"See saw" balance/instability
"See saw" balance/instability
(OP)
Can someone help me with an explanation to a semmingly simple balancing problem. I would like to have some show me why a balance (or say a see-saw) returns to its equilibrium point mathematically speaking.
If you draw a simple diagram of a see-saw with the fulcrum at the center and two equal weights at equal distance from the fulcrum BUT the see-saw is not horizontal in the starting position, what torque imbalance is causing the see-saw to return to its balanced position? If you do the sum of the torques about the center fulcrum, the force vectors times the distance to the fulcrum, pointing downward, cancel eachother, don't they? So why wouldn't the balance just stay in the "out-of-horizontal" position. My reference x and y are each pointing horizontally to the right and vertically upward respectively.
How do you prove MATHEMATICALLY that the see-saw is NOT in equilibrium when initially positioned as described above?
Thanks for any help.
If you draw a simple diagram of a see-saw with the fulcrum at the center and two equal weights at equal distance from the fulcrum BUT the see-saw is not horizontal in the starting position, what torque imbalance is causing the see-saw to return to its balanced position? If you do the sum of the torques about the center fulcrum, the force vectors times the distance to the fulcrum, pointing downward, cancel eachother, don't they? So why wouldn't the balance just stay in the "out-of-horizontal" position. My reference x and y are each pointing horizontally to the right and vertically upward respectively.
How do you prove MATHEMATICALLY that the see-saw is NOT in equilibrium when initially positioned as described above?
Thanks for any help.





RE: "See saw" balance/instability
RE: "See saw" balance/instability
RE: "See saw" balance/instability
RE: "See saw" balance/instability
RE: "See saw" balance/instability
The balance would stay in the "out-of-horizontal" position only if the point it is hanging from and the center of gravity are the same.
RE: "See saw" balance/instability
RE: "See saw" balance/instability
SAP
RE: "See saw" balance/instability
Picture an empty seesaw with constant cross section and weight per foot. If the fulcrum is positioned AT the centroid of the cross section, midway along the seesaw, the seesaw will theoretically be in equillibrium in any position. If it is slightly below or above the centroid, the moment arms change slightly with rotation.
Then again, most of the seesaws I ever played on weren't that well balanced.
RE: "See saw" balance/instability
Always return to equilibrium (level);
0
IIIIIIIIIIIIIIIIIII
Will stabilise anywhere;
IIIIIIIII0IIIIIIIII
Where 'O' is the fulcrum.
Correct?
Speedy
RE: "See saw" balance/instability
Hope this helps......
Ralph
RE: "See saw" balance/instability
RE: "See saw" balance/instability
Reguards, consider the inertial point at the fulcrum.