I was just curious. The problem is innocently simple, but yields a differential equation...

I finally solved my issue: the answers in the books are wrong! I found the same problem (only with different numbers) in the latest edition of the book (8th), and this time my analytical solution gives the correct answer. Furthermore, the solution of the problem is available online as an...

'You do not really understand something unless you can explain it to your grandmother.' — Albert Einstein (?) Math is a very convenient way to describe nature, but it is by no means the only way.

One way to look at degrees of freedom is to ask yourself: if I have a particle of the system (an atom, a molecule, anything), how many numbers do I have to give to specify its position / orientation (what we call the configuration)? So for instance, for a gas of monoatomic particles, you need...

As tiny-tim says, just call the mass 'm'. When I ask the force, you don't need to give a number -maybe that's what's bugging you-, just the mathematical expression, the formula. For example, if I told you an object experiences a force 'F' and has mass 'm', you could write that its...

As the lorry brakes, it undergoes a certain acceleration \vec{a} directed backwards. This means the surface of the flatbed wants to slide backwards under the crate. Friction tries to prevent this, by making the crate decelerate at the same rate as the lorry. However, this only happens up to a...

I don't see why you'd introduce such an arbitrary modification of the equation of energy. To me it's simple: (total mechanical energy at instant 1) = (total mechanical energy at instant 2), if there are no losses. The total mechanical energy before the collision is in the form of the kinetic...

I'm a TA in an introductory course of (classical) mechanics at the university. I've been baffled for the couple two hours at this problem, taken from Resnick, Halliday & Krane (Fourth Edition in english; it's the 3rd ed. in spanish). I initially solved the problem, thinking my reasoning was...

In my opinion it's as Ich said. It simply comes from the fact that all inertial frames are equivalent. Hence, it doesn't matter which one we call S and which S', the Lorentz transformation should look the same. Changing all primed quantities with unprimed ones (or viceversa) is valid simply...

Well, there's one thing we should consider first. In my understanding, nuclear reactions (Hydrogen fusion, for instance) in the center of stars occur based on probabilities; there's no strict mass/temperature limit for a single nuclear reaction to occur - it just becomes less and less probable...