Calculate distribution of mass

[Mikey-D]

I asked a similar question a while back, but am still unclear on something.

If I have some arbitrary object (a box, for instance) with known centre of mass that is held up at four (or more) planar points, is it possible to calculate exactly what portion of the mass of the box is at each of the points?

I know it can be done with three points (using three equations: sum of forces, and both components of the sum of torques about an arbitrary point), but am unsure whether it is even possible with more than three points. Seems to me it must be possible to calculate, but my searching has turned up nothing thus far.

Can anyone point me in the right direction here??

Thanks a lot!

Edit: Assume zero elasticity in the supports and object.

 

[Cruikshank]

Try engineering. I think that is what they call an overdetermined system. The method of sections might help; essentially, cut the object at some point conceptually into two objects. Work out the equilibrium equations for each separately. I believe you need to know more than the center of mass position, which is just one summary term; I think you need the entire mass distribution. More details I do not have off the top of my head. Good luck.