The two-ball bounce problem is popularly demonstrated to show that the laws of physics can have counterintuitive effects.
The problem is demonstrated by dropping a small ball with a larger one together. A tennis ball and a basketball are often used for the demonstration.
The tennis ball is positioned on top of the basketball and when the two are dropped together, the smaller ball bounces higher than expected, or up to several times higher than where it was originally dropped.
Now researchers from the University of Bristol revisited the classic physics demonstration and identified flaws in its explanation.
Although textbooks explain that the phenomenon demonstrates two basic laws of physics namely Isaac Newton's law of restitution and the law of conservation of momentum, the researchers, led by PhD student Yani Berdeni from the University of Bristol's Department of Engineering Mathematics, found that this explanation is flawed.
Based on traditional explanation, the bigger ball bounces off the floor and the smaller ball bounces off the rebounding ball. The researchers tested this explanation using a computer and a high-speed camera and determined that the assumed order of the balls' collision was wrong.
Unless there is sizable separation distance, the basketball remains in contact with the surface of the floor when it collides with the tennis ball and the order of collision is reversed.
The researchers found that the bigger ball acts like a trampoline. When it impacts the floor, the compression of the basketball rouses an elastic wave that hurls the smaller ball back into the air. The closer the two balls are together when they are dropped, the less impressive the bounce.
"An alternative continuum model based on elastic membrane theory is developed to explain the limit in which the balls are initially touching," the researchers wrote in their study, which was published in the Proceedings of the Royal Society A on June 24. "The model assumes the lower ball deforms to a truncated sphere upon its impact with the floor, exciting an elastic wave which subsequently launches the upper ball like a particle on a trampoline, before the lower ball leaves the ground.
The researchers said that having a better understanding of the behavior of spherical bodies during collision has implication when it comes to modeling granular materials because these can be considered as a collection of tiny spheres.