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
| ' , '
| , ,
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|___________________'____________________________________________________

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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