Characteristic ripples that form in rubber bands just after they are launched into the air have been studied in detail by two physicists in the US.
Alexandros Oratis and James Bird at Boston University used a high-speed camera to reveal for the first time how stretched rubber bands develop longitudinal waves when released. The duo then used their observations to model the dynamics of the launching process and simulate it on a computer.
Many of us are familiar with the satisfying experience of stretching one end of a rubber band away from the thumb and then releasing it. The thumb seems to automatically move out of the way as the band shoots out into the air. This takes place over about 10 ms and so the dynamics that govern the band’s release – and the mechanism that causes the thumb to get out of the way – was a bit of a mystery.
Early on in their study, Oratis and Bird recognized that a retracting rubber band differed from the well-studied case of a single elastic strip being stretched and released. Unlike a simple strip, they reasoned, a rubber band adopts a straight-sided teardrop shape when stretched away from the thumb. This means that both ends of a stretched rubber band are highly curved immediately after release, and this must be included in any model describing the band’s subsequent behaviour.
Forward propagation
The high-speed camera images reveal that immediately after a band is released, a longitudinal stress wave begins to develop at its rear – something that had not been predicted by previous theoretical models. This wave then propagates forward at a well-defined speed – which is faster than the speed of band itself. Furthermore, the wavelength of the wave increases over time.
Rolling rubber bands stretch students
The videos also reveal how the shooter’s thumb avoids being hit by the band. As the band is stretched, the tension in the elastic is counteracted by the thumb pushing forward. Upon release, the thumb rotates forward and out of the path of the rubber band.
Oratis and Bird used their observations to construct wave equations for the ripples. Their model included stretching and inertia as well as the thickness and curvature of the band. The equations were used in numerical simulations that accurately reproduced the precise dynamics of retracting rubber bands for the first time.
The duo believes their findings can now better explain the dynamics underlying a wide variety of systems from from slingshot rides at amusement parks, to nanometre-scale molecular slingshots used for drug delivery.
The research is described in Physical Review Letters.
