Parallelogram Law/Examples/3 Weights from Pulleys

Example of Use of Parallelogram Law
Let $3$ bodies with mass be suspended by cords from pulleys like so:


 * Three-weight-equilibrium.png

The bodies will arrange themselves into equilibrium when the vector corresponding to the weight $\mathbf F_3$ of the middle body is equal and opposite the vector corresponding to the vector sum of the weights $\mathbf F_1$ and $\mathbf F_2$ according to the Parallelogram Law.