### 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/s2, 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:

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