Bounce time of a ball against the ground measurement of variables using Tracker

International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Issue 5 2025 DOI: 10.5281/zenodo.17498692 1 Original Article Bounce time of a ball against the ground measurement of variables using Tracker Author 1 #1 , Author 2 #2 ,Author 3 #3 ..(Times New Roman, Font size:12 ,Bold ,Center aligned) #1 Address, Phone no. and email Id of Author 1(Times New Roman, Font size:12,Center ABSTRACT This article calculates the coefficient of friction using different formulas when balls made of different materials bounce on a ceramic floor and finds the energy loss in the collision with the ground. The experimental measurement of some variables is done using the Tracker program from a video of the experiment. The equations that allow us to obtain the time it takes for the balls to stop after colliding with the ground are verified with the value of the coefficient obtained, and the results are excellent. In addition, the calculation of the loss of potential energy from the bounces was also measured using the Phypox app. This practice can be used by students in their first years of mechanical physics. Key words: Coefficient of restitution, Phypox, Rebound, Time to stop, Tracker. Corresponding Author: Germán Melo M. International Journal of Research in Engineering & Science Available online on http://rspublication.com/IJRES/IJRE.html ISSN:(P) 2572-4274 (O) 2572-4304 Germán Melo M 1 , Susana Melo L 2 , Sebastián Gómez H 3 and Samuel Álzate Q 4 1 Distrito especial de ciencia, tecnología e innovación de Medellín. Colombia [email protected] 2 Universidad Nacional de Colombia. Medellín. Colombia [email protected] 3 Instituto Tecnológico Metropolitano ITM. Medellín. Colombia [email protected] 4 Institución Educativa Caracas. Medellín. Colombia [email protected] Cite This Paper: Germán Melo M, Susana Melo L, Sebastián Gómez H and Samuel Álzate Q (2025). "Bounce time of a ball against the ground measurement of variables using Tracker". INTERNATIONAL JOURNAL OF RESEARCH IN ENGINEERING & SCIENCE (IJRES) {ISSN- (PRINT) 2572-4274 (ONLINE) 2572-4304}, vol. 9, no. 6, 2025, pp. 1-6. DOI: https://dx.doi.org/10.5281/zenodo.17498692 International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Issue 5 2025 DOI: 10.5281/zenodo.17498692 2 Original Article INTRODUCTION Articles [1-3] analyze the coefficient of restitution in two-body collisions. This dimensionless quantity, which in a sense measures the elasticity of surfaces, is a dimensionless number between 0 and 1. Studying this factor is important in that it measures the loss of energy in a collision. In this work, two balls were recorded separately when they collided with the same surface, and the collision was analyzed using Tracker [4-5]. First, the value of the coefficient of restitution was determined, and then the time it took for the ball to stop against the surface was calculated and measured, obtaining a very acceptable percentage of error. It is hoped that this study will be useful to students of mechanical physics because it is an experiment that is easy to reproduce. THEORETICAL FRAMEWORK A ball dropped from an initial height ℎ will bounce repeatedly when it hits the ground, as illustrated in Figure 1. In this situation, an energy study can be carried out on the loss of energy (and height) from collision to collision until it comes to rest, because the collision is not perfectly elastic. Fig 1: Ball bouncing repeatedly on the floor, own creation. The coefficient of restitution  can be calculated using the formula [6]:             (1) If the ground is considered to be body 1, then [7]:           √      ⋯ (2) For a perfectly elastic collision 1 and for one that is perfectly inelastic 0, for the others 01. These rebounds have been vertical. If the ball is thrown in a parabolic motion, the coefficient can be calculated as [8]:      (3) International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Issue 5 2025 DOI: 10.5281/zenodo.17498692 3 Original Article The time it takes for the ball to stop   in a collision can be calculated in two ways, the first is given by [9]:            (4) Where   is the speed at which it hits the ground on the first bounce,  is the coefficient of restitution and  Earth's gravity. The second form is [10]:         (5) Here ℎ is the initial height. RESULTS ANALYSIS By conducting the experimental part of the study and analyzing the recorded video with Tracker, the following data were obtained, as shown in Table 1. Ball 1 (red) is made of rubber and ball 2 (yellow) is a Ping Pong ball. The initial height is 0.35 m. Table1. Results table, some experimental data were measured with Tracker. The initial height is the same for both balls, there is a difference of hundredths when finding the coefficient of restitution by applying equations (1) and (2), and taking one value or the other will be irrelevant in the following calculations. In the time columns, the differences are minimal, with a percentage error in the measurement of times between 7.7% and 12.5% for ball 1 and between 5.9% and 11.8% for ball 2, which is very acceptable in the experiment. The values were calculated using formulas (4) and (5), demonstrating their validity in an experimental case such as the one studied here. Figure 2 shows a screenshot of the Tracker program analyzing balls 1 and 2. As shown in other studies [10-11], Tracker allows step-by-step tracking of the trajectory and measurement of variables of interest, in this case measuring speed before and after the collision, as well as measuring heights and times. Impact Speed [m/s] Restitution coefficient (1) Restitution coefficient (2) Restitution coefficient (3) Experimental time in rebounding [s] Time to bounce back [s] ( 4 ) Time to bounce back [s] ( 5 ) Energy loss first collision Ball 1 2.60 0.75 0.71 0.71 1.4 1.3 1.6 51.4% Ball 2 2.57 0.89 0.92 0.81 6.8 6.0 6.4 15.7% International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Issue 5 2025 DOI: 10.5281/zenodo.17498692 4 Original Article Fig 2: Tracker capture, analysis of balls 1 and 2. Own work. The final column presents energy analysis obtained from the first rebound. There is no conservation of mechanical energy because it is not a perfectly elastic collision. The calculation is performed by measuring the heights with Tracker. The results show that there is greater energy loss in the rubber ball compared to the ping pong ball, and this is also evident in the number of rebounds: 6 rebounds for the rubber ball and 20 for the ping pong ball before stopping. The measurement of gravitational potential energy with Phypox is shown in Figure 3. As can be seen, the data coincide with the final column of Table 1. Fig 3: Ball capture 1 and 2 analysis in Phypox, own work. Figure 4 shows the graph of Log  Based on the number of rebounds measured in Tracker, by finding the slope and performing the calculation, the coefficient of restitution can be obtained as mentioned in [9], but it should be clarified that the slope is equal to #$  as shown in equations (5) and (6). International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Issue 5 2025 DOI: 10.5281/zenodo.17498692 5 Original Article Fig 4: Graph of ln   Based on the number of rebounds for balls 1 and 2, the graph is our own creation. Ball 1. % 0.148#$  (5) Where 0.71 Ball 2. % 0.036#$  (6) Where 0.92 CONCLUSION The results confirm that the coefficient of restitution depends on the materials involved. The coefficient for ball 1 is 0.71, while for ball 2 it is 0.92, obtained using formula (2) for heights. Both balls have the same surface area. The collision is not elastic, and there is a loss of energy that also depends on the materials involved in the collision. Equations (4) and (5) were verified to determine the time it takes for the balls to stop when the coefficient of restitution is known. Tracker is useful for calculating the numerical value of the coefficient of restitution because it allows the velocities before and after the collision to be found very accurately, as well as determining heights and times during the trajectory, demonstrating its functionality [10-11]. Phypox proved similar values and offers an additional measurement the energy calculation. Acknowledgments The authors would like to thank Juan Felipe Builes for his helpful comments during the writing of this article. Authors contribution The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Issue 5 2025 DOI: 10.5281/zenodo.17498692 6 Original Article Compliance with ethical standards Conflict of interest The authors declare that they have no conflict of interest. REFERENCE 1. O.D. Pavioniand, F.M. Ortega. (2015), Obteniendo los coeficientes de restitución y arrastre en un solo experimento. Revista Mexicana de física 61, 11-16. 2. Universidad de Burgos. Estudio del coeficiente de restituciónmecánica de la particula7. Recuperado el 8 septiembre 2025 de: https://www.ubu.es/sites/default/files/portal_page/files/7-coeficiente_de_restitucion_0.pdf 3. S. C. Zuñiga Martínez, E. Zermeño Pérez, O. A. Briones Rico, N. Moreno Martínez. (2019), laboratorio sin aula de bajo costo mediante tecnologías aplicadas al conocimiento para formar ingenieros. Revista electrónica ANFEI digital N. 11. 1-10. 4. Douglas, Brown. Wolfgang, Christian. Robert, M Hanson. (2007). Tracker vídeo analysis and modeling tool (versión 3) [Software]. Recovered from https://physlets.org/tracker/ 5. D. A. José G, Melo M. Germán, Melo L. Susana, Melo L. Isabel C. (2023). Discusiones y actividades experimentales en física general. Editorial Germán Melo M. Pág. 111. 6. Paul A. Tipler, G. Mosca (2005). física par la ciencia y la tecnología 5 edición volumen 1. Editorial Reverte. 7. Orlando B. Escalona Toro. (2011). Sendero pedagógico para la enseñanza y divulgación de la ciencia. Recuperado el 8 de octubre de 2025 de: https://senderospedagogicos.blogspot.com/2011/11/la-pelota-la-pelota-bola-elasticaque.html 8. Garrido C, Victor. (2009). Determinación del Coeficiente de Restitución (e) de una pelota de ping-pong. TI Technology education. Recuperado el 14 octubre 2025 de: https://education.ti.com/~/media/D39B4A13C6EA450BBC9C89EB01B99569 9. Universidad de los Andes. Experimentos demostrativos del departamento de física. Recuperado el 8 de octubre de 2025 de: https://fisicaexpdemostrativos.uniandes.edu.co/CoeficienteRestitucion.html 10. A. F. García. (2010). Física con ordenador Curso Interactivo de Física en Internet. Caída libre y sucesivos rebotes. Recuperado el 8 de octubre de 2025 de: http://www.sc.ehu.es/sbweb/fisica/dinamica/con_mlineal/restitucion/restitucion.htm 11. D. A. José G, Melo M. Germán, Melo L. Susana. (2024). Solución experimental de un sistema mecánico con Tracker, South Florida Journal of Development, Miami Vol. 5 No. 12. 12. D. A. José G, Melo M. Germán, Melo L. Susana. (2025). Comprobación experimental de la simetría en la tensión de un sistema mecánico utilizando Tracker. Revista mexicana ciencia latina revista multidisciplinar. Vol. 9 No. 1.