Three identical weights are to be suspended from the ends of a rigid light¹ "Y"-shaped frame. Each arm of the frame is to be of a different length.

How is this to be accomplished (ie, how do you shape the "Y") so that the 'system' is in equilibrium within a horizontal plane?

¹ "light" is meant as being weightless, having no concern for mass.
Note too, the colours are the radial ring extremeties of the "Y" arms within the horizontal plane.

In order for the system to "balance", the sum of lengths of the shortest two legs must be > the longest.  This is equivalent to forming a triangle, with the centroid of the triangle being at the connection point of the three legs of the "Y" .  For any such system, angles between the legs of the "Y" can be determined such the the net vertical forace and moment is at the vertex where the legs intersect.  There is also a degenerate case where the sum of the shorter legs = the length of the the longest.  This is the case where the shorter two legs are on top of each other and 180 degs around from the longer leg.  If this is what is intended, I'll let someone else supply the trig formulae

Posted by Kenny M on 2009-12-22 22:25:03