Given:

$d$ = {width} {units[0]} $\qquad r_1$ = {r1} {units[0]} $\qquad W_1 = $ {w1} {units[1]} $\qquad r_2$ = {r2} {units[0]} $\qquad W_2 = $ {w2} {units[1]}

Draw free body diagrams of the two cylinders.

{geogebra_applet('rchz6eew', [["width", width], ["r1",r1], ["r2",r2]] )}

Find angle $\theta$ from the geometry of the problem.

$\theta =cos^{-1} \left( \dfrac{d - r_1- r_2}{r_1+r_2} \right) = \var{siground(theta,4)}°$

Find force $A$ using equilibrium of the yellow cylinder

$\begin{align} \Sigma F_y &= 0\\A_y - W_2 &= 0\\ A \sin \theta &= W_2\\ A &= W_2\,/\,\sin \theta &=\var{show(A)}\end{align}$

Find forces $B$ and $C$ using equilibrium of the blue cylinder

$\begin{align} \Sigma F_y &= 0 & \Sigma F_x &=0\\ B - A_y - W_1 &= 0 & C-A_x &=0\\ B &= W_1 + A \sin \theta & C &= A \cos\theta \\&= \var{show(B)} & &=\var{show(C)} \end{align}$




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