Super-Ball Physics
Porter W. Johnson              Illinois Institute of Technology
                               Professor of Physics
                               Chicago IL 60616-3793
                               (312) 567-5745
Objectives:
    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.  
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