```Super-Ball PhysicsPorter W. Johnson              Illinois Institute of Technology                               Professor of Physics                               Chicago IL 60616-3793                               (312) 567-5745Objectives:    To study the motion of a ball in the air, its collision with a hard surface,     and subsequent bouncing.  The idea is to take an familiar toy and use it to     demonstrate basic features of moving and colliding objects. Materials Needed:    A large supply of various types of balls to demonstrate some that bounce     well, some that don't bounce at all, and some that bounce only a few times.    A meter stick [or better, a two meter stick] is needed for each set-up. Strategy:1.  Begin by showing a variety of balls that bounce to different degrees and     with different vigor on a hard surface [table or floor].  Show that Super-    Balls of various shapes and sizes bounce more strongly than tennis balls,     ping-pong balls, soccer balls, etc.  Then give each team of two or three     students a Super-Ball and have each team release the ball from a specified     height.  Have the students measure the "bounce height" of their balls, and     enter their measurements on the board, as shown below:                      Little Super-Balls

Release Height           Bounce Height

0 cm                    0   cm
25 cm                  ____  cm
50 cm                  ____  cm
75 cm                  ____  cm
100 cm                  ____  cm
125 cm                  ____  cm
150 cm                  ____  cm

Draw a graph of bounce height [vertical] versus release height [horizontal]
for the various types of objects, and note that the graph is roughly a
straight line passing through the origin.

2.  The next phase is to study how many times the Super-Ball bounces in the     vicinity of the spot at which it makes initial contact with the floor.  It     is convenient to use the tiles on a tile floor, which are squares of     standard size [8 x 8 inches, or 12 X 12 inches].  Give each group a Super-    Ball and a ruler, have them drop the ball a specified distance above the     center of a tile, and record their data in a chart on the board, like the     one below:                            Little Super-Balls

Drop Height             Number of Bounces

25  cm                   ____
50  cm                   ____
75  cm                   ____
100  cm                   ____
125  cm                   ____
150  cm                   ____

You would expect to see that the balls will bounce only a few times within
the alloted square.  In general, the balls bounce fewer times inside the
region when they are dropped from a greater height.  This tendency of balls
to wander from the drop point is a reflection of their chaotic motion, a     feature that they have in common with motion of the invisible molecules in a     gas. Performance Assessment:     Draw a graph of the vertical component of height of the Super-Ball above the     floor/table [vertical axis] as a function of time [horizontal axis].     Acceptable solution:  Note that the ball starts out at an initial height at     the initial time, starts down slowly, picks up speed, and hits the     table/floor after some time.  Then it bounces upward, coming up to a bounce
height that is somewhat less that the height from which it was dropped.                            Graph of Height versus Time
Height
|
|
|__________________  Initial Height
| '  ,
|      ,
|____________________________________________   Bounce Height      |        '                        ,  '    |          ,                    ,    |           ,                       |            ,               '    |             ,    |                         '    |               ,    |                       '    |                '        |                     '    |                  '    |___________________'____________________________________________________                               Time

Conclusions:    The Super-Ball can be used to illustrate a variety of basic concepts of     motion [kinematics].  Its relatively elastic behavior makes it well-suited     to illustrating the incessant motion of molecules. Alternate Performance Assessment:    "A Wham-O Super-Ball is a hard spherical ball.  The bounces of a Super-Ball     on a surface with friction are essentially elastic and non-slip at the point     of contact.  How should you throw a Super-Ball if you want it to bounce back     and forth?  [Super-Ball is a registered trademark of Wham-O Corporation.      San Gabriel, California.]"    This problem is taken from the book          Newbury, Newman, Ruhl, Staggs, and Thorsen          Princeton Problems in Physics [with solutions]
Princeton University Press 1991
ISBN 0-691-02449-9

The analytic solution to this problem appears in that book.  It is shown
there that the initial horizontal velocity v, the radius a of the ball, and
the initial angular velocity w are related by

v =  0.4 w a

in order for the ball to bounce elastically back and forth.

The performance-based exercise involves launching a super-ball with just the
right horizontal speed and spin so that it will bounce back and forth on the
floor.

References:     Additional information and phenomenological exercises on the Super-Ball      [and a myriad of other interesting matters!] are described in the classic      reference            Jearl Walker           The Flying Circus of Physics with Answers
Wiley 1977
ISBN 0-471-02984-X

Exercises 2.18 [The Super-Ball as a Deadly Weapon] and 2.28 [Super-Ball      Tricks] are directly relevant.  ```