I have decided to investigate how the height from which a squash ball is dropped affects the height of its bounce.
When a ball is dropped, it accelerates until it collides with the surface – an impact. It then recoils, and some of the energy is reflected back upwards, causing it to bounce. I believe that as the height from which the ball is dropped changes, the speed of the ball at the moment of impact will also change. This is because when the ball is dropped, it accelerates due to the force of gravity.
Newton’s law states that if the force acting on an object is not zero or the resultant force acting is not zero then the object will accelerate. In this case, the force acting on the object (gravity) is greater than the air resistance, so the object accelerates downwards.
Theoretically, when the ball is travelling at a faster speed, there will be more force at the point of impact (due to the increased kinetic energy).
Therefore, more potential energy will be stored in the ball as the collisions takes place, which will then be converted back into kinetic energy as the ball bounces. This increase in force due to the faster speed means that the ball will, theoretically, bounce higher.
This is true up to a certain point. As the ball speeds up, the air resistance against it increases. At a certain point, the air resistance and the pull of gravity will balance each other out, so there will be no net force affecting the ball.
Newton stated that if the force acting on an object is zero or the resultant force acting is zero, the object will stay still or move at constant speed in a straight line (constant velocity). This means that once the squash ball reaches a certain speed (its constant, or terminal velocity), it will cease to accelerate. Therefore, no additional speed will be acquired, and so the impact force will be the same. This means that once the terminal velocity can be reached, the drop height should no longer affect the bounce height.
There are also a number of variables other that could affect the bounce height of a squash ball. In order to make this experiment fair, I need to eliminate any other variables that might affect the results.
Table to show the possible variables in this experiment, and how to control them
To be investigated in this experiment.
This will be the independent variable.
Temperature of ball.
If the ball is hotter, when it impacts the surface it could change shape more easily. This would mean that it would become more compressed, which could increase the amount of potential energy stored by ball, and therefore its bounce height.
Keep the ball temperature (room temperature) the same in each experiment, and carry out all experiments on the same day to prevent variations in room temp affecting the results.
Different surfaces may disperse energy at different rates, so different amounts of energy may be reflected back into the ball, thus affecting its bounce height.
Always drop the ball onto the same surface.
Force with which the ball is dropped (starting speed of ball)
The starting speed of the ball may affect the time taken for the ball to reach its terminal velocity, altering its speed on impact and therefore bounce height.
Make sure that no extra pressure is applied to the ball when it is dropped, so that the starting speed is always 0 m/s.
The constitution of the ball
It is unlikely that all squash balls will be identical, and therefore some might bounce more than others.
Use the same ball throughout the experiment
Bounce height
This is the dependent variable, and it will be investigated, measured and recorded
Measured in m.
4) Preliminary Work
My preliminary work involved running the experiment through as I planned to do to obtain the results to be used in this investigation. In order to get enough data, I decided to get five pieces of data for each height. All measurements will be taken from the bottom of the squash ball, as this will touch 0.0 m (the surface).
My method was as follows:
i) Set up the equipment – a clamp stand, clamp, and metre ruler.
ii) Drop the squash ball from 0.2 m, and record how high it bounced.
iii) Repeat this so that 5 pieces of data are obtained for this height.
iv) Repeat stages ii to iii, increasing the height by 0.2 m each time, and ensure that each height has been tested 5 times.
Table to show bounce height of a squash ball
when dropped from different heights
Fall Height/ m
Bounce height/ mx10��
1
2
3
4
5
Average
0.2
2
2
2
3
1
2
0.4
7
7
8
9
8
8
0.6
10
11
12
11
11
11
0.8
14
15
14
15
14
14
1.0
17
16
18
17
17
17
1.2
19
20
19
20
20
20
1.4
20
21
20
22
21
21
5) Comments on Preliminary Work:
From my preliminary work, I gained some useful experience in running this experiment. As well as having a chance to check my methodology, I learned that a few things needed to be changed in order to make the experiment run more smoothly and efficiently.
I found that it was very difficult to drop the ball from some heights and then get low enough to note how high the bounce was. I therefore decided to employ the assistance of a ball-release mechanism to allow me to release the ball with my eye lower down, so I could get a better idea of how high the bounce was.
Even after changing this, I found that it was fairly difficult to accurately measure how high the squash ball bounced. Ideally, I would be able to film the bouncing of the ball in order to take still images and therefore accurately see the height of the ball at the top of its bounce. Unfortunately, I have not got this equipment available, so I will have to try to repeat the experiment many more times in order to get some useful results.
Originally, I had felt that a range of 5 heights to be dropped from would be sufficient. However, when carrying out the preliminary experiment, I decided to extend this range to 8 heights – extending the uppermost value by 0.4 m, and also including 0.0 m. This was because, when dropped from the height of 1 m it was evident that the terminal velocity of the ball had not been reached by the time it hit the surface. I thought that increasing the highest drop height would allow me to find the height from which the ball needed to drop in order to achieve terminal velocity before impact, or, at least, enable me to estimate this height better.
6) Prediction
I predict that the higher the ball is dropped from, the higher its bounce will be. As well as being intuitive, there is a scientific reason for this too.
I believe that as the height from which the ball is dropped increases, the speed of the ball at the moment of impact will increase. This is because when the ball is dropped, it accelerates due to the force of gravity. Newton’s law states that if the force acting on an object is not zero or the resultant force acting is not zero then the object will accelerate. In this case, the force acting on the object (gravity) is greater than the air resistance, so the object accelerates downwards.
When the ball is travelling at a faster speed, there will be more force at the point of impact (due to the increased kinetic energy). Therefore, more potential energy will be stored in the ball as the collisions takes place, which will then be converted back into kinetic energy as the ball bounces. This increase in force due to the faster speed means that the ball will, theoretically, bounce higher.
This is true up to a certain point. As the ball speeds up, the air resistance against it increases. At a certain point, the air resistance and the pull of gravity will balance each other out, so there will be no net force affecting the ball. Newton stated that if the force acting on an object is zero or the resultant force acting is zero, the object will stay still or move at constant speed in a straight line (constant velocity). This means that once the squash ball reaches a certain speed (its constant, or terminal velocity), it will cease to accelerate. Therefore, no additional speed will be acquired, and so the impact force will be the same. This means that once the terminal velocity can be reached, the drop height should no longer affect the bounce height.
7) Experimental Plan
a) Apparatus:
* Squash ball
* Stand
* Clamp
* 1 m ruler
b) Diagram of apparatus:
a)
c) Full method:
i) Set up the equipment – a clamp stand, clamp, and metre ruler.
ii) Drop the squash ball from 0.2 m, and record how high it bounced.
iii) Repeat this so that 10 pieces of data are obtained for this height.
iv) Repeat stages ii and iii for all heights, and ensure that each height has been tested 10 times.
d) Range of measurements:
I decided that I would record data for the bounce heights from balls dropped from 8 different heights:
0.0 m 0.2 m 0.4 m 0.6 m 0.8 m 1.0 m 1.2 m 1.4 m
I believe that these will give me a good range of results for several reasons. Firstly, I felt that this range would be appropriate because it would be relatively easy to control the experiment. If I dropped the ball from a greater height (for example, 2 m), I would not be able to bend down quick enough (even with the aid of the release mechanism) to get a reasonable idea of how high the bounce was. It would also present a much greater health and safety risk, as I would have to stack objects underneath the clamp stand in order to get it high enough.
I decided to spread my heights in intervals of 0.2 m, because I felt that it would give me a good spread of data. I used 0.2 m intervals because I thought that if the spacing was any less, it might be difficult to accurately measure see the difference between the bounce heights. This would mean that any slight inaccuracies in the measuring process (which I have already identified as a potential problem) would be less significant.
e) Reliability of evidence:
To get reliable results from this experiment, there are a number of things which must be addressed. The most important of these is controlling all other variables which may affect the investigation. Therefore, it is of utmost importance that I hold a fair test, which can be achieved by doing the following:
* Dropping the ball on the same surface each time.
* Measuring the bounce height from the same place (the bottom of the ball) in each case.
* Measuring bounce height to a common degree of accuracy (measured in metres to 2 decimal places).
* Not holding onto the ball for too long in order to try and keep the ball temperature constant.
f) Sufficiency of Results:
In order to ensure that I provide sufficient data to support my conclusions and proving my theory, I will aim to collect ten pieces of data from each drop height value. This will enable me to identify any anomalous results, to get a fairly reliable average, and to therefore have a more accurate set of results.
g) Safety
Having equipment stacked at a height of 1.4m (above desk height) could present a health and safety risk. If the equipment collapses, the heavy clamp stand could strike someone nearby, potentially causing injury. To overcome this hazard, I will ensure that I am careful and do not allow the equipment to fall.
2. Obtaining Evidence
1) Modifications to method
As a result of my preliminary work, I made a number of modifications to my original method. Firstly, I found that it was very difficult to drop the ball from some heights and then get low enough to note how high the bounce was. I therefore decided to employ the assistance of a ball-release mechanism to allow me to release the ball with my eye lower down, so I could get a better idea of how high the bounce was.
Even after changing this, I found that it was fairly difficult to accurately measure how high the squash ball bounced. Ideally, I would be able to film the bouncing of the ball in order to take still images and therefore accurately see the height of the ball at the top of its bounce. Unfortunately, I have not got this equipment available, so I will have to try to repeat the experiment many more times in order to get some useful results.
Originally, I had felt that a range of 5 heights to be dropped from would be sufficient. However, when carrying out the preliminary experiment, I decided to extend this range to 8 heights – extending the uppermost value by 0.4 m, and including a release height of 0.00 m. This was because, when dropped from the height of 1m it was evident that the terminal velocity of the ball had not been reached by the time it hit the surface. I thought that increasing the highest drop height would allow me to find the height from which the ball needed to drop in order to achieve terminal velocity before impact, or, at least, enable me to estimate this height better.
2) Variables
* The variable that I had control over in this experiment – the independent variable – was the height that the ball was dropped from, measured in m.
* The variable that I was recording – the independent variable – was the bounce height, measured in m.
* There were several controlled variables in this practical. They were:
o Temperature of ball.
o Surface onto which the ball is dropped.
o Force with which the ball is dropped (starting speed of ball).
o The constitution of the ball.
3) Results Table
Table to show bounce height of a squash ball when dropped from different heights
Release height/m
Bounce height/ m x 10��
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.2
4
3
3
5
5
4
3
3
5
4
5
4
3
3
3
0.4
6
5
7
7
7
6
8
7
7
8
5
8
7
6
7
0.6
10
9
10
10
12
11
11
10
10
12
11
10
11
10
11
0.8
13
12
14
14
13
12
12
14
12
13
14
13
13
14
13
1.0
15
15
16
16
14
16
15
17
16
16
15
16
17
16
15
1.2
18
17
17
18
17
17
19
18
19
18
18
17
19
18
18
1.4
20
21
21
20
20
21
22
20
21
21
22
20
21
20
22
3. Analysis
1) Process Results
In order to process my results to give a useful graph, I decided to find an average bounce height for each release height. This would enable me to plot a graph that would be functional and represented all of the data I collected.
In order to get an average, I simply added all the data values up for one release height and divided the result by 15 (as this was the number of data that were collected for each). This was then repeated for every release height.
I also converted all of the data into metres so that it could form a better graph.
These were displayed in a table, as below.
Release height/ m
Bounce height/ m
0.0
0.00
0.2
0.04
0.4
0.07
0.6
0.11
0.8
0.13
1.0
0.16
1.2
0.18
1.4
0.21
I then used this information to create a graph using the Microsoft Excel program.
2) Graph
3) Comment on Results
My results show that the higher the release height, the greater the bounce height. The relationship between release and bounce heights appears to be linear.
4) Analysis
I know that when a collision takes place, momentum is conserved. This applies when the squash ball hits the surface – a collision takes place. Although some of the momentum is lost through the surface, some of it is reflected back up (due to the fact that the surface does not move). This means that the squash ball bounces back as it hits the surface.
To explain why the bounce height got higher as release height increased, I will refer to the Newton’s second law, which states the following:
“If the force acting on an object is not zero or the resultant force acting is not zero then an object will accelerate, where F = m x a.
F is in Newtons, m is in kilograms and a is in m/s2.”
[Note: If the resultant force on an object changes, is not constant, then the acceleration is not constant (uniform) either.]”
This equation shows us that when a force (gravity) is applied to an object (the squash ball), in accelerates. Therefore, the further the squash ball is from the surface, the longer it will have to accelerate, and therefore the faster it will be travelling on impact.
Kinetic energy is found by the following formula: KE = 1/2mv�
This formula shows that the higher the velocity of an object (v), the more kinetic energy it will have. Therefore, an object falling faster will have more energy, and so when it collides with a surface, it will bounce higher. This explains my results.
5) Conclusion
I conclude that my results strongly support the prediction. I predicted that the higher the release height, the higher the bounce height would be, and this was verified by my experiment.
4. Evaluation
1) Accuracy of Observations/Measurements
I feel that the accuracy of my measurements could have been improved drastically. I had to take crude approximations due to the nature of the squash ball bounce – it was impossible to tell exactly how high the bounce was with the naked eye alone. In order to improve this, I feel that it would have been beneficial to use a video recorder or similar device in order to record the bouncing on tape. I could therefore have reviewed the recordings, and paused them at the zenith of the bounce, thus enabling me to accurately measure and record the precise bounce height on each occasion.
2) Anomalous Results
My results, although slightly varied at each interval, did not seem to have any anomalous values. I believe that this is because I took the utmost care to prevent anything from causing a significant discrepancy between items of data.
3) Explanation of Anomalous Results
If I had had any anomalous results, it could have been for one of the following reasons:
* The ball bounced up at an angle.
If the ball had bounced on an angled surface, it would not have bounced straight back up. This would affect the results. To prevent this from happening, I made sure that the surface was reasonably flat.
* The ball was affected by another force.
If the ball had been affected by another force, such as a movement of air (for example, a draught), it could have altered the way it fell and bounced. To avoid this, I made sure that the windows were closed while doing this experiment.
4) Suitability of the Method
I feel that the method I used was entirelysuitable, and I can find no problems with its design.
5) Reliability of the Evidence
From my analysis, I feel fairly certain that my prediction has been proven to be correct, and my conclusion is true. I think that I repeated the experiment enough times to show this. In order to obtain reliable values, however, I believe that it would be necessary to repeat this experiment whilst measuring the bounce height correctly (e.g. with a video camera) in order to obtain precise measurements.
6) Improvements to the Method
In order to improve my method, I could use a video recorder in order to measure the bounce accurately. I could also have used a perfectly flat, smooth surface to bounce the ball on, ensuring that any (however small) irregularities in the worktop surface which I used would not affect the results.
7) Extension Work
In order to investigate squash ball bounce heights further, there are a number of things I could do. Firstly, I could extend the range of heights that I investigated – maybe up to 2 m – to try to ascertain how high the drop had to be before terminal velocity was reached. I could also decrease the intervals between each release height – maybe from 0.2 m to 0.1 m – to get a clearer idea of the pattern, and to prove that it is in fact linear. Furthermore, I might examine the effect of other variables, such as temperature, on the bounce height of the squash ball.
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