A uniform rectangular block of length 37.0 cm is placed so that its ce

[cmkc109]

Homework Statement

A uniform rectangular block of length 37.0 cm is placed so that its centre of mass is a distance of 1.50 cm away from the edge of the table. Since its centre of mass is still over the table (i.e. not sticking out past the edge), the block is stable. An identical block is placed on top of that block. How far from the edge of the table can the centre of mass of the top block be before the blocks become unstable? Take the edge of the table to be the origin of your coordinate system, with negative values representing positions that are over the table, and positive values representing positions that are past the edge.

Homework Equations

no eqns

The Attempt at a Solution

so i know the answer is 1.5cm.
Does it mean no matter how many blocks i put on top, the center of mass is still at 1.50cm?

 

[Tiroth]

Just imagine doing the experiment yourself. If the blocks are uniform, then their individual centers of mass are right in the middle of the block. So, your first block is balanced with 20 cm on the table, 17 cm off the table. If you put another block on top, it can extend up to 20 cm off the table, putting the combined CoM right at the edge. You couldn't put another block directly on the second, because then there would be an extra 1.5 cm of block hanging over the edge, and it would tip. You could match a third block to the first, because then the extra 1.5 cm would be over the table.

The original block's CoM is at -1.5 cm. The second block is at +1.5cm. They balance each other out.

 

[CWatters]

Diagram helps (not to scale). When it's just about to tip over the torques about the edge of the table sum to zero.