The legs of an elephant are much thicker in proportion to its body than the legs of a mouse. This is due to the "square-cube" law. The mass of an animal is (roughly) proportional to the cube of its height, while the strength of a limb is proportional to the square or the animal's height. So if an animal doubles in height, its mass will be 8 times greater than it was, but its strength will only be 4 times greater than it was, assuming the limbs maintain their original proportions. This can be represented using 2 the relations = where s is the strength factor (or thickness factor) required for the limbs, 1 is the original height, and h is the new height. Both k1 and h, are measured in units of length, so the ratio is a number without any units, as is s. a) A giant ape in a science fiction movie has 10 times the height of the 2 m tall gorilla from which it is modelled. To comply with the square-cube law, how much thicker must the legs be, compared with the gorilla's? b) A brachiosaur was typically 15.2 m in height. Its build resembled that of several small lizards that are alive today and that grow to a height of about 50 cm. Predict how the relative thickness of the brachiosaur's legs compares with the thickness of the lizard's legs.
The legs of an elephant are much thicker in proportion to its body than the legs of a mouse. This is due to the "square-cube" law. The mass of an animal is (roughly) proportional to the cube of its height, while the strength of a limb is proportional to the square or the animal's height. So if an animal doubles in height, its mass will be 8 times greater than it was, but its strength will only be 4 times greater than it was, assuming the limbs maintain their original proportions. This can be represented using 2 the relations = where s is the strength factor (or thickness factor) required for the limbs, 1 is the original height, and h is the new height. Both k1 and h, are measured in units of length, so the ratio is a number without any units, as is s. a) A giant ape in a science fiction movie has 10 times the height of the 2 m tall gorilla from which it is modelled. To comply with the square-cube law, how much thicker must the legs be, compared with the gorilla's? b) A brachiosaur was typically 15.2 m in height. Its build resembled that of several small lizards that are alive today and that grow to a height of about 50 cm. Predict how the relative thickness of the brachiosaur's legs compares with the thickness of the lizard's legs.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter14: Sequences And Mathematical Induction
Section14.3: Another Look At Problem Solving
Problem 29PS
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Transcribed Image Text:The legs of an elephant are much thicker in proportion to its body than the legs of a
mouse. This is due to the "square-cube" law. The mass of an animal is (roughly)
proportional to the cube of its height, while the strength of a limb is proportional to
the square or the animal's height. So if an animal doubles in height, its mass will be 8
times greater than it was, but its strength will only be 4 times greater than it was,
assuming the limbs maintain their original proportions. This can be represented using
(A)
the relation s =
where s is the strength factor (or thickness factor) required for
the limbs, k1 is the original height, and h is the new height. Both k1 and are
measured in units of length, so the ratio is a number without any units, as is s.
a) A giant ape in a science fiction movie has 10 times the height of the 2 m tall gorilla
from which it is modelled. To comply with the square-cube law, how much thicker
must the legs be, compared with the gorilla's?
b) A brachiosaur was typically 15.2 m in height. Its build resembled that of several
small lizards that are alive today and that grow to a height of about 50 cm. Predict
how the relative thickness of the brachiosaur's legs compares with the thickness of
the lizard's legs.
M|N
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