Investigating the Bounce of a Tennis Ball after It Has Been Dropped From Certain Height


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Investigating the Bounce of a Tennis Ball after It Has Been Dropped From Certain Height

Aim

To investigate how high a tennis ball will bounce back after it has
been dropped from a certain height

How a Tennis Ball Bounces

As the ball is elevated the ball gains gravitational potential energy
equal to the ball's weight multiplied by its change in height1. When
the ball is dropped, the height decreases, and therefore so does the
gravitational potential energy. At the same time, the velocity of the
ball increases due to gravity, and therefore the kinetic energy
increases, as kinetic energy half the mass of the object (in this case
the falling ball) multiplied by velocity squared (Source: Physics for
You GCSE textbook). When the ball hits the floor the kinetic energy
goes into deforming the ball from its original round shape to a
squashed, oval shape. A tennis ball contains a rubber shell, which is
filled with compressed gas. The ball is most stable in a round shape,
so the gas inside expands to push the ball back to form the round
shape. This forces the outside of the ball to push out and therefore
bounce back up2. However, the ball will not bounce back to its
original height due to it losing energy as heat and sound energy when
hitting the floor.

Relevant Variables

The independent variable in this investigation is the height that the
ball is dropped from. The dependent variable that will be measured is
the height that the ball bounces back. The control variables that will
need to be kept constant if the results are to be as accurate as
possible are:

1. The weight of the ball; we will use the same ball throughout the
experiment to ensure that the results are as accurate as possible.

2. Material of the ball; as the ball is the same one used, this will
be kept the same also.

3.

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Temperature of the ball; if the ball is cooler or hotter, it may
bounce up to a less or greater distance. As the temperature of the
ball is not easily controllable we left approximately a minute
between each drop to ensure the ball had returned to room
temperature.

4. Air pressure (acting on the ball). Although this is not easily
controllable, we can assume the air pressure is kept fairly
constant as the experiment was conducted in the same classroom.

Prediction

I predict that the higher the ball is dropped from the higher it will
bounce back. This is due to the fact that the higher the ball is
elevated, the greater its gravitational potential energy, the greater
amount of kinetic energy it will gain when falling, and therefore the
greater the energy the ball has to bounce back with. I predict that
the ball will never bounce back to its original height, due to the
energy the ball loses as mentioned above.

The ball will not back at all when it is "dropped" from a height of
0cm, as there is no gravitational potential energy gained by the ball.
Due to this when I plot a graph of The Height the Ball is dropped from
against the average height that the ball bounces back I expect that
the line of best fit will look something like this:

[IMAGE]

The line of best fit will go through (0,0) indicating direct
proportionality.

Preliminary Work

A preliminary experiment was carried out to enable us to predict and
to make the actual experiment as reliable as possible by adapting the
method suitably.

Preliminary Method

Equipment List

* Meter ruler

* Retort stand and clamp

* Tennis Ball

Method

1. Attach the clamp to the retort stand

2. Clamp the ruler so it stands vertically, as parallel to the
retort stand as possible to ensure that the readings are accurate.

3. One person will hold the ball at 100cm, and when the second
person knows that the ball is about to be dropped, they will drop
the ball.

4. The second person will, as accurately as possible, read the
height at which the ball bounced back to.

5. This will be repeated twice more, and an average found of the
results for greater accuracy.

6. This method will then be repeated at 90cm, 80cm, 70cm, 60cm,
50cm, 40cm, 30cm, 20cm, 10cm and then left at 0cm.

Safety Precautions

The experiment is fairly hazard-free, although bags and stools were
removed from the vicinity of the experiment, to ensure that any injury
caused by tripping etc was prevented.

Results

Height Dropped (cm)

Height Bounced Repeat 1 (cm)

Height Bounced Repeat 2 (cm)

Height Bounced Repeat 3 (cm)

Average Height of Bounce (cm)

0

0

0

0

0

10

7

7

7

7

20

13

13

14

13

30

18

18

18

18

40

22

23

24

23

50

26

28

27

27

60

33

33

32

33

70

37

39

38

38

80

44

41

43

42

90

49

48

48

48

100

54

53

52

53

As predicted, the graph's best fit line goes through the origin,
indicating direct proportionality between the height from which a
tennis ball is dropped, and the height at which it bounces back to.
There were no blatant anomalies in my results, so I decided to use the
same, unchanged method for my actual experiment.

Results

Height Dropped (cm)

Height Bounced Repeat 1 (cm)

Height Bounced Repeat 2 (cm)

Height Bounced Repeat 3 (cm)

Average Height of Bounce (cm)

0

0

0

0

0

10

7

7

6

7

20

12

11

13

12

30

17

18

17

17

40

22

23

23

23

50

27

27

28

27

60

33

31

33

32

70

36

38

38

37

80

43

43

44

43

90

49

50

47

49

100

52

53

54

53

Analysis

Through our investigation I confirmed my theory that the greater the
height a ball is dropped from, the greater the height it will bounce
back to, the straight best fit line on t both the graphs passing
through the origin also confirm this. As the line of best fit is
straight we can also deduce that the smaller the height the ball is
dropped from the smaller the height the ball will bounce back to.

I thought about what happens after the ball has bounced once, and
whether or not it continues to bounce infinitely at smaller and
smaller heights. However this could not happen, as eventually the ball
loses energy through friction with the air and the material, heat, and
sound energy, causing the ball to eventually stop bouncing.

Relevant Extensions

To extend the experiment, there a number of investigations we could go
through.

For example:

1. The bounce back heights of different balls, of different
materials.

2. The number of bounces a ball will make before stopping.

3. Carrying out these experiments in a vacuum, and testing whether
or not air resistance affects some balls.

By using the coefficient of restitution, we can measure how much
bounce there is, or in other words, how much of the kinetic energy of
the colliding objects before the collision remains as kinetic energy
of the objects after the collision. With an inelastic collision, some
kinetic energy is transformed into deformation of the material, heat,
sound, and other forms of energy, and is therefore unavailable for use
in moving.

A perfectly elastic collision has a coefficient of restitution of 1.
Example: two diamonds bouncing off each other. A perfectly plastic, or
inelastic, collision has c = 0. Example: two lumps of clay that don't
bounce at all, but stick together. So the coefficient of restitution
will always be between zero and one3.

To measure the coefficient of an object falling to the floor the
formula is:

[IMAGE]

Where c is the coefficient, h is the height the ball bounces back and
H is the height that the ball is dropped from.

I worked out the coefficient of restitution for the both the
preliminary experiment and the main experiment.

Results

Preliminary Experiment: Coefficient of Restitution of the tennis ball
used = 0.76

Main Experiment: Coefficient of Restitution of the tennis ball used =
0.74

Although the exact same ball was used for both the experiments, by the
second time, the ball's coefficient of restitution was less.

This could be perhaps due to air seeping out of the ball between to
the experiments, which is why tennis balls sometimes lose their
'bounciness'. For this reason, tennis balls come in pressurized
containers, the pressure exerted on the outside of the ball being
equal to the pressure of the inside of the ball, to prevent any gas
seeping out.

By comparing these coefficients of restitution to what the
manufacturers claim their balls coefficients of restitution to be
(0.75) we can see that our ball is still quite "bouncy".

Evaluation

I feel that the experiment went very well, with no anomalies, and both
experiments confirming my previous predictions. The accuracy of the
experiment was maintained throughout, with constant control variables,
and averages found wherever possible, to give the greatest accuracy.

Improvements

To give greater accuracy, although it is not needed to confirm my
predictions, there are a number of things that could be done. For
example:

1. Increasing the range of the measurements to 0cm - 200cm

2. Using digital imaging to get an exact height at which the ball
bounces back, instead of using our eyes and reactions.

3. Doing more repetitions, and finding averages.

Sources and Bibliography

1 Physics for You GCSE textbook

2 Factors Affecting A Bouncing Tennis Ball website. Address:

http://van.hep.uiuc.edu/van/qa/section/Making_Stuff_Move/Bouncing_Bumping_and_Crashing/20011228194353.htm)

3 Coefficient of Restitution website. Address:

http://www.racquetresearch.com/coeffici.htm


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