Energies and motion involved in bouncing balls.
Physics coursework: An investigation into how the height that a ball is dropped from influences the height of the bounce of different balls.
Plan
I am going to investigate how the height a ball is dropped from can affect the height of the bounce on impact with the ground. To broaden my investigation I will also change the type of ball used in order to evaluate the differences.
To ensure that my experiment will be carried out safely, everyone involved in the experiment will wear safety goggles at all stages of the experiment. The practical will be carried out in plenty of space, clear of bags and coats. It is also imperative to consider the safety of other pupils that may be close to the practical. Therefore no one who is not involved in the practical shall be allowed in close vicinity of the experiment. Great care will also be taken when dropping a ball to ensure that any ball does not strike others in the room.
The only dependent variable in this experiment is the height that the ball bounces, as this is not known or controlled prior to the experiment.
The independent variables in the experiment are the heights that the balls are dropped from, the surface that the ball bounces on, the type of ball used, ball is dropped vertically, and that when dropping a ball no force is applied.
Accuracy of the measurement will be the hardest factor to keep constant because it is almost 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 factors like reaction times, eyesight and our own judgement cannot be changed and the do affect the end result considerably. Such 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 height of the bounce, and they stand in exactly the same place for each test. Also the same person releases the ball without any intentional force each time.
My hypotheses for this experiment are:
> The greater the height a ball is dropped from the greater the height of the bounce.
> The greater the elasticity of a ball the higher it will bounce. Out of tennis, ping-pong, hockey, air flow and golf ball, I predict that the golf ball will bounce the highest on a wooden surface and that the hockey ball will bounce the least.
Using the Gravitational potential energy equation:
Gravitational energy = Mass x gravity x height
Units: mass (kg), gravitational force (9.81 N/kg), height (metres)
The greater the height that a ball is dropped from the more gravitational potential energy there will be. This is clearly shown in the above equation.
It is also possible to work out the efficiency of a bounce when the height of the bounce is measured. The efficiency will show how much energy has been lost on impact with the wooden surface. Also an elastic material will have a high elastic limit. This means that it will have a lot of elastic potential energy. This will add to the gravitational potential energy.
Efficiency = (height of bounce / height dropped from) x 100 (as a percentage)
I can also calculate kinetic energy and velocity at impact with the surface.
Equipment:
* 2 x metre rulers
* Balance
* Range of balls
* Blue tack
Method:
Two metre rulers will be stuck onto a wall with blue tack, from the ground with one exactly on top of the other. One person shall drop a ball from a height while another will see its maximum height that it bounces. This will be repeated five times at each height for each bounce. The results should be taken after each bounce.
To ensure a fair test, the only thing that will be change during the experiment will be the height that a ball is dropped. I will keep everything else ...
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* Blue tack
Method:
Two metre rulers will be stuck onto a wall with blue tack, from the ground with one exactly on top of the other. One person shall drop a ball from a height while another will see its maximum height that it bounces. This will be repeated five times at each height for each bounce. The results should be taken after each bounce.
To ensure a fair test, the only thing that will be change during the experiment will be the height that a ball is dropped. I will keep everything else the same to ensure as accurate results as possible.
The heights that I will be dropping the balls from will be from 0.2 metres to 2.0 metres. These will be at 0.2 metre intervals. To ensure an accurate experiment I will repeat each test five times. From this I will take an average height for each ball at each interval.
Information on gravitational potential energy, kinetic energy, velocity, and elasticity will be from preliminary work done in physics in previous years during secondary school as well as from boos and sources from the internet.
Results table
Type of ball
Mass (g==>kg)
Height bal dropped from (m)
Height ball bounces (cm)
For five test for each ball
Average height of the bounce
Tennis ball
56==>0.056
0.2
8
9
8
0
1
9.2
0.4
8
21
22
24
23
21.6
0.6
34
32
35
33
33
33.4
0.8
47
49
48
49
46
47.8
.0
50
51
52
51
51
51
.2
61
61
57
57
58
58.6
.4
65
66
60
66
68
65
.6
76
78
80
77
82
78.6
.8
88
91
92
94
94
92.8
2.0
05
04
02
07
09
05.4
Ping pong ball
2.3==>0.0023
0.2
2
1
3
5
2
2.8
0.4
22
24
23
24
23
23.2
0.6
34
32
34
32
33
33
0.8
46
48
50
49
49
48.4
.0
57
58
60
57
59
58.2
.2
67
68
69
70
68
68.6
.4
81
79
78
82
81
80.2
.6
81
82
80
81
80
80.8
.8
88
87
86
86
87
86.8
2.0
90
96
95
91
92
93
Air flow ball
2.8==>0.0128
0.2
2
3
3
2
3
2.6
0.4
22
23
23
23
22
22.6
0.6
32
33
34
33
33
33
0.8
39
37
38
38
39
38.2
.0
46
45
45
44
43
44.6
.2
47
47
48
48
48
47.6
.4
55
53
52
53
52
53
.6
54
53
53
53
52
53
.8
61
59
56
55
56
57.4
2.0
58
59
57
59
60
58.6
Hockey ball
29==>0.129
0.2
9
9
0
9
0
9.4
0.4
7
6
7
7
7
6.8
0.6
26
27
27
26
27
26.6
0.8
32
31
33
32
32
32
.0
36
36
37
36
37
36.5
.2
42
44
41
43
41
42.2
.4
46
47
48
46
48
47
.6
53
55
54
54
56
54.4
.8
57
56
55
56
58
56.4
2.0
59
59
60
61
59
59.6
Golf ball
44.6==>0.0446
0.2
2
3
3
2
4
2.8
0.4
20
22
23
22
23
22
0.6
39
38
38
38
37
38
0.8
48
48
49
50
49
48.8
.0
57
57
58
59
59
58
.2
80
79
76
76
79
78
.4
83
89
87
82
85
85.2
.6
02
01
99
04
04
02
.8
08
09
12
17
15
12.2
2.0
17
21
24
22
25
22.8
Analysis
From my results it is clear that the higher a ball is dropped from the greater the height of the bounce. The different heights of bounces not only depend on the height that the ball is dropped from but also the type of ball. Factors such as size, weight and material can greatly affect the height of the bounce. Here is the order of the highest bounce of a ball to the lowest:
. Golf ball
2. Tennis ball
3. Ping-pong ball (table tennis)
4. Hockey
5. Air-flow
From the results and the graph, it is reasonable to say that there is a linear relationship between height of the bounce and height ball dropped from. This shows that the two terms are directly proportional to each other.
My prediction that the golf ball would bounce the highest was correct reaching an average maximum height of 122.8 cm, whereas the other part of the hypothesis was rejected as it was thought that the hockey ball would bounce the least, but in fact the air-flow ball bounced the least at an average maximum height of 58.6 cm, when dropped from 2m.
Using the gravitational potential energy equation, I will be able to show that gravitational potential energy increases with the height, giving a greater energy for the bounce, as I predicted. This will be done for each of the balls at the lowest (0.2m) and greatest (2.0m) heights that these were dropped from.
Gravitational energy = Mass x gravity x height
Type of ball
Height ball dropped from (metres)
Mass of ball (kg)
Gravitational force (9.81 N/Kg)
Gravitational potential energy (Joules)
Tennis
0.2
0.056
9.81
0.109872
2.0
0.056
9.81
.09872
Ping-pong
0.2
0.0023
9.81
0.0045126
2.0
0.0023
9.81
0.045126
Air flow
0.2
0.0128
9.81
0.0251136
2.0
0.0128
9.81
0.251136
Hockey
0.2
0.129
9.81
0.253098
2.0
0.129
9.81
2.53098
Golf
0.2
0.0446
9.81
0.0875052
2.0
0.0446
9.81
0.875052
The heaviest ball out of the 5 tested was the Hockey ball at 0.129 Kg, and the lightest ball tested was the Ping-pong ball at 0.0023 Kg.
It is also possible to calculate the efficiency of bounce for each of the balls use din the experiment. The efficiency will tell us how much energy has been lost in impact with the ground. This will be done for the biggest dropping height (2.0m), and for the average height of the bounce at that particular interval.
Height of the bounce (metres)
Efficiency = Height dropped from (metres) x 100
Tennis ball: 1.05
2.0 X 100 = 52.7%
Ping-pong: 0.93
2.0 X 100 = 46.5%
Air flow: 0.586
2.0 X 100 = 29.3%
Hockey: 0.596
2.0 X 100 = 29.8%
Golf: 1.228
2.0 X 100 = 61.4%
Here is the order of the most efficient to the least:
. Golf ball
2. Tennis ball
3. Ping pong
4. Hockey
5. Air-flow
Some of the areas where energy is lost are air resistance; sound and thermal energy at impact with surface.
When a ball is dropped onto a hard surface it will rebound, but it will not rise back to its initial starting position. When a ball hits the surface it exerts a force on the surface and the surface also exerts a force on the ball. This force causes the ball to be compressed. Hooke's law states when an elastic substance is stretched the extension is proportional to the applied force provided the elastic limit is not exceeded. As long as the compression is small, Hooke's law is satisfied the force is proportional to the displacement of the ball from its equilibrium shape. The force that the ground exerts on the ball does work on the ball, since it is in the same direction as the displacement. The gravitational potential energy the ball has before it is dropped is converted into Kinetic energy while the ball is falling and then into elastic potential energy as the force from the ground does work on the ball. But because the material the ball is made from is not perfectly elastic, internal friction converts some of the energy into thermal energy. The elastic potential energy stored in the ball when it has lost all its kinetic energy is converted back into kinetic and gravitational potential energy. The thermal energy however is converted back. Because some of its initial gravitational potential energy has been converted into thermal energy it does not regain its initial height.
It is also possible to calculate the velocity of a ball when dropped from the greatest and smallest heights.
Gravitational Potential energy= kinetic energy at impact
Gravitational potential energy = 0.5x mass x Velocity ²
Velocity ² = Gravitational Potential Energy
0.5 x Mass
This is assuming that no energy losses.
Tennis ball: 0.2m 0.109872
0.5 x 0.056 = 3.924 ==> 3.924= 1.981 m/s
2.0m 1.09872
0.5 x 0.056 = 39.24 ==> 39.24= 6.264 m/s
Ping-pong: 0.2m 0.0045126
0.5 x 0.0023 = 3.924==> 3.924= 1.981 m/s
2.0m 0.045126
0.5 x 0.0023 =39.24==> 39.24= 6.264 m/s
Air flow: 0.2 0.0251136
0.5 x 0.0128 =3.924 ==> 3.924= 1.981m/s
2.0 0.251136
0.5 x 0.0128 =39.24==> 39.24= 6.264 m/s
Hockey: 0.2 0.253098
0.5 x 0.129 =3.924==> 3.924= 1.981m/s
2.0 2.53098
0.5 x 0.129 =39.24==> 39.24= 6.264 m/s
Golf: 0.2 0.0875052
0.5x 0.0446 =3.924==> 3.924= 1.981m/s
2.0 0.875052
0.5x 0.0446 =39.24==> 39.24= 6.264 m/s
Even though the masses of the balls varied the velocities were similar, at the heights selected.
Evaluation
The purpose of this experiment was to determine how high certain balls bounced when dropped from different heights on the same surface.
In my opinion this experiment was fairly accurate as the same person's vision was used to see how high a ball bounced. Also the same person was used to drop the ball, and also no force was exerted when dropping the balls, as this would greatly affect the results. I used intervals of 0.2m; this was up to the height of 2.0m. To carry out this experiment two one metre rulers with centimetre increments were used. Five balls were used in this experiment, which were tennis, ping-pong, airflow, hockey, and golf ball. I ensured that the experiment carried out was fair, as the same surface was used to drop the balls onto, and the same ball, with the same mass was used for each test. In all, five tests were carried out.
However, the accuracy of this experiment could be improved. Firstly instead of using human vision to pinpoint the exact climax of the bounce for each ball, a camcorder could be used, and then shown in slow motion, this would ensure a more accurate result. Also to improve the accuracy and reliability of the experiment more tests could be done, in this experiment five tests were carried out for each ball at each interval, but to ensure a more accurate and reliable final results ten test could be done, then from this a an average for that interval for the ball could be used to calculate certain things, such as velocity. Using metre ruler with millimetre increments would give amore accurate and reliable result, but human vision may not be capable of pinpoint the peak of the bounce to the nearest millimetre.
The results for the ping-pong ball at the heights of 1.4 and 1.6 metres show the same height of bounce of 81cm for the first test at these intervals. This can be seen as inaccurate as it is stated that 'the higher a ball is dropped from the higher the bounce', in this particular case this does not show this. For the average of these heights the results were 80.2 cm for 1.4metres and 80.8 metres for the 1.6 metre interval. There is only a slight difference between these averages and clearly shows that this test can at times be unreliable, as human vision cannot be relied upon in such experiment that needs to be more or less exact, to guarantee a fair and reliable experiment.
Another result that appeared to be inaccurate was that of the height of 1.4metre and 1.6metre for the airflow ball. The average results appeared to be identical, one would see these results as 'wrong' or unreliable as one would expect the ball to bounce at a greater height when dropped from a greater height, but in this case the results do not show this. For the airflow ball in particular the results for each interval were very close together, which makes it more difficult for the person reading the height to pinpoint the climax of the bounce. This is an example why a camcorder would ensure a more accurate and reliable result, when the results for each height are so close together.
If I were to repeat this experiment again I would certainly ensure that I would use a camcorder/ camera to give amore reliable and accurate results. I would use millimetre increments to ensure more detailed and accurate results. I would make the maximum interval height to be 3metres instead of 2metres. This should give a more varied and may give more reliable results. By using the camcorder I would be able to use the slow motion feature to pinpoint the climax of the bounce. By doing ten tests instead of five for each ball at each interval, this would ensure more reliable results, but time needs to be considered.
I could take this experiment further by using a different variety of balls that vary in size and mass for example. I could extend this investigation by using different surfaces such as concrete and glass and see how the bounce is affected. Real surfaces are not perfectly hard. They distort when hit by a ball. They store energy themselves, and return some of it to the ball as it rebounds. Some surfaces, such as a trampoline, store energy very efficiently and return almost all of it to the rebounding object. Work out the time taken for each ball and compare the distance to the time taken for the ball to hit the surface, or the mass of the ball to the time taken. Or I could drop the balls in different areas that have different temperatures and see how this would affect the height of the bounce. I could use only one ball such as a tennis ball and compare how height it bounces to the height it is dropped from, and see if there is any relationship between the intervals and the maximum height they bounce. I could use on particular type of ball, such as golf balls, but use five of them and see how the mass of the ball can affect the height that it bounces. Such ideas could give more evidence, or extend my investigation in this subject field.
Tarik Saif 10 SN
