Porter Johnson - Illinois Institute of Technology 

Superball Physics

Porter Johnson                 Illinois Institute of Technology 
                               Biol Chem Phys Sci Dept
                               CHICAGO IL 60616-3793
                               (312) 567-5745 

Objective(s):

This lesson is suitable for an 8th grade student.  To study the motion of 
superballs in the air, colliding with and bouncing off smooth surfaces.  Basic 
features of moving and colliding objects can be demonstrated and studied using 
this familiar and fascinating toy. 

Materials Needed:

A supply of superballs of various sizes and colors for use by students in 
teams of two.  A supply of meter sticks [with some two meter sticks] is needed 
for each set-up. 

For the initial demonstration of bouncing you will need a supply of various
types of balls, some of which bounce very well, some poorly, and some not at 
all.  In particular, you should get a happy ball sad ball set [available 
at toy stores everywhere].

Strategy:

Begin by bouncing superballs and showing that their bounce is quite "springy" or 
"elastic".  Show that the smaller superballs bounce just as well as the big 
ones.  Show that superballs bounce better than tennis balls, ping-pong balls, 
and golf balls.  

Show the "happy and sad balls", and ask the group to predict how they will 
bounce.  In particular, have the class discover that the "sad ball" feels a
lot like a superball, so that it might bounce rather well.  Unfortunately, it 
does not bounce at all, even though the result is not obvious from handling 
it.

Practice dropping the ball in front of the class, showing how to release the
ball from rest, measuring the height of the bottom of the ball above the 
floor.  Also, show how to measure the bounce height, again defined as the 
maximum height of the bottom of the ball above the floor on first bounce. 
Divide the class into groups of two, and have them each drop a superball from 
a height of 100 cm [one meter], and record the bounce heights on the board.  
Here is a set of typical bounce heights [in cm], arranged in increasing order:

72  76  78  79  80  80  80  81  82  83  85 

Note that there are eleven independent measurements on the list, and that the
median height is 80 cm, with seven of the eleven measurements lying between 

77 and 83 cm.  Thus, an "eye-ball" estimate of the measured bounce heights is 
(80 $\pm$ 03) cm.
       <-------------- RANGE -------------->
72  76  78  79  80  80  80  81  82  83  85 
                  MEDIAN
If your students are sufficiently advanced or "calculator literate", you should
show them how to compute the mean and standard deviation of these numbers;

The elasticity coefficient r, which we define as the ratio of the bounce height
to
the initial height, is roughly independent of bounce height, as the class can 
demonstrate by studying the dropping the ball from initial heights of 50 cm 
and 200 cm. 

Have the class drop the ball from an initial height of 100 cm and measure 
the maximum heights for second bounce.  The data [in cm] may look something like 
this:

56  58  59  60  63  64  64  66  68  69  72

By "eyeballing" the data, we estimate the measured heights on second bounce to 
be about (64 $\pm$ 6) cm.  Note that, for two
bounces, the ratio of
second 
bounce height to initial height is about r x r = r2.  Correspondingly, for three 
bounces the ratio would be about r x r x r = r3.  One can count 10 - 20 
independent bounces for the ball, each of lesser amplitude, before the ball 
seems to stop on the floor.

One can summarize by saying that on each bounce, the ball returns to r = 0.80 
of its initial height, corresponding to the fact that the fraction 1. - r = 0.20
of the initial energy is dissipated upon collision with the floor.

Impress upon the class that, because the ball loses some mechanical energy 
after each bounce, it can never, never bounce higher than the initial release 
height, and get them to agree with this basic consequence of energy 
conservation.   Having thoroughly convinced them of this point, take out a 
smaller super ball and put it into a small indentation in the bigger ball.  
Hold the bigger ball in your hand, with the smaller one sitting on top of it, 
and carefully drop it.  Repeat the exercise several times, and observe that, 
under optimal conditions, the smaller ball goes several times higher than its 
initial drop height.  The smaller ball is, in effect, drawing energy from the 
larger ball, so that is can go much higher than otherwise.  [The Jupiter 
slingshot maneuver, in which a satellite can increase its speed by doing a 
"hairpin" loop around a major planet, which is used to extend the range of
inter-planetary rockets, operates because of similar principles. 

Performance Assessment:

A superball can be made to bounce several times near its initial location, 
but it will eventually bounce away because of mis-alignments, imperfections, 
etc.  Can you make a superball bounce back and forth about a given location.  
This is a skill which each class member can acquire, simply by bouncing the 
ball on the floor, trying various schemes, and the like.  The trick is to 
release the ball with an initial horizontal velocity and spin.  By picking the 
right initial conditions, the ball can be made to bounce back and forth. 


Conclusions:

The vigorous bouncing of the superball is an useful vehicle for illustrating 
and studying the basic concepts of energy conservation, energy transfer, and 
dissipation of mechanical energy as heat.

Multi-cultural Component:

In various types of sponsored gambling, whether legal or illegal, the "house" 
gets to keep a certain percentage p of the total amount of the wagers.  In 
other words, the total amount paid to the winners is the fraction r = 1. - p, 
multiplied by the total amount of the wagers.  The fraction paid back after 
two bets [just like two bounces of the ball] is r2, after three bets it is r3, 
etc.  Eventually, or course, the "house" ends up with all the money, for the 
same reason that the balls stop bouncing.  Urge your students to keep these
points in mind when they think of placing bets.  If they persist in 
gambling, they might wish to learn about the super ball lottery:


http://www.super-ball.com
                    
References:

A web-based reference on bouncing baseballs is given at the following
site:


http://www.exploratorium.edu/baseball/bouncing_balls.html

This site, developed by the Exploratorium [an excellent interactive science 
museum in San Francisco], outlines experiments with baseballs, tennis balls,
and golf balls, and in particular the temperature dependence of the bounce.