A wolf of mass is imagined scaled up by a factor of in every linear dimension
PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body
Life at Thermal Energy, Ch Bones, muscles, blood and body size
Problem
A wolf of mass M=40kg is imagined scaled up by a factor of 2.5 in every linear dimension, keeping its shape and posture exactly the same (this is a hypothetical exercise in geometric similarity; the chapter explains that real large mammals do not scale this way). Recall that muscle force scales with the muscle's cross-sectional area and body weight scales with body volume, and that the basal metabolic rate of a mammal of mass M (in kg) follows Kleiber's law, Bmet=3.4M0.75W.
((a)) Find the mass of the scaled-up animal.
((b)) By what factor does the scaled-up animal's strength-to-weight ratio change relative to the original wolf's?
((c)) Find the basal metabolic power and the power per kilogram of each animal.
((d)) By what factor does the power per kilogram fall between the two animals? State whether this factor is the same as the one found in part (b), and explain in one sentence why the two need not agree.