probably this is what you are talking about.....just redrawing the same thing for convenience
a rope passes over a fixed pulley such that it makes an angle (A) at its centre. if (u) be the coefficient of static friction between the rope and the pulley, determine the relation existing between the values T1 and T2of the tension in the two parts of the rope when the rope is just about to slide towards the RIGHT.
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3 Answers
for any segment of the rope, at an angle 'a' to the starting radius perpendicular to T1,
we have dT=dF
where dT is the slight increment in the tension, for an increment of a by da,
we have dF=kdN=dT
we also have dN=Tda
so kTda=dT
or Kda=dT/T
\int_{0}^{A}{da}= 1/K \int_{T1}^{T2}{dT/T}
so AK=log(T2/T1)
or T2=T1e^kA
cheers!!
http://targetiit.com/iit_jee_forum/posts/30_5_09_easy_pulleys_9308.html
look at #7