Consider geometrically similar animals of different linear size, L. Assume that the distance an animal can jump, H, is a function of L, the average density ρ, the average muscle stress σ (that is, muscle force over leg cross-sectional area), and the gravitational constant g. (a) Find a nondimensional functional expression for H. (b) In Swift’s Gulliver’s Travels, the Lilliputians were a race of very small people, tiny compared to Gulliver’s size. If the Lilliputians had the same ρ and σ as Gulliver, what conclusions can you draw on dimensional grounds? Would they jump higher than Gulliver? The same height as Gulliver? Lower than Gulliver?
Consider geometrically similar animals of different linear size, L. Assume that the distance an animal can jump, H, is a function of L, the average density ρ, the average muscle stress σ (that is, muscle force over leg cross-sectional area), and the gravitational constant g. (a) Find a nondimensional functional expression for H. (b) In Swift’s Gulliver’s Travels, the Lilliputians were a race of very small people, tiny compared to Gulliver’s size. If the Lilliputians had the same ρ and σ as Gulliver, what conclusions can you draw on dimensional grounds? Would they jump higher than Gulliver? The same height as Gulliver? Lower than Gulliver?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Consider geometrically similar animals of different linear size, L. Assume that the distance an animal can jump, H, is a function of L, the average density ρ, the average muscle stress σ (that is, muscle force over leg cross-sectional area), and the gravitational constant g.
(a) Find a nondimensional functional expression for H.
(b) In Swift’s Gulliver’s Travels, the Lilliputians were a race of very small people, tiny compared to Gulliver’s size. If the Lilliputians had the same ρ and σ as Gulliver, what conclusions can you draw on dimensional grounds? Would they jump higher than Gulliver? The same height as Gulliver? Lower than Gulliver?
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