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6.055J / 2.038J The Art of Approximation in Science and Engineering
Spring 2008
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View Full Document Chapter 4
Proportional reasoning
4.1 Animal jump heights
We next proportional reasoning to understand how high animals jump, as a function of
their size. Do kangaroos jump higher than ﬂeas? We study a jump from standing (or
from rest, for animals that do not stand); a running jump depends on different physics.
This problem looks underspeciﬁed. The height depends on how much muscle an animal
has, how efﬁcient the muscles are, what the animal’s shape is, and much else. The ﬁrst
subsection introduces a simple model of jumping, and the second reﬁnes the model to
consider physical effects neglected in the crude approximations.
4.1.1
Simple model
We want to determine only how jump height varies with body mass. Even this problem
looks difﬁcult; the height still depends on muscle efﬁciency, and so on. Let’s see how far
we get by just plowing along, and using symbols for the unknown quantities. Maybe all
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This note was uploaded on 02/24/2012 for the course MECHANICAL 6.055J taught by Professor Sanjoymahajan during the Spring '08 term at MIT.
 Spring '08
 SanjoyMahajan

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