Measurement of the Coefficient of Restitution and Energy Loss in the Collision of Spherical Objects with a Fixed Surface

Document Type : Original Article

Authors
Abbasian Motlagh Mohammad
Hasan Tashakori
Department of Physics, Qo. C., Islamic Azad University, Qom, Iran
10.22034/jmrph.2026.137631.1001
Abstract
The coefficient of restitution is one of the most important parameters in collision mechanics and plays a significant role in the analysis of elastic and inelastic impacts, dynamic system modeling, and engineering design. In this study, a method for measuring the coefficient of restitution and the energy dissipated from the collision of spherical bodies with a fixed surface, and its relationship with the impact angle, was experimentally investigated. First, the relations among these quantities and the measurable quantities were derived from the conservation laws and the equations of motion and collision; then, by designing an experiment, a single steel spherical ball (a chrome-steel bearing, 1 cm radius, 7.8 g mass) was released from a fixed height and made to collide, at impact angles of 10–65°, with two steel surfaces of different alloy composition, and the coefficient of restitution and the percentage of dissipated energy were calculated for both surfaces. The results showed that, besides the materials’ mechanical properties, the coefficient of restitution depends on the contact conditions and the impact angle, and a lower coefficient of restitution corresponds to greater energy dissipation. The experimental trends of the coefficient of restitution and the dissipated energy with impact angle are reported together with their measurement uncertainties. The proposed approach provides a simple and effective experimental framework for evaluating collision behavior and can be applied in impact mechanics, shock absorption systems, rigid-body dynamics, and undergraduate physics laboratories.
Keywords
Coefficient of Restitution
Collision Mechanics
Energy Dissipation
Spherical Bodies
Experimental Physics
[1] R. Garwin, "Kinematics of an ultraelastic rough ball," American Journal of Physics, vol. 37, pp. 88–92, 1969.
[2] W. Benson and W. Bauer, "Frame grabbing techniques in undergraduate physics education," American Journal of Physics, vol. 61, pp. 848–851, 1993.
[3] P. A. Maurone and F. J. Wunderlich, "Bouncing ball experiment," American Journal of Physics, vol. 46, pp. 413–415, 1978.
[4] R. Cross, "The bounce of a ball," American Journal of Physics, vol. 67, pp. 222–227, 1999.
[5] H. Brody, "That’s how the ball bounces," The Physics Teacher, vol. 22, pp. 494–497, 1984.
[6] R. Cross, "The coefficient of restitution for collision of happy balls, unhappy balls, and tennis balls," American Journal of Physics, vol. 68, pp. 1025–1031, 2000.
[7] R. Cross, "Measurements of the horizontal coefficient of restitution for a superball and a tennis ball," American Journal of Physics, vol. 70, pp. 482–489, 2002.
[8] G. Barnes, "Study of collision," American Journal of Physics, vol. 26, pp. 5–12, 1957.
[9] M. Hubbard and W. Stronge, "Bounce of hollow balls on a flat surface," Sports Engineering, vol. 4, pp. 49–61, 2001.
[10] W. Stronge and A. Ashcroft, "Oblique impact of inflated balls at large deflection," International Journal of Impact Engineering, vol. 34, pp. 1003–1019, 2007.
[11] S. Knoche and J. Kierfeld, "Buckling of spherical capsules," Physical Review E, vol. 84, 046608, pp. 1–13, 2011.
[12] Adli Haron and K. A. Ismail, "Coefficient of restitution of sports balls: A normal drop test," IOP Conference Series: Materials Science and Engineering, vol. 36, 012038, 2012.
[13] R. Cross, "Impact behavior of hollow balls," American Journal of Physics, vol. 82, pp. 189–195, 2014.
[14] R. Cross, "Impact behavior of a superball," American Journal of Physics, vol. 83, pp. 238–248, 2015.
[15] J. R. Kensrud, A. M. Nathan, and L. V. Smith, "Oblique collision of baseballs and softballs with a bat," American Journal of Physics, vol. 85, pp. 503–509, 2017.
[16] R. Cross, "Measuring coefficients of restitution with a piezo disk," Physics Education, vol. 55, 035008, 2020.
[17] G. R. Fowles, Analytical Mechanics 4th ed., CBS International Editions, 1987.
[18] D. W. Preston and E. R. Dietz, The Art of Experimental Physics, John Wiley & Sons, 1991.
Journal Of Modern Research Physics
Volume 11, Issue 1 - Serial Number 20
September 2026
Pages 32-41