Modern physics can get complicated. Sure, researchers know exactly what forces act on a ball rolling down an incline—an experiment that helped Galileo develop universal laws for movement and acceleration. But what happens when a deformable shape like a rubber band rolls around? A new study reveals that the faster it goes, the more squashed it gets.
Understanding how pliable materials interact with the world around them can help scientists predict all sorts of interesting phenomena, from how volcano lava might flow on Mars to the speediest shape for an airplane's inflatable emergency-exit slide. Physicists have studied rolling liquid drops and how fixed objects move on deformable surfaces, but no one had studied how a deformable "elastic" object—"elastic" because it regains its shape after a force deforms it—rolls on a fixed surface.
So researchers at the Massachusetts Institute of Technology in Cambridge and École Polytechnique in Paris turned to a common elastic object, the rubber band, which they made by molding circular polymer loops of vinyl polysiloxane. But the team couldn't just roll the rubber band down an incline like Galileo did with his bronze ball. "It would have taken several meters to get the loops rolling fast enough to deform, and that was larger than the size of our room," says co-author Cristophe Clanet, a physicist at École Polytechnique. "So we replaced the incline with a rotating drum."
Like a hamster in its wheel, the researchers placed the rubber band loops at the bottom of a drum and set it spinning. At lower speeds, the circular bands squashed into a long oval; at higher speeds, the top collapsed so that its center nearly touched the bottom. (The team couldn't study what happened when the two sides touched: The friction of the two sides moving in different directions sent the rubber bands flying out of the drum.)
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Next, the researchers modeled what they'd seen. They combined equations for the effects of gravity, bending forces, centrifugal forces, and internal stiffness to explain the loop's movement. Initially, the rubber band's natural stiffness balances with gravity to keep it in shape. As the rolling begins, gravity works to help the loop keep its shape. But at higher speeds of rotation, the other forces overwhelm gravity, and the loop begins to collapse.
Harvard University mathematician Lakshminarayanan Mahadevan, who studies the motions and deformation of objects, is a fan of the study. He says the model, described in a paper published this month in Physical Review Letters, will help scientists make predictions about the movement of other elastic materials.
As far as the potential applications, Clanet waxes futuristic. "I can imagine [designing] a car. The faster it goes, the more it deforms and the less friction it has with surrounding air, so it can go even faster. It would be a fantastic car."