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I'm doing an experiment that requires me to balance a ring, tied to four strings, in the middle of a force table; in other words, the objective is to set the ring at equilibrium. Each string is mounted on a pulley, with different mass hanging off of them. Tension and friction are really the only forces acting on this set up.

I've reached the configuration where the ring is very reasonably in equilibrium, but it's just slightly "out of focus". But I've also noticed that sometimes, when the ring is very noticeably not in equilibrium, ie. it's wildly far away from the center of the force table, the ring will still remain stationary, as if it's at equilibrium.

My personal guesses is that it has something to do with static friction (I'm not familiar with static friction, this is just a blind stab at it) or each strings also exerting some horizontal force in the groove of their pulleys, in addition to vertical tension they're pulling the ring from the hanging mass. Or maybe the x/y components cancels out, and the remaining components is not enough to overcome friction to continue pulling the ring, or it's just to small altogether to do anything.

I'm also thinking that since my configuration is just slightly out of center, whatever is making the way out of center configuration stationary also affects my configuration, but to a much smaller and negligible degree.

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If the ring is stable it is in equilibrium even if it is not in the center of your force table. In that case, while the forces will be given by the $mg$ values, the angles that you are reading are not the actual vector angles. The ring will move so that the forces balance out. The angles you read on the edge of the table are correct only if the ring is centered.

One reason that the ring might be slightly off center is you may have neglected to include the mass of the hanger that you attach the mass to. If you have a decent quality setup, the static friction is usually not a factor. When I do this experiment I push the ring away from center to make sure it comes back just to be sure some static friction isn't holding it. If it doesn't center after disturbing it, the masses or the angles are wrong.

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  • $\begingroup$ Can you please elaborate on why "the angles that you are reading are not the actual vector angles"? $\endgroup$ – L to the V Mar 24 '15 at 2:44
  • $\begingroup$ The typical force table has angle markings around the edge. Those show the angle between a conceptual line segment which starts at the center and extend to the $0^o$ and the line segment starting at the center and going to the angle you are reading. The angle reading depends on the string actually going to the center. Say a string is on a pulley at the $75^o$ mark but the string doesn't go toward the center; the angle of that vector is NOT $75^o$. $\endgroup$ – Bill N Mar 24 '15 at 4:48

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