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If you have a board, say a standard 2x4 of finite length, where one end is fixed in a cement wall and the other end is free, and you begin adding weight to the free end until it breaks, where will the board break? Assume the board is made of typical wood and it is perpendicular to the wall in which it's affixed.

I was asked this question over 20 years ago in a job interview and I never knew if I answered correctly.

I answered that I thought the board would break in the middle. I figured the force bending the free end would be countered by an opposite force from the other end and they'd meet in the middle. I also noted that I'd never seen a tree branch break at the trunk. They always seem to break near the middle.

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I think you can apply Euler Bernoulli beam theory. This means that the highest stress should take place closest to the wall.

Why a tree branch does not break there is because it gets thicker closer to the trunk spreading the load over more material.

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Interesting link and surely it contains the mathematical basis for an answer. I just wish my math skills were sufficient to tease the answer from it. At the time of the job interview it seemed that the obvious answer was that it would break at the wall but I went with the middle, assuming it was a trick question. It looks like I should have went with the intuitive answer after all. –  Johnsonium Jul 30 at 1:10

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