A capsule-shaped object, unlike a sphere, can rebound to a higher height than it is dropped from if it has an initial spin. In this paper, we compare two quantitative models of this phenomenon: an impulse-based analytic model and a force-based Hertzian model. We experimentally studied the effects of impact angular velocity and contact angle on the capsule's rebounding velocity and angular velocity. Our experimental findings showed successful agreement with our Hertzian model but not with our impulse model. We attribute the comparative success of the Hertzian model to its intricate treatment of the slip–stick behavior of friction during the collision.
REFERENCES
1.
See https://youtu.be/RQ5R-0l7wdY?t=196 for “
Rugby World Cup Final 2015 New Zealand v Australia
.”2.
R.
Cross
, “ Bounce of an oval shaped football
,” Sports Technol.
3
(3
), 168
–180
(2010
).3.
Xing-Xing
Yao
,
Zi-Wen
Wang
,
Liang-Liang
Zhao
, and
Yuan
Zheng
, “ The rebound height of a capsule-shaped object
,” Eur. J. Phys.
44
(4
), 045001
(2023
).4.
Bowen
Pang
,
Xinkai
Wang
,
Liu
Shuo
,
Junxi
Guo
,
Guancheng
Hao
,
Wang
Pan
, and
Liping
Ju
, “ Study on rebounding height of capsule-shaped object based on serial coefficient of restitution
,” J. Phys.: Conf. Ser.
2282
(1
), 012007
(2022
).5.
D.
Gugan
, “ Inelastic collision and the Hertz theory of impact
,” Am. J. Phys.
68
(10
), 920
–924
(2000
).6.
M.
Nagurka
and
S.
Huang
, “ A mass-spring-damper model of a bouncing ball
,” in Proceedings of the 2004 American Control Conference, 30 June-2 July 2004, Boston, MA
(IEEE, New York, 2004).7.
G.
Kuwabara
and
K.
Kono
, “ Restitution coefficient in a collision between two spheres
,” Jpn. J. Appl. Phys., Part 1
26
(8R
), 1230
–1233
(1987
).8.
Théophile
Rémond
,
Vincent
Dolique
,
Franck
Vittoz
,
Sheedev
Antony
,
Renaud G.
Rinaldi
,
Lionel
Manin
, and
Jean-Christophe
Géminard
, “ Dynamical buckling of a table-tennis ball impinging normally on a rigid target: Experimental and numerical studies
,” Phys. Rev. E
106
(1
), 014207
(2022
).9.
Heike
Sommerfeld
,
Christian
Koch
,
Anna
Schwarz
, and
Andrea
Beck
, “ High velocity measurements of particle rebound characteristics under erosive conditions of high pressure compressors
,” Wear
470–471
, 203626
(2021
).10.
T.
Wanheim
, “ Friction at high normal pressures
,” Wear
25
(2
), 225
–244
(1973
).11.
V. I.
Mossakovskii
, “ Compression of elastic bodies under conditions of adhesion
,” J. Appl. Math. Mech.
27
(3
), 630
–643
(1963
).12.
H.
Hertz
, “ On the contact of elastic solids
,” J. Reine Angew. Math.
92
, 156
–171
(1881
).© 2024 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2024
Author(s)
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