/sci/ - Science & Math

ψ(r,R)=N (s(r)·p(R) - s(R)·p(r))
with
∫ |s(x)|^2 dx = 1
∫ |p(x)|^2 dx = 1

we want
∫ |ψ(r,R)|^2 dr dR = 2

|ψ(r,R)|^2=N^2 ( |s(r)·p(R)|^2 + |s(R)·p(r)|^2 - 2 *combinations of s(r)p(r) and so on* )

now if you integrate you'll use

∫∫ f(x)g(y) dx dy = ∫f(x)dx · ∫g(y)dy = ... = 1 in your case for the two sides. the mixed terms will probably be zero due to orthogonality and you'll solve for N. I guess it'll be 1/sqrt(2)

http://en.wikipedia.org/wiki/List_of_paradoxes

hf

The two force vectors F_Weight and F_Gravitation=mg have to have the same length but point in different directions, so F_W=-F_G is what you want.
Assuming that the pulley translates F_W exactly, you need the projection of the Force of the string F_S (which has an direction angle of 45° in your pic) onto the vertical line. I guess it's |F_S|=|F_W|/sqrt(2)=Mg/sqrt(2), so M=sqrt(2)|F_G|/g
You get |F_G| by angular momentum considerations, maybe you got a fixed formula already for the situation. I don't know it from the top of my head. You obviously only need m=3, l=1.5 and g=10.
(You can also maybe approximate that the whole 3kg sit on the end so |F_G|=mg=30N. But that doesn't take into account the length of the plank)

>>3692209
a line
a plane

>>3679346
>implying scientists

The obvious answer is Feynman or Dirac.

oh, and btw. this also reminds me of this talk:

http://www.youtube.com/watch?v=RPicL1AWrs8&feature=channel_video_title

>>3613976
The speed is the speed of light.
http://en.wikipedia.org/wiki/Gravitational_waves

>>3613891
Instantaneous action violates causality (hence Newtons Gravity theory and the special theory of relativity don't work together.)