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Backpack Weight and the Scaling of the Human Frame
2. H. David Sheets and James. C. Lauffenburger, “Looking for scaling laws, or physics with nuts and shells,” Phys. Teach. 37, 376–378 (Sept. 1999).
5. David A. Winter, Biomechanics and Motor Control of Human Movement, 4th ed. (Wiley, New York, 2009), see Table 4.1.
7.The quantity L is any linear dimension of the hiker and could for example be the height.
8. Irving P. Herman, Physics of the Human Body (Springer-Verlag, Berlin, 2007), see Table 1.13 and references therein.
9. R. J. Maughan, J. S. Watson, and J. Weir, “Strength and cross-sectional area of human skeletal muscle,” J. Physiol. 338, 37–49 (1983).
10.We have assumed that when the human frame is scaled up, muscle and bone are scaled up by the same linear dimensions as the human frame. Evidence that this is approximately true comes from the fact that (muscle mass)∝(body mass)1.0 and (skeletal mass) ∝ (bodymass)1.08, with both exponents being close to or equal to 1.0. See Ref. 8, Table 1.13.
11.A note on notation: the largest backpack weight for a particular weight is denoted by . The maximum value of as a function of is denoted by .
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Modeling real-life situations is an important part of introductory physics. Here we consider the question “What is the largest weight of backpack a hiker can manage?” A quick perusal of the Internet suggests that as the weight of a healthy adult increases, the largest backpack weight also increases and should be about 25–30% of a person's body weight for a reasonably fit adult.1 We show here that a careful modeling of the hiker and backpack leads to a somewhat different result, with hikers of sufficiently large (but otherwise healthy) weight not being able to carry as much backpack weight as hikers of smaller weight.
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