Abstract
A popular classroom demonstration is revisited in which a light ball and a much larger heavier ball are vertically aligned and dropped together onto a hard surface. Careful experimental data obtained using a highspeed camera is compared to a lumpedmass Newtonian restitution model. Good macroscopic agreement is found, provided there is sufficient separation between the two balls as they are dropped. An alternative continuum model based on elastic membrane theory is developed to explain the limit in which the balls are initially touching. 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. A favourable comparison with experimental data is found for the case of negligible initial separation between the balls.
Original language  English 

Article number  20150286 
Pages (fromto)  120 
Number of pages  20 
Journal  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 
Volume  471 
Issue number  2179 
DOIs  
Publication status  Published  8 Jul 2015 
Bibliographical note
Date of Acceptance: 22/05/2015Keywords
 Coefficient of restitution
 Contact problems
 Elastic wave
 Impact
 Membrane theory
 Multiball collision
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Profiles

Professor Alan R Champneys
 Department of Engineering Mathematics  Professor of Applied Nonlinear Mathematics
 Cabot Institute for the Environment
 Applied Nonlinear Mathematics
 Systems Centre
Person: Academic , Member