Recent content by haruspex

The exact wording suggests that is the intention. This is reinforced by its asking for the velocity vector, not the speed. If we only take ##s## as the modulus of the displacement then the sign of ##v## is indeterminate. To avoid confusion, I'll use ##S## for the displacement (which is never...

… has to be assumed to be constant (or we do not have enough information) … an idealised mechanical system is often assumed to consist of..

And at that point, ##s=\pi/\alpha##. When will ##s## exceed that?

Enumeration problems do not, in general, fall neatly into just the two categories. See https://en.wikipedia.org/wiki/Twelvefold_way.

Consider a small patch of the inner surface. If it has charge ##\Delta Q##, what potential does that produce at A? You can use the method for grounded spherical conductors too. See e.g...

Can we argue that all the field lines from the point charge must terminate at the inner surface? We need that argument anyway in order to say that the induced charge is -q on the inner surface, so +q on the outer surface. Looks ok to me, though I have the nagging doubt that we should be using...

Your reasoning is correct and I agree with your answer. It might shed light on the problem, possibly leading to a smarter method, if you figure it out for all numbers of boxes up to 10. I observe an interesting pattern in how the average number of questions increases as the number of boxes...

You can use any frame of reference you like as long as you are consistent and include "fictitious" forces as appropriate.

You wrote R3-R1 both times. What did you mean to write? I am unable to comment without seeing your whole solution. Please post a translation of the text in the (partial) solution.

Very neat. Small typo: in your diagram under (1), you have -F at top right instead of F.

Ah, yes, I missed that. But not if B is pinned and A is free, right?, because F acts to the right. So does this mean the two horizontal forces there can be determined? It rules out the horizontal force at B being zero.

You are missing the point. There is an error in the algebra. Think about that again.

It says they are pin connected together. I agree the diagram is unclear though.

Wrong.

I'll fix up your LaTeX by replacing each occurrence of [ tex ] and [ \ tex ] with a double #. It is clearly not valid to conclude that F=0. Such a structure could be created and a force F applied and yet the structure resist movement. I am having trouble guessing what your labels for forces...