Chapter 9.1, Problem 38E

LIFE SCIENCE APPLICATIONS

Dinosaur Running An article entitled “How Dinosaurs Ran” explains that the locomotion of different sized animals can be compared when they have the same Froude number, defined as

$F=\frac{v^2}{gl}$,

where $v$ is the velocity, $g$ is the acceleration of gravity $\left(9.81\text{m}\text{per}{\text{sec}}^{\text{2}}\right)$, and $l$ is the leg length (in meters). Source: Scientific American.

a. One result described in the article is that different animals change from a trot to a gallop at the same Froude number, roughly $2.56$. Find the velocity at which this change occurs for a ferret, with a leg length of $0.09\text{m}$, and a rhinoceros, with a leg length of $1.2\text{m}$.

b. Ancient footprints in Texas of a sauropod, a large herbivorous dinosaur, are roughly $1\text{m}$ in diameter, corresponding to a leg length of roughly $4\text{m}$. By comparing the stride divided by the leg length with that of various modern creatures, it can be determined that the Froude number for these dinosaurs is roughly $0.025$. How fast were the sauropods traveling?

c.

d.