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.
REFERENCES
1.
James
Stewart
, Calculus: Early Transcendentals
, 5th ed. (Brooks/Cole
, Pacific Grove, CA, 2003
).2.
Eric
Weisstein
, http://mathworld.wolfram.com/BookStackingProblem.html.3.
Paul B.
Johnson
, “Leaning tower of lire
,” Am. J. Phys.
23
(4
), 240
(1955
).4.
Leonard
Eisner
, “Leaning tower of the physics reviews
,” Am. J. Phys.
27
(2
), 121
(1959
).5.
6.
Arthur P.
Boresi
and Richard J.
Schmidt
, Engineering Mechanics: Statics
(Brooks/Cole
, Pacific Grove, CA, 2001
), p. 190
.7.
David J.
McGill
and Wilton W.
King
, Engineering Mechanics: Statics
, 2nd ed. (PWS-Kent
, Boston, 1989
), p. 215
.8.
George W.
Housner
and Donald E.
Hudson
, Applied Mechanics: Statics
, 2nd ed. (D. Van Nostrand
, New York, 1961
), pp. 78
–79
.9.
I. V.
Meshchersky
, Sbornik Zadach po Teoreticheskoi Mekhanike (A Collection of Problems in Theoretical Mechanics)
(Dover
, New York, 1965
).10.
Henry C.K.
Plummer
, The Principles of Mechanics: An Elementary Course
(G. Bell
, London, 1929
), p. 187
.11.
George M.
Minchin
, A Treatise on Statics: with Applications to Physics
, 6th ed. (Clarendon
, Oxford, 1907
), Vol. 1
, p. 341
.12.
William
Walton
, A Collection of Problems in Illustration of the Principles of Theoretical Mechanics
2nd ed. (Deighton, Bell
, Cambridge, 1855
), p. 183
.13.
© 2005 American Association of Physics Teachers.
2005
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
