# balancing a weight on a table without tipping over

I have a statics problem.

Here is a model for a table:

• a circle of radius 1.5 ft
• a pole in the center
• a base in the shape of an X.

I place a weight on the table on the edge. How much weight can the table support before it tips over?

This is from an actual thing I am trying to build. The point mass is in fact a coffee mug (with coffee in it), the flat disc is in fact 1 inches thick. The 3 feet long pole is made of steel (and it's not quite centered). And I'm concerned the table might tip over (so far it hasn't).

Any advice how to formulate this problem more accurately? Certainly, a point mass approximation loses information. I'll try to have a picture later.

This problem should depend on a few parameters, the size of the $\times$ and the radius $R$ of the table, and the height $h$ of the table, the mass $m$ of the mug (could be very heavy $\gg 100kg$ or something absurd) and the location $r < R$ of the mug.

I'm very interested in the stability condition. This table is quite stable as long as the coffee mug is light or the $\times$ is large or maybe even if the pole is heavy...

• The combined center of mass needs to be within the supports of the base. – ja72 May 1 '18 at 15:28