The area, A, and the duration of contact, T, have been measured as a function of impact speed, U, for balls striking a flat surface. The balls lost about 40% of their kinetic energy over the range of speeds studied, but, surprisingly, the results for and appear to be consistent with Hertz’s elastic theory of impact. Possible reasons are discussed for this unexpected behavior.
REFERENCES
1.
J. F. Bell, “The experimental foundations of solid mechanics,” Handbuch der Physik (Springer-Verlag, Berlin, 1973), Vol. VIa/1, especially pp. 313–331.
An interesting comparison of the (elastic) impact of cylinders and balls is made by
D.
Auerbach
, “Colliding rods: Dynamics and relevance to colliding balls
,” Am. J. Phys.
62
, 522
–525
(1994
).2.
[cf. also his later work on more complicated collisions,
R.
Cross
, “Impact of a ball with a bat or a racket
,” Am. J. Phys.
67
, 692
–702
(1999
)].3.
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944), 4th ed., pp. 193–200, 440.
4.
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics (Pergamon, Oxford, 1959), Vol. 7, pp. 26–31.
5.
B.
Leroy
, “Collision between two balls accompanied by deformation: A qualitative approach to Hertz’s theory
,” Am. J. Phys.
53
, 346
–349
(1985
).A. E.
Kennelly
and E. F.
Northrup
, “On the duration of electrical contact between impacting spheres
,” J. Franklin Inst.
172
, 23
–38
(1911
). They were interested in short electrical pulses, not in testing Hertz’s theory (which they do not mention), however their results agree well with his predictions for The best experiments, on identical steel balls in pendulum collision, give for the exponent for speeds between 0.44 and 2.8 m s−1 (cf. −0.2), while the measured values of T agree with those calculated from the elastic constants to within the uncertainty of ≈1%.Kennelly and Northrup do not consider the possibility of inelastic behavior, but later work by
J. P.
Andrews
, “Theory of collision of spheres of soft metals
,” Philos. Mag.
9
, 593
–610
(1930
), develops Hertz’s theory to deal with deformation of the surface of the ball due to plastic flow on impact. Andrews’ model leads to a decrease of the coefficient of restitution with impact speed, similar to results reported by Raman, but it does not appear to be generally applicable[cf.
J. P.
Andrews
, “Experiments on impact
,” Proc. Phys. Soc. London
43
, 8
–17
(1931
)].7.
W. A.
Prowse
, “The development of pressure waves during the longitudinal impact of bars
,” Philos. Mag.
22
, 209
–239
(1936
).8.
P. G. Tait, “On impact,” Scientific Papers (Cambridge U.P., Cambridge, 1900), Vol. 2, pp. 221–279.
9.
G. W. C. Kaye and T. H. Laby, Tables of Physical Constants (Longmans, London, 1995), 16th ed., p. 48.
10.
R. F. S.
Hearmon
, “The elastic constants of anisotropic materials
,” Rev. Mod. Phys.
18
, 409
–436
(1946
).
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2000
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