Recent content by DaTario

Hi, wrobel. But why is it not appropriate or correct to calculate the average velocity in this context from an integration in x (spatial coordinate) of the velocity as a function of the position, ##v(x)##, defined as $$ v(x) = \begin{cases} v_1, & 0 \leq x < L, \\ v_2, & L \leq x \leq 2L...

I guess I got it (with the help of yours). We can say that the expression $$ \frac{v_2}{v_1 + v_2} $$ is the fraction of the total time that the car has moved with velocity ##v_1##, since, $$ T_{total} = \frac{L}{v_1} + \frac{L}{v_2}, $$ so that the fraction of the time the car has moved with...

Given a set of numbers, the harmonic mean is the inverse of the artithmetic mean of the inverses of these numbers, namely, $$ \bar v = \frac{1}{ \big( \frac{\frac{1}{v_1}+ \frac{1}{v_2}}{2}\big)} = \frac{2v_1 v_2}{v_1 + v_2}.$$ A weighted mean can be defined in this context as $$ \bar v =...

Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two...

Notice that you are describing some color issues of the sky. When sunlight enters the atmosphere, it scatters more intensely blue light. At the end of its journey (ray of sunlight in the atmosphere) it shows us a red sky.

Perhaps it is worth trying to find a set containing infinitely many integers but which, given its formation rule, imposes serious restrictions on the counting process, to the point of making this task impossible even for a being that lives for an unlimited time. An example of the difficulties I...

In the hope that it will be possible today to translate an article in PDF format from Portuguese to English, I think this reference may be useful. It tells us that the historical origin of the cross product is in Hamilton's work on quaternions...

Thank you PeterDonis, I understand my discussion is off limits here.

Ok, the entanglement has to do with the interaction between the apparatus and system. After this it seems somewhat contradictory (at least in most cases) to say that there is no change in amplitudes of the state of the particle, since a new interaction usually means that the hamiltonian is...

Hi All, We say that the Schroedinger equation stipulates a smooth and unitary evolution for the wave function, and that the measurement causes the wave function to collapse into one of the eigenstates of the operator that represents the observable parameter being measured by the apparatus. My...

A process that is possibly important in explaining the phenomenon of color by subtractive synthesis is the fact that once excited, the electron decays and emits a photon in a superposition of momentum states (Weisskopf-Wigner theory for spontaneous decay). In practice, this means that the red...

This approach seems to be really interesting.

The notion that the curvature happens in the space-time is a very rich one. I had a positive experience here on the forum related to the maturation of GR ideas in my head. That's when I asked about the transition from straight 'geodesics' to circular 'geodesics' that are presented in many...

Finding the shortest path would be very nice, and the (high school) students are not supposed to have mastered variational calculus. But college ones may have at the moment this exercise is put in front of them.

Are you taking this exercise I am proposing as consisting of one spatial dimensional and one time dimension (1+1), aren't you? In this case, sorry. I was proposing a purely spatial question (x and y being spatial dimensions with no time dimension included).