Standard university or high-school physics teaching material on projectile motion is usually based on Newton's second law in vacuum, neglecting aerodynamics. We present a low-cost experiment for teaching projectile motion using the students' cell phones and sports equipment, which allows the students to test theory and numerical simulation against experimental data in the real world. For a shot put, theoretical predictions assuming projectile motion in vacuum agree with experimentally obtained trajectories in air to within a few centimeters. However, for a table tennis ball, vacuum trajectories can be almost three times as long as experimentally obtained trajectories. An equation of motion including the aerodynamic drag force has no analytic solution, but it is straightforward to integrate numerically for high-school or first-year university students. Accounting for aerodynamic drag substantially improves the match with experimental data for any ball. In a second experiment, balls are shot with spin resulting in curveball trajectories. Numerical simulations including the Magnus force can give accurate predictions of 3D curveball trajectories, both curving according to the normal and the inverse Magnus effect. Balls shot with topspin and backspin are also accurately modelled. Finally, we model the bounce of an arbitrarily spinning ball using linear and angular impulse-momentum theorems and coefficients of restitution in vertical and horizontal directions. We find agreement with experimental data to within centimeters.
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November 2020
PAPERS|
November 01 2020
Flight and bounce of spinning sports balls
Jacob Emil Mencke;
Jacob Emil Mencke
Department of Physics, Technical University of Denmark
, Fysikvej, 2800 Kgs. Lyngby, Denmark
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Mirko Salewski
;
Mirko Salewski
a)
Department of Physics, Technical University of Denmark
, Fysikvej, 2800 Kgs. Lyngby, Denmark
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Ole L. Trinhammer;
Ole L. Trinhammer
Department of Physics, Technical University of Denmark
, Fysikvej, 2800 Kgs. Lyngby, Denmark
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Andreas T. Adler
Andreas T. Adler
Team Danmark, House of Sports
, Brøndby Stadion 20, 2605 Brøndby, Denmark
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a)
ORCID: 0000-0002-3699-679X.
Am. J. Phys. 88, 934–947 (2020)
Article history
Received:
March 20 2020
Accepted:
July 14 2020
Citation
Jacob Emil Mencke, Mirko Salewski, Ole L. Trinhammer, Andreas T. Adler; Flight and bounce of spinning sports balls. Am. J. Phys. 1 November 2020; 88 (11): 934–947. https://doi.org/10.1119/10.0001659
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