# Why can an object not be pulled beyond the polygon which is forming from the attachment points?

I am looking for the physical equations that explains why a 2D object on a 2D surface, e.g. a rectangle cannot be pulled further than the greatest/smallest x/y coordinates of the points it is attached to. This becomes particularly obvious if the points are not placed on a rectangle but form an irregular polygon. The ropes can be shortened and lengthen without any limitation.

As my sketch indicates, I assume that the X and Y components of the forces acting through the ropes have to be looked at. I also know that in the first sketch, with equal forces acting on all ropes I have an equilibrium state that I would like my system to be in. I also assume that the y component in the second scetch does not simply disappear but what happens to it? Does it become indefinitely large or small?

Can someone help me to structure this problem, I am struggling to put it into the relevant physical context. Thanks so much.

EDIT: In the case of irregularly arranged anchoring points:

1. Would it be possible to reach an equilibrium state with the rectangle still being axis aligned but at the same y-height as the top left anchoring point?
2. What causes the shape to rotate if the forces are not balanced and is this caused by the momentum induced by a lever?
3. What is that lever?

• Where should the force come from that pulls the shape above the upper pivots? Jun 19, 2018 at 19:42
• Simple as that? Would the system still be in a state of equilibrium in the second sketch? Jun 19, 2018 at 19:44
• Is there an external force pulling this polygon, or is it just being pulled by these ropes? If it's just the ropes, then the right half of your first diagram is not in equilibrium. Jun 19, 2018 at 20:01
• That is what I assumed. No there is no force acting other than the force acting through the ropes. Jun 19, 2018 at 20:13