




The information below is intended to provide a description of the demonstration,
an explanation for elementary students, and further explanation for
high school students.
Please keep in mind that not all demonstrations are presented
at each show.




DOUBLE BALL BOUNCE




Figure I.


Figure II.




Equipment:

Basketball (approximately 580g)
Racquetball (approximately 40g)

Step 1:

The basketball and racquetball are dropped from a certain height (usually shoulder height) and bounce back to a shorter height (generally above the waist).
(See Figure I.)

Step 2:

The racquetball is placed directly on top of the basketball and both are dropped simultaneously. (See Figure II.)
(A small rubber ring has been glued to the top of the basketball to make it easier to balance the racquetball).
The basketball rebounds to a much smaller height (usually below the waist), but the racquetball goes shooting off, sometimes hitting the ceiling!




Basic Ideas:

Energy can be neither created nor destroyed, but it can be converted from one form to another and it can be
transferred from one object to another.
During a collision, energy is usually transfered from one object to another.
Energy can be stored in an object by lifting the object to a certain height.
This energy is called gravitational potential energy.
The gravitational potential energy of an object depends on how heavy the object is and how high it is.
The heavier an object is, the more gravitational potential energy it has, and the higher an object is, the more gravitational potential energy it has.

Step 1:

When the basketball is dropped from shoulder height, it possesses a certain amount of gravitational potential energy.
As the ball falls, that energy is converted to kinetic energy. When the ball collides with the floor, some of this kinetic energy is transferred to the floor and converted to heat.
The remainder of the energy is used to bounce the ball back up to above waist height.
The same is true of the racquetball.

Step 2:

When the racquetball is placed on top of the basketball, the two balls fall until the basketball collides with the floor.
During the collision, the basketball loses some of its energy to the floor and to heat.
As it rebounds with the remainder of its energy, it transfers some energy to the racquetball.
The basketball (having less energy than in Step 1) only rebounds to below the waist.
The racquetball (having more energy than in Step 1) rebounds to a great height.
The energy that the basketball transferred to the racquetball caused the basketball to bounce less high than in Step 1.
This same amount energy, however, caused the racquetball to bounce much, much higher than in Step 1.
The reason for this is that the racquetball weighs much less than the basketball, and the increase in energy causes it to bounce much higher.




Basic Ideas:

Energy can be neither created nor destroyed, but it can be converted from one form to another and it can be
transferred from one object to another.
During a collision, energy is usually transfered from one object to another.
U = mgh, where U = gravitational potential energy, m = mass, g = gravitational constant, and h = height.
To perform the calculations, we have estimated that shoulder height is about 5 feet or 1.5 meters, above the waist is about 4 feet or 1.2 meters, and below the waist is about 2.5 feet or 0.75 meters.

Step 1:

When the basketball is placed at shoulder height it contains gravitational potential energy, but no kinetic energy.
The original gravitational potential energy of the basketball is calculated to be 8.53 Joules. (see below for calculations)
When the basketball collides with the floor, some of its energy is lost to the floor and some is lost due to the slight deformity of the ball during the collision.
Since the basketball rebounds to above the waist, the rebound gravitational potential energy it now contains is calculated to be 6.82 Joules.
This means that approximately 1.71 Joules of energy was transferred to the floor.
Doing the same calculations with the racquetball, we see that the original gravitational potential energy is
0.588 Joules, the final gravitational potential energy is 0.470 Joules, and 0.118 Joules of energy was transferred to the floor.
Basketball
U_{original} = 580 (g) * 9.8 (m/s^{2}) * 1.5 (m) = 8.53 (Joules)
U_{rebound} = 580 (g) * 9.8 (m/s^{2}) * 1.2 (m) = 6.82 (Joules)
U_{lost} = 8.53 (Joules)  6.82 (Joules) = 1.71 (Joules)
Racquetball
U_{original} = 40 (g) * 9.8 (m/s^{2}) * 1.5 (m) = 0.588 (Joules)
U_{rebound} = 40 (g) * 9.8 (m/s^{2}) * 1.2 (m) = 0.470 (Joules)
U_{lost} = 0.588 (Joules)  0.470 (Joules) = 0.118 (Joules)

Step 2:

When the racquetball is placed on top of the basketball and both balls are dropped, the results are much different.
The basketball loses the same amount of energy during the collision, but upon rebounding, the basketball now collides with the racquetball.
Since the basketball only rebounds to about knee height this time, we know that its final gravitational potential energy is calculated to be 4.26 Joules.
We can therefore calculate that the basketball transferred 2.56 Joules of energy to the racquetball.
The racquetball now has its original energy plus the transferred energy from the basketball.
We can calculate that the racquetball now has a total of 3.16 Joules of energy.
All of this energy will send the racquetball to a height equal to approximately 25 ft!
Basketball
U_{final} = 580 (g) * 9.8 (m/s^{2}) * 0.75 (m) = 4.26 (Joules)
U_{transfer} = 6.82 (Joules)  4.26 (Joules) = 2.56 (Joules)
Racquetball
U_{final} = 0.588 (Joules) + 2.56 (Joules) = 3.15 (Joules)
h_{final} = 3.15 (Joules) / {40 (g) * 9.8 (m/s^{2})} = 8.0 (m) = 25 (ft)



The following physics topics are discussed during this demonstration:



Sponsored by the Physics Department and the Center for Science, Mathematics, and Engineering Education  University of Virginia
