Bouncing Balls

Porter W. Johnson              Illinois Institute of Technology
                               Physics Department
                               Chicago IL 60616-3793
                               (312)567-3375

Objective:

The student will make careful observations of a ball bouncing off a hard surface 
one time or sequentially for several trials, to study how the ball travels as it 
bounces across the room.  From these observations, he/she will then be able to 
describe and explain the motion of the ball. 

Materials Needed:

    1.  A box containing several small super balls, medium-sized super balls, 
        hollow rubber balls, solid rubber balls, tennis balls, golf balls, 
        baseballs, and whatever other types of balls are available. 

    2.  Several meter sticks for measuring the height of the bouncing ball. 

    3.  Several smooth hard flat horizontal surfaces suitable for bouncing 
        balls---floors, lab tables, sidewalks, and the like. 

Strategy:

The initial phase of the activity involves making careful, qualitative 
observations of a single bounce.  Next, the students in teams should take a ball 
and measure quantitatively how high it bounces when dropped from a given height.  
Then the various types of balls are categorized as to how well they bounce.  
Finally, one should consider the same ball bouncing several times and study the 
progressive decrease in the heights to which it goes. 

                      A.  Procedures for qualitative study:

Bounce a ball a number of times off the table or desk in front of the class, 
catching it on first bounce, and ask students to describe carefully what they 
see.  Make a list of the qualitative observations---a list of typical 
observations is given below: 

    1.  The ball is released from rest and picks up speed until it hits the 
        surface and bounces off. 

    2.  After bouncing off the surface the ball comes back up to a height which 
        is less than the height at which it started, before stopping to climb. 

    3.  The higher the distance from which the ball is dropped, the higher it 
        will bounce. 

    4.  The ball makes very brief contact with the table, seeming to leave it 
        almost instantaneously. 

    5.  The ball makes a sound when it hits the table, which changes with the 
        height from which it is dropped. 

    6.  The ball may bounce differently when it hits different points on the 
        table. 

                      B. Procedures for quantitative study:

    1.  Each student should be given a ball to drop from a height h of one 
        meter and measure the distance d to which it bounces upward.  The 
        results should be arranged according to the types of balls and the 
        group should discuss which balls bounce well, and why. 

    2.  Each student should release the ball from several heights [h =  50 cm, 
        75 cm, 100 cm, 125 cm, 150 cm, etc] and measure the distance d to which 
        it bounces.  The ratio d/h, which we call the elasticity coefficient,
        should be roughly the same for each height. 

    3.  If there is time, a given ball should be allowed to bounce several times 
        after being released from an initial height h.  The sequence of bounce 
        heights, d1, d2, d3, ..., should be measured.  Each time the bounce 
        height reduces by roughly the same factor, the coefficient of 
        restitution: 
                             d1/h = d2/d1 = d3/d2 = ...



The ball begins at rest from height h with potential energy mgh, where m is its 
mass and g is the acceleration due to gravity.  On first bounce it comes up to a 
height d, corresponding to potential energy mgd.  The coefficient of 
restitution, d/h, is the fraction of mechanical energy remaining after first 
bounce. 

Energy is dissipated in the form of heat and acoustical energy.  Physicists 
believe in the principle of conservation of energy as a consequence of the 
symmetry of the basic interaction under translations in the time coordinate. 

Performance Assessment:

Bounce a ball across the room to an assistant so that it strikes the floor 
several times.  Have each student draw the trajectory of the ball in the 
notebook, describing its motion as completely as possible. 

Conclusions:

A ball bounced off a hard surface loses a specific fraction of its mechanical 
energy with each bounce. 

Multicultural:

The bouncing of a ball on a hard surface is essential for an understanding of 
baseball, which is played with gusto in Asia, Latin America, the Caribbean 
Region, and North America.  English Cricket [played throughout the British 
Commonwealth Nations] requires similar knowledge of the physics of bouncing 
objects. 

The deep connection between symmetries and conservation laws was first 
understood by the Mathematical Physicist Amelia Emmy Noether [1882 - 1935]. 

References:

Robert K. Adair, The Physics of Baseball, 2nd edition [Harper 1994].
                 ISBN 0-060095047-1.