Return to Physics IndexPorter Johnson - Illinois Institute of TechnologySuperball Physics

Porter Johnson Illinois Institute of Technology

Biol Chem Phys Sci Dept

CHICAGO IL 60616-3793

(312) 567-5745Objective(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 ahappy ball sad ballset [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 thebottomof 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 808080 81 82 83 85

MEDIANIf your students are sufficiently advanced or "calculator literate", you should show them how to compute the mean and standard deviation of these numbers; Theelasticity 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 aboutr x r = r. Correspondingly, for three^{2}

bounces the ratio would be aboutr x r x r = r. One can count^{3}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 tor = 0.80

of its initial height, corresponding to the fact that the fraction1. - r = 0.20of 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 cannever,neverbounce 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. [TheJupiterslingshotmaneuver, 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 percentagepof the total amount of the wagers. In

other words, the total amount paid to the winners is the fractionr = 1. - p,

multiplied by the total amount of the wagers. The fraction paid back after

two bets [just like two bounces of the ball] isr, after three bets it is^{2}r,^{3}

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.comReferences:

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.