How can a given number of rigid, rectangular blocks be stacked in a planar arrangement to produce the maximum overhang over a support edge? To answer this question, three cases of increasing complexity are considered: single-wide stacks, multiwide stacks that do not rely on friction, and multiwide stacks that do rely on friction. The solution to the first case has existed for more than 150 years; the answer to the second case is attempted in this paper; and the considerable complexity of the third is demonstrated. Many mathematical aspects of block stacking are discussed, and a new challenge is posed. The analysis uses the principles of static equilibrium and stability and free body diagrams, key concepts in classical mechanics.
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PAPERS| December 01 2005
Fun with stacking blocks
John F. Hall; Fun with stacking blocks. Am. J. Phys. 1 December 2005; 73 (12): 1107–1116. https://doi.org/10.1119/1.2074007
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