Super-Ball Physics

Objective:

    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.

Indiana Science Standards Addressed:

     4.2.4 Use numerical data to describe and compare objects and events.

    5.3.11 Investigate and describe that changes in speed or direction of motion of an object are caused by forces. Understand that the greater the force, the greater the change in motion and the more massive an object, the less effect a given force will have.

Materials:

• 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

Estimated Time:

    This activity should be split up over two class periods of about 45 minute to an hour each day. Steps 1 & 2 should be done on the first class period, and steps 3 & 4 can be don on the second class period.

Procedure:

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

                    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 allotted 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.

 

    3. (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

    4. (alternate assessment, would be more challenging) "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.

Rationale:

       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.

Week 3