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.

There are multiple solutions.  The first solution is to bend the arms in a straight line from the pivot point (either above or below the plane, although below is more stable) so that the circles corresponding to each end point are aligned in the form of a cylinder.  If the arms of the Y are spaced at 120 degrees, the configuration will look like an equilateral triangle when viewed from above, and the system will be in equilibrium. when the weights are added.

2) Second solution: Bend the frame of the Y corresponding to the green and red circle 90 degrees downward at the distance corresponding to the blue circle.  Now all the weights are at different heights, but all equidistant from the central axis, and the system is in equilibrium.

3) There is a third solution where the weights are placed so that they can slide along weightless strings connected to two ends of the Y frame.  The weights can then be shifted along the strings toward the smaller arm so that most of the weight is on the short arm of the Y and the system is in equilibrium.  Notice that the problem does not say that the weights must be suspended from only one end of the Y.  In this case each weight is suspended from two ends of the Y.

Posted by Tony on 2009-12-27 04:00:42