Equilibrium of Forces on the Table

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Homework Statement


This is a simple research problem that I am dealing with. It would be better to explain it with a diagram. There are three weights attached to some strings and tied together in a knot. There is an obstacle on the table. What happens to the weights under the situation illustrated in the diagram. Assume that there is no friction.

Homework Equations


We can draw a FBD on the edge of the obstacle. There are forces by the weights and there is a reaction force by the obstacle.


The Attempt at a Solution


I think that because the weights on either side of the obstacle is equal to each other, and the gravity does not affect the forces, the weights will remain in equilibrium when the knot is at the edge of the obstacle. If we move the knot towards the hole of 2w, the knot will remain at the place where we move it. Because the forces will be equal to each other in opposite directions (2w = w + w). But if we move the knot towards the other two weights, the knot will come back to the edge of the obstacle since their combined weight will not be enough to keep the knot in its new location. Furthermore, in order to keep the knot at the edge, we may use a smaller weight than 2w on the left side of the obstacle, such as the combined x-axis forces of the other two weights. But we may see very tiny movements of the knot at the edge of the obstacle.
I guess I am just opening it for a discussion.
 

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