# A pulley question

by jprg
Tags: pulley
 P: 799 No, calculus is unnecessary Since total force on the pulley = 0, the sum of 2 tensions due to the blue rope must be in the same direction of the green rope (assume that friction is negligible). Denote x the angle needed, then the angle between the 2 sections of the blue rope is 2x. We have: tanx = 1/(b/a+1) and tan2x = a/b, so: $$\frac{1}{tan2x}+1 =\frac{1}{tanx}$$ Moreover: $$tan2x=\frac{2tanx}{1-tan^2x}$$ From here, you may solve for x. Then the tension in the green rope can be easily found.