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The MIT team made a variety of “ribbons” using polymers that have different degrees of flexibility. Image: Pascal Raux and Pedro Reis
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Galileo Galilei’s experiments on the
motions of falling and rolling objects, described in his 1638 book, Two New Sciences, are considered by many
to be the beginning of modern science. Now researchers at MIT have conducted a
variation on his experiments that has produced unexpected results.
Galileo used rigid materials—metal balls
and a wooden ramp—for his tests on how bodies move down an inclined plane.
Since then, a few tests have been done with solid balls rolling down a flexible
surface. But until recently, nobody had tried rolling flexible objects down a
solid plane. MIT professors Pedro Reis and John Bush, along with visiting
student Pascal Raux and visiting professor Christophe Clanet, have now carried
out experiments using a variety of flexible, hollow cylinders—essentially wide
rubber bands—with different degrees of elasticity, and have derived a set of
equations to describe the behavior of these “rolling ribbons.” The work was described in a paper published in the journal Physical Review Letters.
Flexible ribbons initially settle into
an oval shape because of gravity, and one might expect them to get rounder as
they roll due to centrifugal force. But the opposite occurs. The faster the
ribbons roll, the more they lose their circular shape, eventually assuming a
two-lobed “peanut” shape. At even higher speeds, the sagging middle droops so
far that it comes in contact with the bottom of the ribbon, causing friction
that makes the loop suddenly lurch backward. The researchers say the behavior
is the result of “a delicate coupling between rolling, bending and stretching.”
Though this was basic research, Reis
speculates that the resulting analysis might ultimately be useful for
applications as varied as predicting the motions of carbon nanotubes, the
behavior of drill casings in deep wells, and the way blood cells move through
veins and arteries. Bush, a professor of applied mathematics, explains that
“one of our goals is to better understand the role of flexibility in
locomotion.”
The research was prompted by a
suggestion from Clanet, who taught a course at MIT during a stint as a visiting
lecturer. He is a professor working at the Laboratory of Hydrodynamics at the
Ecole Polytechnique in Palaiseau, outside Paris.
Raux, a student visiting MIT from Paris,
was the lead author of the paper.
Why has it taken almost four centuries
for scientists to take this next step from Galileo’s work? Reis explains that
despite their apparent simplicity, the behavior of flexible structures is often
nonlinear—that is, it requires more complicated mathematical equations to
describe than that of simple rigid objects, and so the analysis wasn’t feasible
before the advent of computers. And in addition, only relatively recently has
it become easy to make objects out of flexible polymers with any desired degree
of elasticity and shape using modern fabrication tools.
In this case, team members had to create
the flexible cylinders from scratch—they employed a polymer that dentists use
to make casts—because commercially available versions, such as wide rubber
bands, do not have precise enough shapes with constant thickness.
Lakshminarayanan Mahedevan, a professor
of applied mathematics at Harvard
University, has published
research on a different variation of Galileo’s experiments but was not involved
in this work. Mahedevan says this basic research “has implications for how
surfaces in contact move relative to each other.” But what really matters, he
says, is the basic principles discovered in this way: “The particular
manifestation is less important than the general principles that underlie these
types of deformations.”
As with much basic research, the
ultimate usefulness of the work is hard to predict, although there are clear
examples of areas where such rolling behavior occurs. But for the researchers,
there was a real thrill in finding a way to extend work that has such a fabled
history. “One thing that made it really neat for us from the start was the
connection with Galileo, to take an experiment that has been a classic” and
extend it in a new direction, says Reis, the Esther and Harold E. Edgerton
Assistant Professor of Civil and Environmental Engineering and Mechanical
Engineering.
SOURCE
