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### The Bouncing Ball Experiment

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The Bouncing Ball Experiment

Aim:

An investigation into the relationship between bounce and drop height
for a ping-pong ball And how the forces involved change the outcomes

There are many other factors other than dropping height that affect
the bounce height of a ball. Here is a table that shows our chosen
variable (in red) and the other possible variables:

Variable

Drop Height

Surface area of ball

Pressure inside the ball

Material of ball/type of ball

Surface on which ball is dropped

Dropping the ball

The Preliminary Experiment:

I need to carry out some preliminary experiments so that I can
effectively plan my investigation. If I carry out preliminary
experiments, I can predict what will go wrong for the real thing, and
I will be able to exclude anything that wasn't quite right from my
method. The main things I need to establish are how many repeats are
necessary and the range and number of heights.

Aim/Method of Preliminary Experiment:

Apparatus:

* Two metre rules

* Boss

* Two Clamps

* Ping pong ball

Here is a diagram as to how it should be set up:

1). Set up apparatus as shown above

2). Chose the start height and then go up the metre rules in a pattern
of numbers, e.g. every 5 (5, 10, 15, 20, 25 etc) or 10 (10, 20, 30,
40, 50, etc), but start wherever you want

3). Write them down on a piece of paper in a table like this:

Bounce Height (cm)

Average bounce Height (cm)

Drop Height (cm)

1

2

3

4

5

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

4). Line up the bottom of the ball at your first height

5). Get your partner to watch where it bounces back up to and then you
can drop the ball, (this is a practice)

6). Get your partner to get parallel to this height to avoid parallax
errors.

7). Repeat step 4 (at the same height) and then drop the ball; get
your partner to record the height at which the ball bounces back up
to.

8). Repeat this another 4 times (5 times for each height in total)

9). Repeat from step 4 onwards again but this time change the drop
height to your next chosen height.

For my preliminary experiment I first of all needed to find the
correct height to start dropping the ball from:

Finding Starting Drop Height:

10cm=Un-recordable

20cm=Un-recordable

30cm=Un-recordable

40cm=Unclear

I then dropped the ping-pong ball from 50cm to see how many repeats
would be necessary. I would first of all start with three repeats and
then find an average bounce height to see if three repeats are
sufficient, if not I would move onto five repeats.

Finding Repeats: At 50cm

[IMAGE]1=34cm

2=36

3=34.5

Conclusion:

There were no obviously anomalous results. I would say that my results
are probably quite reliable because we made every effort to make the
trial experiment fair, and my results turned out to be as I expected.
My preliminary helped me find problems with my method, like getting
the ball held at the right height, my original idea for five repeats
was proved wrong, three repeats are sufficient and the starting drop
height was too low (also with time we had, we could not take readings
every 10 cm as it would be too time consuming, so 15cm seemed a more
suitable unit to go up in). These problems will be addressed in the
final method for my main experiment

Now that I have completed my preliminary experiments, and I know what
to expect, I can start my main experiment.

Method:

Apparatus:

* Two metre rules

* Boss

* Two Clamps

* Bouncy ball

* 30cm ruler

Here is a diagram as to how it should be set up:

1). Set up apparatus as shown above

2). Chose the start height and then go up the metre rules in a pattern
of numbers, e.g. every 5 (5, 10, 15, 20, 25 etc) or 10 (10, 20, 30,
40, 50, etc), but start wherever you want

3). Write them down on a piece of paper in a table like this: (next
page)

Bounce Height (cm)

Drop Height (cm)

1

2

3

Average Bounce Height

50

65

80

95

110

125

140

155

170

185

200

4). Using you 30cm ruler line it up at your first height and then put
the bottom of the ball on top of it so that the bottom of the ball is
at this height

5). Get your partner to watch where it bounces back up to and then you
can drop the ball, (this is a practice)

6). Get your partner to get parallel to this height to avoid parallax
errors.

7). Repeat step 4 (at the same height) and then drop the ball; get
your partner to record the height at which the ball bounces back up
to.

8). Repeat this another 2 times (3 times for each height in total)

9). Repeat from step 4 onwards again but this time change the drop
height to your next chosen height.

How I Plan to Make my Results as Accurate and Reliable as Possible:

I will try to do as much as I can with my experiments to reduce the
chance of human experimental error and to make my results reliable and
accurate.

I will go through all the factors that affect the bounce height of a
ball, and change only the drop height. I will try to keep all the
other factors constant if I can.

Factor one is surface area of the ball. This factor will be kept
constant because the same ping-pong ball is being used for each
experiment. The surface area won't vary from experiment to experiment.

Factor two is pressure inside the ball. If the same ball is being used
for each experiment, the pressure inside the ball will also remain
constant.

Factor three is the material of the ball. Again, if the ball is not
changed then this factor will remain constant. This is the same for
factor four. The material of the floor will not change because the
experiment is being carried out in the same place each time and the
floor alongside the stairs is the same all the way up.

Factor five; the force at which the ball is dropped at will not change
because the same person is going to be the one to drop the ball each
time. This means that if a person exerts a force on the ball without
realising it, they probably do it with all the experiments. Using the
same person means that although the results will be slightly incorrect
due to this human error, the percentage error will always be roughly
the same. The incorrect results will be relative to what they would
have been. Also, the person dropping the ball will try as hard as they
can to simply hold the ball lightly between finger and thumb, then
simply letting go without pushing it at all. Hopefully, there should
be very little percentage error due to this factor.

Factor six, accuracy of measurement will be the hardest factor to keep
constant because it is impossible to get completely accurate results
in an experiment like this with the equipment we are provided with.
Human experimental error is a problem because things like reaction
times, eyesight (parallax errors) and our own judgement cannot be
changed and they do affect the end results quite considerably. Unlike
some other factors, the percentage error cannot reliably be found when
it comes to human error. This is because it is impossible to know how
long someone's reaction time was to read the measurement on the ruler
when the ball stopped bouncing. The ball might have already been on
its way down when the person read the measurement on the ruler. It is
also impossible for us to measure how much accidental force the person
dropping the ping-pong ball exerted onto it when it was dropped.
no way for this error to be found. These problems cannot be fully
controlled with the equipment available but steps can be taken to
avoid them. This is why the same person reads the bounce height off
the rulers, and they stand in exactly the same place for each
experiment. This is why the same person drops the ball each time. This
is why the rulers are attached as straight as possible by sella-tape
and clamps to prevent human error in reading the results.

Safety Precautions:

For most experiments, safety precautions have to be made so that no
one gets harmed in any way. My experiment carries little health risk.
But just to be certain I will make sure my equipment is secure and
safe so it doesn't fall on someone and I will pick up any dropped
balls immediately so that nobody trips on them.

What I can do with my Results:

When I have got a set of results, I can use them to prove or disprove
my prediction, relating bounce height with drop height. I can exclude
any obviously anomalous results from my results. I can then draw a
graph of my results. The line of the graph will show me what my
results mean. A straight line through the origin will show direct
proportionality. If all my points line up neatly along the line of
best fit, I will know that my results are likely to be reliable and
correct.

Prediction:

I predict that an increase in dropping height will bring about a
directly proportional increase in Gravitational Potential Energy. This
is because as the ball ascends higher from the surface of the earth,
the gravitational force of the earth will try to pull it back down.
This gives it a certain energy, which is called gravitational
potential energy. The equation for gravitational potential energy is:

Gravitational Potential Energy = mass (kg) x Gravitational Field
Strength x Height (m)

An increase in gravitational potential energy will give the ball more
energy to convert into kinetic energy with which it moves. The amount
of kinetic energy needed for the ball to reach the ground will
increase as I increase the dropping height. The GPE is transformed
into kinetic energy and this is stored, making the ball move faster.
If a ball has more kinetic energy/velocity when dropped from greater
heights, this energy will not all be lost when the ball is falling and
hitting the ground. As soon as there is a collision, both the floor
and the ball dent slightly and the remaining energy in the ball is
converted into elastic potential energy. The ball and the floor have
no energy being exerted on them to stop the potential energy from
being used, so this energy is converted back into kinetic energy as
the ball and the floor repel each other to return back to their
natural shape. The ball leaves the floor and keeps rising upwards due
to the amount of kinetic energy stored in it. The more kinetic energy
the ball had to begin with, the more it will have stored now and the
more it will be able to keep on rising before its energy runs out.
With the height it gains in the bounce, it again has gravitational
potential energy to come down again, but this cannot be used to make
the ball continue rising even further because gravitational potential
energy is stored as a result of the gravitational attraction of the
earth for the ball and it can only be used to reach the ground. A ball
having more gravitational potential energy when it is dropped means it
will have more kinetic energy when it hits the ground. There will be
more energy left stored in the ball after the ground has been hit and
the ball with bounce higher. Therefore overall, I predict that the
drop height of the ball will be directly proportional to its bounce
height. I predict that my graph of results showing this will show
direct proportionality, and have a straight line through the origin.

Here is a diagram of my predicted graph:

[IMAGE]

Obtaining Evidence:

All my tests dropping the ping-pong ball from varying heights behaved
in the same way. The higher I moved the ping-pong ball up, the higher
the bounce of the ball became:

Bounce Height (cm)

Drop Height (cm)

1

2

3

Average Bounce Height

50

34

35.5

36

35.2

65

48

47

47.5

47.5

80

56

57

56

56.3

95

61.5

60

61

60.8

110

74

72.5

73

73.2

125

80.5

81

80

80.5

140

90

88.5

89

89.2

155

94

93.5

93

93.5

170

100

101

100

100.3

185

103

102.5

102.5

102.7

200

108

109

109.5

108.8

[IMAGE]My results on the whole came out much like I'd expected. The
experiment went to plan and I didn't find there were any major
unexpected difficulties I had to overcome. I also seem not to have an
anomalous result

Conclusion:

My prediction was slightly incorrect. I predicted that my graph would
have a straight line through the origin. Instead, my graph was a
curve, showing that when I was using the lower drop heights, more of
the available kinetic energy was stored and used in the bounce. As the
drop height increased, more and more of the kinetic energy in the ball
is lost during the fall and collision with the ground and so the
difference between the bounce heights gets smaller. The average bounce
height starts increasing less and less the higher the drop height
becomes.

I think this is because there is an energy-wasting factor that I
overlooked. I overlooked friction due to air resistance in my
hypothesis. The higher the ball is dropped from, the more GPE it has
to convert into Kinetic energy, and the faster the ball goes. As the
velocity of a ball increases, so does the air resistance acting on it.
The ball will lose much energy this way.

When the ball is falling, it loses some kinetic energy due to friction
with the air resistance. The faster the ball's velocity when it is
falling (i.e. the more kinetic energy it has stored), the more air
resistance it will have and therefore the more kinetic energy it will
lose with friction. Therefore, the higher the drop height, the more
energy the ball loses while it is falling. Obviously, this makes the
line of our graph gradually get less steep and form a curve. In an
ideal world, where there is no air resistance and no energy is lost or
wasted with friction and sound, I predict that there would be an
element of direct proportionality and my graph would be a straight
line through he origin.

In order to prove my prediction correct that drop height is directly
proportional to the amount of gravitational potential energy stored in
the ball I am going to make some calculations using the formula for
GPE, which should then also help me prove my new theory.

The GPE formula is:

GPE = Height x mass x Gravitational Field Strength.

Using this formula, I can work out how much GPE the ball had at the
start of each experiment, and after the ball has bounced. I can then
work out how much energy has been lost overall and work out how
efficient the ball is.

Drop height (cm)

Calculation

GPE at start (J)

Bounce Height (cm)

Calculations

GPE after bounce (J)

50

50x2.4x10

1200

35.2

35.2x2.4x10

844.8

65

65x2.4x10

1560

47.5

47.5x2.4x10

1140

80

80x2.4x10

1920

56.3

56.3x2.4x10

1351.2

95

95x2.4x10

2280

60.8

60.8x2.4x10

1459.2

110

110x2.4x10

2640

73.2

73.2x2.4x10

1756.8

125

125x2.4x10

3000

80.5

80.5x2.4x10

1932

140

140x2.4x10

3360

89.2

89.2x2.4x10

2140.8

155

155x2.4x10

3720

93.5

93.5x2.4x10

2244

170

170x2.4x10

4080

100.3

100.3x2.4x10

2407.2

185

185x2.4x10

4440

102.7

102.7x2.4x10

2464.8

200

200x2.4x10

4800

108.8

108.8x2.4x10

2611.2

Now, the amount of energy lost between the dropping and the end of the
first bounce can be measured:

Drop Height (cm)

GPE at Start (J):

GPE after bounce one (J):

Energy Lost (J)

50

1200

844.8

355.2

65

1560

1140

420

80

1920

1351.2

569

95

2280

1459.2

820.8

110

2640

1756.8

883.2

125

3000

1932

1068

140

3360

2140.8

1219.2

155

3720

2244

1476

170

4080

2407.2

1672.8

185

4440

2464.8

1975.2

200

4800

2611.2

2188.8

[IMAGE]

[IMAGE]

This shows that my new theory on why the graph is a curve is probably
true. These results clearly show that the higher the drop height, and
the more energy the ball has to begin with, the more energy that is
lost altogether. The only way of explaining all of this is with my
theory that air resistance is to blame for the wasted energy, causing
my graph to curve.

Evaluation:

Overall, I think that my results were as accurate and reliable as I
could make them with the equipment I was provided with. I don't think
that seeing how far a ball bounces alongside a ruler and getting a
person to measure the bounce is a very accurate or reliable way of
carrying out the experiment. There is too much risk of human or
experimental error. The ball could have been dropped by mechanical
means to make sure that no force was exerted on it. All my results did
fit the line of best fit quite closely, which helps to prove that my
results are reliable.

I had enough evidence that I could study to work out why my graph was
a curve instead of a straight line. I also feel that I had enough
evidence to back up my conclusion. All my results did follow a
pattern. I didn't have any unexplainable results because I took enough
tests and averages to even out any slight glitches in the pattern.

If I could extent this experiment even further, I think I would carry
out the same experiment with a different ball. This way, I could
relate the results I have gained with a ping-pong ball with results
with say a tennis ball. The pressure inside a tennis ball is different
to that of a ping-pong ball, so it would be interesting to see what
difference this makes to the results. Also, the tennis ball is made of
a different material and is squashy. A tennis ball has a bigger
surface area than a ping-pong ball because it is bigger. If I was to
do this extension I predict that air resistance has more effect on a
tennis ball than it does on a ping-pong ball. Therefore I predict that
the graph will look very similar in direction, but the graph for the
tennis ball will start to curve more dramatically quicker than the
ping-pong ball does. This is because the tennis ball will be losing
more energy due to air resistance.

MLA Citation:
"The Bouncing Ball Experiment." 123HelpMe.com. 23 Apr 2014
<http://www.123HelpMe.com/view.asp?id=147925>.