We investigated a very long chain falling from the pile on the edge of a table to the floor both experimentally and theoretically. In this very simple and novel configuration we showed that the velocity of the chain quickly converges to its asymptotic value, and that the steady-state velocity is proportional to the square root of the height of the table. The results are general and do not depend on the type of chain. We explained our measurements using simple dimensional analysis and Newton’s second law. The measurements do not require any special instrumentation other than a stopwatch, a desk, and a chain. This experiment can be performed in any classroom.
REFERENCES
1.
F.
Behroozi
, “The sliding chain problem with and without friction: A universal solution
,” Eur. J. Phys.
18
(1
), 15
–17
(1997
).2.
Kirk T.
McDonald
, “A Falling, Folded String,” Problem set, http://www.hep.princeton.edu/∼mcdonald/examples/string.pdf, accessed Jan. 30, 2020
.3.
Célia A.
de Sousa
, Paulo M.
Gordo
, and Pedro
Costa
, “Falling chains as variable-mass systems: Theoretical model and experimental analysis
,” Eur. J. Phys.
33
(4
), 1007
–1028
(2012
).4.
C. A.
de Sousa
“Author’s reply to ‘Remarks on Newtonian analysis of a folded chain drop’
,” Phys. Teach.
57
, 4
(Jan.
2019
).5.
Willem H.
van den Berg
, “Force exerted by a falling chain
,” Phys. Teach.
36
, 44
–45
(Jan.
1998
).6.
P-T.
Brun
, Basile
Audoly
, Alain
Goriely
, and Dominic
Vella
, “The surprising dynamics of a chain on a pulley: Lift off and snapping
,” Proc. Math. Phys. Eng. Sci.
472
(2190
), 20160187
(2016
).7.
8.
Giovanni
Romano
, Raffaele
Barretta
, and Marina
Diaco
, “On the role of control windows in continuum dynamics
,” Acta Mech.
229
(4
), 1849
–1868
(2018
).9.
Epifanio G.
Virga
, “Chain paradoxes
,” Proc. Math. Phys. Eng. Sci.
471
(2173
), 20140657
(2015
).10.
Waldemar
Tomaszewski
and Piotr
Pieranski
, “Dynamics of ropes and chains: I. The fall of the folded chain
,” New J. Phys.
7
(1
), 45
(2005
).11.
Mark
Denny
, “A uniform explanation of all falling chain phenomena
,” Am. J. Phys.
88
, 94
–101
(Feb.
2020
).12.
Readers may view the appendices at TPT Online, http://dx.doi.org/10.1119/10.0009107, under the Supplemental tab.
15.
Zuma model produced by Virgo Mfg
. Corporation Zuma, Copyright by Virgo Mfg. Corporation
2004
, Torrance CA, and Conway, AR
.16.
G. L.
Hazelton
, “A force amplifier: The capstan
,” Phys. Teach.
14
, 432
–433
(Oct.
1976
).© 2022 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2022
Author(s)
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.