Recent content by Acala

Hi everyone, I'm hoping to get some advice from people who are more experienced in things like this. I am an undergraduate, freshman physics major, and I have made plans this summer to do research with my department. Of course it's not going to be anything too advanced, but I thought it was...

I don't see the problem; identical is good enough. The assumptions you require are indeed necessary, and in this view we take the number of possible states as finite or countably infinite. I don't see how it can be demonstrated either way; I think it's a reasonable assumption to start with...

Hi, Thomas! Here's a talk you might like; Brian Greene is not the most scientific of scientists, but he addresses some of the concepts of an infinite universe that you're thinking of: http://www.radiolab.org/blogs/radiolab-blog/2008/aug/12/the-multi-universes/ Essentially, if space is...

Ah, I see! Thank you for this!

I think I see what you mean, slider. Thanks. I was under the impression that lim (kx) = k lim (x), which would make my two equations equivalent. Is this not the case, and I am just thinking of most other operations in calculus that I've learned?

Let's consider this problem: 0 × lim(n→∞) n If the limit were evaluated first, it would be 0 × ∞ = undefined. If the limit were rewritten as lim(n→∞) 0n, it would be lim(n→∞) 0 = 0. I cannot tell which is the correct interpretation. It seems that if we consider n to be a finite and...

Yes, cepheid's interpretation of my question was correct. This does make sense, and it's quite insightful, but why, in that case, was the bottom box the first box that was called upon to provide the static friction? It seems that even if its maximum potential static friction force were...

I mean that if we were given no information about the acceleration of the system, then we would have to assume that there would be a friction force from the top box, whatever value it may be. I say this because I calculated the friction force from the top box under the assumption that it was...

Let's consider a system of three boxes stacked vertically, resting on the ground. There is friction acting between all surfaces involved. I push on the middle box, but without enough force to move the system at all. If we are to analyze the middle box, we'll see a static friction force...

This is certainly possible. In fact, you can take a lot of classes geared directly toward aerospace engineering with or without the minor, assuming you've completed the pre-requisites. It's difficult to say. That would depend on your experience, your grades, your college, etc. Your best bet...

Mathematically, an instant has a time length of zero. I would think of it another way, though. Ask yourself, if you throw it upwards at 10 m/s, does it reach 5 m/s at some point or does it go straight from above 5 m/s to below 5 m/s. It will be going 5 m/s for the same amount of time as it...

I believe I've come up with something. The height in terms of the radius is going to be 2r for the portion of the height enclosed by the circle plus some remaining height x. If we solve for the ratio of the height to the other sides as mentioned previously, we get that the height is h, the...

That is certainly correct. From this calculation, though, he obtained the ratio of the height to the other sides, which would be 3:5:8. I don't think it does any harm, either, to think of the triangle in terms of these lengths, since the answer has to be in terms of the radius of the circle...

He is saying that he halved line AC in order to get a half-length of 4, and he used the Pythagorean theorem with side AB (or BC) in order to get length BD in terms of the other sides' lengths. The problem is that the illustration is not drawn to scale. Side BC should be shorter than AC, as can...

Ah, that is a clever solution, Rap. And thanks Ken G, that always troubled me about the concept. I can see how it's virtually completely true even if it's possible to be broken in exceedingly rare circumstances.