A uniform rectangular block of length 29.0 cm is placed so that its centre of mass is a distance of 2.0 cm away from the edge of the table. Since its centre of mass is still over the table (i.e....

A uniform rectangular block of length 29.0 cm is placed so that its centre of mass is a distance of 2.0 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.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Initially, a uniform rectangular block of length 29.0 cm is placed so that its center of mass lies on the table and is 2.0 cm away from the edge of the table. A second block identical to the first is placed on top of it but its center of mass is past the edge of the table. The two blocks are in a stable position until their combined center of mass lies on the table.

Using the coordinate axis specified in the problem, if the second block's center of mass is a distance D past the edge of the table, stability is maintained till (D - 2)/2 = 0 or D = 2. For the two blocks to remain stable, the second block can only be shifted past the edge of the table till the maximum distance of its center of mass is 2 cm past the edge.

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