Recent content by z0r

By massless, one would expect you mean "rest mass." In that case, the particle would probably behave most like a photon, traveling at speed c in free space. Unlike a photon, however, such a particle would be affected by electromagnetic fields. One could only speculate, but I imagine if the...

I went to discuss the problem with my professor and he told me that indeed the form xg = \dot{x}^2 + x\dot{x} \frac{d\dot{x}}{dx} is correct, so thanks to those who set me straight. The method he used for solving it is assuming that the velocity is some function of x... \dot{x} = v = a...

Mathematics as an expression of a culture/civilization I found this post interesting because at the moment I am reading Spengler's Decline of the West. I have just finished the introduction and started the second chapter: Meaning of Numbers. Spengler argues that the idea of a universality of...

Hmm... so the differential equation to solve is: \dot{x}^2 + x \ddot{x} = xg or xg = \dot{x}^2 + x\dot{x} \frac{d\dot{x}}{dx}. It doesn't appear we can easily isolate the two variables. The goal would be to get an expression for x and one for \dot{x} and integrate the x from L to...

Very well. Let us take the time derivative of the momentum P = \mu x \dot{x} and set it equal to the force F = \mu x g . We get: \mu \dot{x}^2 + \mu x \ddot{x} = \mu x g . Right off the bat this makes no sense to me. When the rope has completely left the table, the acceleration will be...

I am having difficulty understanding how to solve this mechanics problem... A rope rests in a bundle on a table with a small hole in it. One end of the rope slides through the hole and gravity steadily pulls on it until the total length of the rope slides through the hole. The length of the...

True... reminds me of what my professor says: grad students get to such advanced levels that when they come across a truly simple problem, they don't know how to deal with it because they've been doing the hard stuff for so long. :smile:

I think it's a bit simpler than that... Haha, what is all this silliness about the mass of the plate or the radius of the electron? I think "gravitational force" simply means Earth's gravity, no? We simply say, F_g = mg and F_E = qE . Now, F_g \approx 10^{-29} N and F_E \approx...

Perhaps this problem has two parts to the solution. I am imagining a regular pendulum at its lowest point, where the string's angle with the ceiling would be 90 degrees and the velocity at a maximum. Here, we have the angular acceleration and also the gravity contributing to the total tension...

I found the bit about the regression to lower evolutionary forms interesting. But certainly, I don't find it surprising. Humans are animals, like any other, and animals primarily run on instinct. I think the only thing which makes humans any different is that many humans are convinced that...

I suppose that's the kinetic coefficient of friction... in that case, we know that the kinetic frictional force will be: F = \mu_k N , where mu is the kinetic coefficient of friction and N is the normal force (the mass of the vehicle times gravitational acceleration). Now, we know...

Use x = 2 \sin \theta ... then, dx = 2 \cos \theta d\theta , and your integral becomes: 16 \int \cos^4 \theta d\theta . Use \cos{2\theta} = 2\cos^2 \theta - 1 , etc...