Five identical wood blocks of sides L and thickness H are shifted in one direction to form a leaning tower of the maximum protrusion. How should you stack the blocks to achieve the maximum protrusion? What is the maximum protrusion? What if you had an infinite number of blocks?(adsbygoogle = window.adsbygoogle || []).push({});

For any block the center of mass of the blocks above it must be to the left of the block's right edge. So suppose we have n blocks. Consider the ith block. There are n-i blocks above the ith block. If we denote the protrusion of each block from the right edge of the ith block as x_{j}, then the center of mass of the blocks above the ith block is the sum of all these x_{j}, call it X, since each block has the same mass. We want X = L/2. Since we have no negative protrusions, the maximum protrusion is then L/2. It doesn't matter how they are stacked. This is true even if we have an infinite number of blocks.

Is this right?

BTW, how can I express the fact the CM must be to the left of the right edge using physics? Intuitively I know this is right.

See if I consider torques I can't come up with this result because I don't know where the normal force acts or how great it is. Any suggestions?

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# How should you stack the blocks to achieve the maximum protrusion?

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