Question:

Four bricks are to be stacked at the edge of a table, each brick overhanging the one below it, so that the top brick extends as far as possible beyond the edge of the table.

- To achieve this, show that successive bricks must extend no more than (starting at the top) $\dfrac{1}{2}$, $\dfrac{1}{4}$, $\dfrac{1}{6}$, and $\dfrac{1}{8}$ of their length beyond the one below (Fig. 9–75a).
- Is the top brick completely beyond the base?
- Determine a general formula for the maximum total distance spanned by $n$ bricks if they are to remain stable.
- A builder wants to construct a corbeled arch (Fig. 9–75b) based on the principle of stability discussed in (a) and (c) above. What minimum number of bricks, each 0.30 m long and uniform, is needed if the arch is to span 1.0 m?

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer:

- see video
- yes, the top brick is completely beyond the edge of the table
- $x = l\sum_{i=1}^{n}\dfrac{1}{2i}$
- 35 bricks (see the spreadsheet in the video for the numerical solution and explanation)

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