The particle M in Figure 1 is suspended by using the two (soft) ropes MA and MB, which are made of the same material and have equal diameters. The x and y coordinates of points A and B, measured in metres, are (-1,2) and (1,2), respectively. In the design, point M is required to be located at a grid point (blue circle) on the grid that is uniform and defined over the region ?1.2 m ? x ? 1.2 m, 0.5 m ? y ? 1.5 m with the elements being squares of side length?x=?y=0.1m. LetF1??andF2??be the internal force vector in MA and MB, respectively. Your tasks are to find possible grid points for particle M to be suspended, and which grid points the ropes can have a minimum diameter. It is noted that one can adapt the lengths of the ropes to new locations of point M, the ropes are soft (i.e. subjected to only tensile forces), and the lower the internal force magnitude the smaller the diameter of the rope will be.

2 A 1.8 1.6 1.4 1.2 1 F 1 0.8 M 0.6 0.4 Y W 0.2 0 -1 0.5 0 0.5 Figure 2: Free body diagram.