Analysis of energy transformation in a non-ideal spring popper

Sarah Afzal; Ansh Modani; Shreena Desai

doi:10.64804/8gevmp74

Authors

Sarah Afzal Science & Engineering Magnet Program , Manalapan High School
Ansh Modani Science & Engineering Magnet Program , Manalapan High School
Shreena Desai Science & Engineering Magnet Program , Manalapan High School

DOI:

https://doi.org/10.64804/8gevmp74

Keywords:

potential energy, work, forces, energy, popper, physics, mechanics

Abstract

This experiment looks at how energy is transformed in a spring-loaded toy popper by comparing the work done to compress it with the gravitational potential energy it has at its highest point. Using a scissor jack and a high-precision scale, the work input (W ) was calculated using the trapezoidal Riemann sum of the force-displacement curve, totaling 0.255 J. Following ten launch trials of the popper, we observed maximum height h = 1.12 ± 0.11 m, corresponding to gravitational potential energy (GPE) of 0.062 ± 0.006 J. The results indicate a large mechanical energy loss of 76 ± 2 %. This discrepancy is likely due to non-conservative forces, such as friction or aerodynamic drag during flight. This system illustrates the substantial role of energy dissipation in non-ideal mechanical systems such as this one.

References

P. A. Tipler and G. Mosca, Physics for Scientists and Engineers, 5th ed. (W H Freeman and Company, New York, 2004).

R. A. Pelcovits and J. Farkas, Barron’s AP Physics C Premium (Kaplan North America, Fort Lauderdale, FL, 2024).

W. Moebs, S. J. Ling, and J. Sanny, University Physics, Vol. 1 (OpenStax, Houston, TX, 2016).

A. Sendrowicz, A. O. Myhre, I. S. Yasnikov, and A. Vinogradov, Stored and dissipated energy of plastic deformation revisited from the viewpoint of dislocation kinetics modelling approach, Acta Materialia 237, 118190 (2022). DOI: https://doi.org/10.1016/j.actamat.2022.118190

R. Larson and R. P. Hostetler, Calculus, 8th ed. (Brooks Cole, Pacific Grove, CA, 2005).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, 2nd ed. (Cambridge University Press, 1992).

C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, M. Picus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del Rı́o, M. Wiebe, P. Peterson, P. Gérard-Marchant, K. Sheppard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke, and T. E. Oliphant, Array programming with numpy, Nature 585, 357 (2020). DOI: https://doi.org/10.1038/s41586-020-2649-2

J. D. Hunter, matplotlib: a 2D graphics environment, Computing in Science & Engineering 9, 90 (2007). DOI: https://doi.org/10.1109/MCSE.2007.55

R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2025).

L. Rohland, Hooke’s law, https://www.ebsco.com/research-starters/law/hookes-law, accessed 27 March 2026.

D. S. Starnes, J. Tabor, D. Yates, and D. S. Moore, The Practice of Statistics, 5th ed. (W. H. Freeman and Company, 2015)