# Recent content by Delta2

1. ### Divergence of a radial field ##F=\hat{r}/r^{2+\varepsilon}##

Well you have compactified some steps (for example i would like to see the representation of the radial field in cartesian coordinates and the derivatives of ##r=\sqrt{\sum x_i^2}## with respect to each cartesian coordinate) but ok i am more than surprised that it can be done in less than half a...
2. ### Divergence of a radial field ##F=\hat{r}/r^{2+\varepsilon}##

Like the others i dont see anything wrong in your work. Maybe it is kind of simple because it is done in spherical coordinates. Try to do it in cartesian coordinates i think it would be one page long or even more!.
3. ### Problem about a triangle -- write the cos, sin and tan as a function of the sides

First use the pythagorean theorem to find the hypotenuse. Then use the definition of sin cos and tan on an angle of a right triangle. For example it is according to the definition that ##\sin\phi=\frac{a}{\text{hypotenuse}}##
4. ### Contradiction with forces in this problem with a ball rolling in a loop-the-loop ramp

You mean because centripetal acceleration "suddenly" appears there? As far as i know acceleration need not be continuous, its velocity that is usually continuous.
5. ### Calculate the New Velocity and the Velocity of a Pendulum Mass

Q2 is straightforward application of conservation of momentum. Q1 both a) and b) are about application of the principle of conservation of energy. I am sorry i am not allowed to say more according to the rules of PF you got to show us your best attempt at solution, which means you have to work...
6. ### What exactly is pulling the man up/down in rocket?

@PeroK post #4 might seem funny but he says a lot, its the force from the floor/seat that is responsible for this effect. Forget my post about fictitious forces.
7. ### What exactly is pulling the man up/down in rocket?

There are two answers in your question depending in which frame of reference we ll answer. In the accelerating frame of reference of the rocket, there is a fictitious force that presses the man down. Maybe its not the right time to be introduced to fictitious forces but you can google about...
8. ### Which direction should you aim to shoot a fish using a laser gun

Your book has its funny aspects, using high power laser to shoot poor fishes lol.
9. ### Proofs in analytic geometry and vector spaces.

There is indeed a problem with #2, you have to prove that it holds in any base but i dont understand the problem with #1, how are you supposed to work with vectors if you dont adapt a vector space(R^3 or R^2)? You are right that the proof with u and v is more general more complete i would say.
10. ### Why didn't ancient civilizations harness the power of electricity?

I think in ancient times, electricity and magnetism effects and phenomena though they were known, they were viewed as toy-like and ancient civilization just didnt put any research on these phenomena. They just couldn't imagine that one could make an electromagnetic engine e.g an electric motor...
11. ### I A real life problem with plumbing at my house

Its from the energy the water has due to its pressure (static pressure) which in turns comes from gravitational potential energy or from some pump that is located somewhere and increases the pressure of the water.
12. ### Distance Formula Problem

You shouldn't cross this in my opinion it was correct. It is just that it turns out that ##t_2=0## and ##d_2=1## which means that he has to run the second mile with infinite speed ##\frac{d_2}{t_2}=\infty##. But the problem asks if it is possible, so i guess the answer here is NO it isnt...
13. ### Vector potential ##\vec A## in terms of magnetic field ##\vec B##

I have to look it up abit more thoroughsly (give me time to think heh ) but we can agree for now that your equation is correct in the case of non time varying currents. It doesnt seem to be correct in the case of time varying currents cause then the well known expression for A contains the...
14. ### Vector potential ##\vec A## in terms of magnetic field ##\vec B##

Are you sure this is the equation derived by Feynman? This equation obviously fails if ##\mathbf{B}=constant\neq 0## cause it gives ##\nabla\times \mathbf{B}=0## and hence ##\mathbf{A}=0##. I have in mind a slightly different equation which i derive from Helmholtz decomposition theorem which is...
15. ### Remainder of polynomial

This formula you wrote $$f(x)=Q(x)(x-1)(x+1)+R(x)$$ says a lot if you know how to interpret it. Since (x-1) divides f(x) what can you say about whether (x-1) divides R(x)? I believe this and together with the answer to the question of @haruspex will get you to the answer of the question.