The two-ball bounce problem

Y. Berdeni, A. Champneys*, R. Szalai

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)
334 Downloads (Pure)


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 high-speed camera is compared to a lumped-mass 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 languageEnglish
Article number20150286
Pages (from-to)1-20
Number of pages20
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2179
Publication statusPublished - 8 Jul 2015

Bibliographical note

Date of Acceptance: 22/05/2015


  • Coefficient of restitution
  • Contact problems
  • Elastic wave
  • Impact
  • Membrane theory
  • Multi-ball collision


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