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Bouncing Batteries
May 14, 2015
Today,
entertainment is more likely enjoyed in a personal, rather than a public, setting. For
music, we apply
earpieces instead of traveling to the
concert hall. For
movies, we stare at the small
display screen of our
cellphone and not the
wide screen of the
movie theater. Instead of interacting with a
machine,
audiences of the past would sometimes
interact with each other; and, in
Shakespeare's time, they might even interact with the
actors by
throwing ripe fruit.
Long before
The Rocky Horror Picture Show, people would participate in public performances by
singing along with the "
bouncing ball." As a
song was sung on screen, the
lyrics would be displayed with a white
ball bouncing from word-to-word to encourage the audience to sing along. This effect originated in a 1925
cartoon version of
My Bonnie Lies over the Ocean. To view a cartoon version of
Little Brown Jug, see ref. 1.[1]
A ball of a different sort.
Buckminsterfullerene, C60, also called a bucky-ball. It's named after Buckminster Fuller, popularizer of the similarly constructed geodesic dome.
(Modified Wikimedia Commons image by Mstroeck.)
From
childhood, we learn not to expect to catch a
sports ball dropped to the
floor at the same height from which it's dropped. It's only in later years that we learn that
energy lost from
friction with the floor and
deformation of the ball prevents a rebound to the original height. This is an example of the
conservation of energy, and the energy balance
equation is quite simple,
where ΔE is the energy lost from friction and deformation,
m is the
mass of the ball,
g is the
gravitational acceleration,
h0 is the initial (drop) height, and
h1 is the maximum height attained after the first bounce.
Not surprisingly, there are strict
standards for the
mechanical properties of balls used in
professional sports. As an example, the
International Tennis Federation's specification for a
tennis ball requires a mass between 56.0 and 59.4
grams, a size between 6.541 and 6.858
cm, and a bounce, onto a
concrete surface from a height of 254 cm, between 135 and 147 cm.[2-3] Taking these values, and a gravitational acceleration of 9.8 m/s
2, gives an energy loss of between 0.587 and 0.693
joules in the tennis ball bounce test.
The energy lost is about 40% of the total drop energy. Although some of this energy is lost from friction, most of it is lost through deformation of the ball by
elastic hysteresis. The energy loss of the
rubber material corresponds to the
area inside the
hysteretic stress-strain curve (see figure).
Hysteresis curve for natural rubber.
The area inside the curve corresponds to the energy loss in the cycle.
(Illustration by the author using Inkscape.)
In 2013, several
YouTube videos were posted demonstrating a
correlation between an
alkaline battery's charge state and how high it would bounce. One of the better videos can be found in ref. 4.[4]
A team of
scientists and
engineers from
Princeton University (Princeton, New Jersey),
Rutgers University (Piscataway, New Jersey), the
City University of New York (New York, New York), the
City College of New York (New York, New York),
Brookhaven National Laboratory (Upton, New York), and
Voltaiq (Brooklyn, New York), decided to
quantify this effect. They've
published their findings in a recent issue of the
Journal of Materials Chemistry.[5-6]
As the online videos show, fully charged alkaline batteries have almost no bounce when dropped, while
discharged batteries bounce higher. The height of the bounce seems to depend on the degree of discharge, so the mechanism appears to be some
chemical change inside the cell.[6] As it turns out, the effect is not very
linear, with a 50% discharge giving about the same bounce as a fully discharged battery. Says
Daniel Steingart, an assistant professor of
mechanical and aerospace engineering at Princeton,
"A year ago a buddy of mine who knows I work on this sent me this video and said did you know this happens? I didn't. But I had a bunch of batteries on my desk and I was able to verify it... The bounce does not tell you whether the battery is dead or not, it just tells you whether the battery is fresh."[6]
Steingart's
research team built a simple
apparatus that uses a
computer microphone to
record the sound made when a battery falls through a
plexiglass tube. The time between bounces was used to determine the height of the bounce.[6] The simplicity of the
experiment makes its results readily accessible to people without a
scientific background (see video, below).[6]
Bouncing batteries, demonstrating the non-linear discharge effect.
(Princeton University video.)
X-ray scans of batteries were done at Brookhaven National Laboratory to determine a possible mechanism for the effect. A fully charged alkaline battery has a layer of
zinc surrounding a
brass core, and the zinc
transforms to
zinc oxide as the battry discharges.[6] The transition from
granular zinc to zinc oxide is responsible for the bounce. The zinc oxide infiltrates the original zinc, decreasing
mechanical damping.[6] Says Steingart,
"The zinc starts out as a packed bed of particles that all move very nicely past each other... When you oxidize the zinc, it makes bridges between the particles and makes it more like a network of springs. That is what gives the battery its bounce."[6]
The
coefficient of restitution was found to correlate with the formation of these zinc oxide bridges in the zinc
anode, and it was found to level off at a value of 0.66 ± 0.02 at 50% discharge, the point at which the anode has
densified into a
porous zinc oxide solid.[5] It's interesting that zinc oxide is added to
golf balls to give them extra bounce.[6] This research was funded by the
National Science Foundation, the
U.S. Department of Energy, and
Brookhaven National Laboratory.[6]
Since I've mentioned the coefficient of restitution, I would be remiss in not mentioning the super bouncy
Super Balls and
bouncy balls. The
synthetic rubber material of the Super Ball was invented by
chemist, Norman Stingley, in 1964 and
patented in 1966.[7] The material is a
polybutadiene matrix containing zinc oxide and
stearic acid, among other
ingredients.[7] It's
vulcanized with
sulfur at high
temperature and
pressure, and the resulting balls have a coefficient of restitution from 0.9 to nearly 1.0.
References:
- Little Brown Jug (Cartoon Sing along), YouTube Video, September 26, 2007.
- Howard Brody, "The tennis‐ball bounce test," Phys. Teach., vol. 28, no. 6 (September, 1990) pp. 407ff., http://dx.doi.org/10.1119/1.2343088. A PDF version of this article can be found here.
- Ball Testing, Tennis Industry Magazine, July, 2007.
- Lee Hite, "Why A Dead Alkaline Battery Bounces!" YouTube Video, December 27, 2013.
- Shoham Bhadra, Benjamin J. Hertzberg, Andrew G. Hsieh, Mark Croft, Joshua W. Gallaway, Barry J. Van Tassell, Mylad Chamoun, Can Erdonmez, Zhong Zhong, Tal Sholklapperh, and Daniel A. Steingart, "The relationship between coefficient of restitution and state of charge of zinc alkaline primary LR6 batteries," Journal of Materials Chemistry A, Advance Article, March 13, 2015, DOI: 10.1039/C5TA01576F.
- John Sullivan, "Battery bounce test often bounces off target," Princeton University Press Release, March 20, 2015.
- Norman H Stingley, "Highly resilient polybutadiene ball," U.S. Patent No. 3,241,834, March 22, 1966.
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