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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.

Scetch of Object, ropes and forces

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?

enter image description here

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  • $\begingroup$ Where should the force come from that pulls the shape above the upper pivots? $\endgroup$
    – Jasper
    Jun 19, 2018 at 19:42
  • $\begingroup$ Simple as that? Would the system still be in a state of equilibrium in the second sketch? $\endgroup$ Jun 19, 2018 at 19:44
  • $\begingroup$ 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. $\endgroup$ Jun 19, 2018 at 20:01
  • $\begingroup$ That is what I assumed. No there is no force acting other than the force acting through the ropes. $\endgroup$ Jun 19, 2018 at 20:13

1 Answer 1

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You have to distinguish carefully between ropes (black in your sketches) and forces. The red arrows in your sketches are not neccessarily forces because a long rope can be under no tension at all (no force acting on it), but in the right sketch, the downward red arrows suggest a large force acting downward. If such force was acting with no corresponding equal force acting upwards, the box would start moving.

In fact, in the right picture there must be no downward force at all because the upper ropes can't provide an upward force to create equilibrium.

You can indeed get the box beyond the pivots if you consider dynamic movement.

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  • $\begingroup$ That is indeed where I made a mistake, thank you. But, assuming the large force I depicted in the second picture was acting, there could be no reacting y-component of that force on the upper pivot points as pivot and fixture point on the object are at the same y-height, is that correct? Would that mean, that it is only possible - with infinitely increasing force - to approach the y-position of the pivot points without ever being able to reach the same height (as depicted)? $\endgroup$ Jun 19, 2018 at 20:08
  • $\begingroup$ Yes, if you don't assume dynamic motion, the box will always be strictly "within bounds". $\endgroup$
    – Jasper
    Jun 19, 2018 at 20:30

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