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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.

  1. 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).
  2. Is the top brick completely beyond the base?
  3. Determine a general formula for the maximum total distance spanned by $n$ bricks if they are to remain stable.
  4. 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?
Problem 39. (a)
Problem 39. (b)

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

Quick Answer: 
  1. see video
  2. yes, the top brick is completely beyond the edge of the table
  3. $x = l\sum_{i=1}^{n}\dfrac{1}{2i}$
  4. 35 bricks (see the spreadsheet in the video for the numerical solution and explanation)

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Giancoli 7th Edition, Chapter 9, Problem 39

(11:52)

Chapter 9, Problem 39 is solved.

View sample solution