Thank you, I appreciate your response.
I think I understand where I was getting confused:
The proper length is a property of objects, not events, and belongs to the object's rest frame: ##L_r = \gamma L_o##.
The proper time between the two events belongs to the frame where they are not...
Suppose there was a light clock on the rod (bouncing a beam of light back and forth, perpendicular to the direction of motion between the rod and the observer.) In the rod's frame of reference, each tick of the clock takes ##T_r## seconds. But our observer, O, would see a longer path-length for...
I'm thinking about a very basic scenario in special relativity, but I've got something backwards, and I could use help understanding why it's wrong.
Suppose a rod R is moving past an observer O at speed v.
The observer wants to know how long the rod is, so he starts his stopwatch as soon...
Thanks, this sounds really interesting. So am I on the right track to think:
1. There is no need for the time-average and distance-average forces to be the same (although sometimes they are), so there's no contradiction there.
2. The kinetic energy lost by the blob could be anywhere from...
I'm still confused.
Using the center-of-mass to wall distance, d/2, doesn't sound right to me: If the mass was distributed unevenly, wouldn't that then change the result of that calculation? Yet, shouldn't we expect the average force to stay the same? From the perspective of the wall, finding...
Well, half the mass has splattered onto the wall, so there's only half still colliding. I don't see how that's relevant, so I guess I'm missing the hint. I wonder if I should be getting that factor of 1/2 from an average quantity, like using Δt = d / (v/2) instead of d/v, which would make the...
This isn't actually a homework problem, I'm just wondering what I'm doing wrong:
Homework Statement
Say we've got a stationary brick wall, and a blob of jello with mass m is launched at the wall with speed v. The blob has length d along the direction of motion.
The blob splatters...
Ahh, perhaps that's it - I see you set up your inner integration bounds as -e and +e, whereas I just used +c in both cases. So, your range of integration never actually includes the singularity, while mine implicitly did. That sounds like a good reason why I'd get the wrong answer.
Hopefully...
Thanks for the reply, Mark!
There's something I still don't get, though: shouldn't the limiting behavior of the function be exactly symmetrical on the left and right sides of the singularity (for some functions, like this one)? And as such, wouldn't those 1/c and 1/b terms still cancel each...
Suppose one needs to evaluate a definite integral over a singularity, like: -\int_{-1}^3 \frac{1}{x^2} dx
The textbook way to do so is to split the integral into two parts around the singularity and take the limit, like so:
\lim_{b\rightarrow 0} -\int_{-1}^b \frac{1}{x^2} dx
and...
This is how Wikipedia summarizes the Poincaré Recurrence Theorem:
This is wrong, isn't it? Don't you need to ensure the phase space is bounded, and isn't conservation of energy an insufficient justification for that? Like, imagine throwing two baseballs away from each other into infinite...