The bounce height of the ball is a function of the intrinsic qualities of the ball. Elevating the ball to a certain height will cause it to gain gravitational potential energy that is equal to the amount given by the equation E = mass x gravity x height. (The value of gravity on earth is approximately 9.81m/s²)
Therefore, the higher the ball is, the higher the potential energy it has.
When the ball is dropped, the gravitational potential energy is transformed into kinetic energy, which is given by the equation E= 0.5 x mass x velocity².
In perfectly elastic collisions, the total kinetic energy of the two bodies that collide stays the same. In inelastic collisions, some of the kinetic energy is lost to internal molecular movement.
When a ball is dropped from a certain height and collides with the ground, it is an inelastic collision. Therefore, some of the ball’s kinetic energy is lost to internal molecular forces, and it has less potential energy than it did before and therefore reduces its bounce height. Thus, a ball that is dropped from a certain height will bounce to a height that is less than the original level from which it was dropped. The physical properties of the ball determine the extent to which the collision will be inelastic. Some materials, such as rubber, preserve more of the kinetic energy, while other materials will dissipate it to a greater extent. That is why different kinds of balls will bounce to different heights after they are dropped.
Variables
The variables in my investigation will be:
Height from where the ball is dropped
Mass of the ball.
Temperature of the ball.
Material of the ball.
Surface area of the ball.
The velocity with which the ball is dropped.
My independent variable will be the height(s) from which I drop the ball as I will be changing this in a uniform manner. I will start with a height of 50cm and add 50cm consecutively for each experiment until a total height of 250cm.
The dependant variable will be the height that the ball reaches once it bounces as this value will depend on the height that the ball is dropped from.
In order to keep the experiment a fair test, the following will be kept constant:
Mass of the ball.
Material of the ball.
Surface that the ball is bounced on.
The velocity at which the ball is dropped.
Surface area of the ball.
In all of the experiments, the ball will be dropped from just above its mark. Ie : The edge of the ball will be touching the 50cm mark for when it is being dropped from 50cm. The same will be repeated for all experiments.
Apparatus
A bouncing ball
Rulers – To measure the height that the ball is dropped from and to measure the height of the bounce.
Balance – To measure the mass of the ball.
Tape – To hold the rulers against the wall.
Method
I will begin by measuring the mass of the ball.
I will then tape the rulers against a wall.
I will then drop the ball from a height of 50cm and record the height of the bounce.
I will record the results in a suitable table.
I will then repeat the same experiment another 4 times so as to get 5 readings in total to ensure that readings are more accurate.
I will then repeat the experiment, dropping the ball from a height of 100cm this time.
This will continue with the height from where the ball is dropped increasing by 50cm each time until the final height is 250cm.
Each height will have 5 corresponding readings.
Readings
Initial height of Ball (±0.0005m)
Height of Bounce (±0.0005m)
Test 1 (cm)
Test 2 (cm)
Test 3 (cm)
Test 4 (cm)
Test 5 (cm)
Average (cm)
50cm
40.6
41.4
39.5
39.1
40.0
40.12
100cm
80.5
78.2
76.1
82.2
83.2
80.04
150cm
115.5
114.2
113.0
109.8
117.3
113.96
200cm
142.2
137.7
144.9
143.0
146.4
142.84
250cm
177.8
180.1
183.1
189.4
182.5
182.58
The average of the results is calculated as follows:
(T 1 + T2 +T3 + T4 + T5) / 5
Put into context:
(40.6 + 41.4 + 39.5 + 39.1 + 40.0) / 5
= 200.7 / 5
= 40.14cm
Graph
Average Graph
Energy of the Ball
To prove that energy transfer takes place, I decided to calculate the potential energies of the ball before and after it has been bounced. To calculate potential energy, the formula PE = MGH is used where:
‘M’ is the mass of the ball.
‘G’ is the gravity (9.81m/s²).
‘H’ is the height of the ball.
The mass of the ball is 4.8g.
Initial height of Ball
Amount of Potential Energy at Initial Position
50cm
23.6 J
100cm
47.1 J
150cm
70.6 J
200cm
94.2 J
250cm
117.8 J
Final height of ball (Average)
Amount of Potential Energy at Final Position
40.12
18.9 J
80.04
37.7 J
113.96
53.7 J
142.84
67.3 J
182.58
86.0 J
From the above tables, the change in the values of energy can easily be noticed. This can be used to show why a ball that is bounced doesn’t attain the same height it is dropped from after it has been bounced. The difference in the values of potential energy can be used to show that some energy is converted into sound, heat or other energies whilst the ball is being bounced.

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Analysis
After analyzing my results, I noticed that there was a trend amongst my readings. As the height from which the ball is increased, the corresponding height of the bounce of the ball will be high. For example, when the ball was dropped from 50cm, the average height of the bounce was 40.12cm. However, when the ball was dropped from 100cm, the average height of the bounce was 80.04cm.
I also noticed that as the height from which the ball is dropped increases, the potential energy increased. For example, when the ball was dropped from 50cm, its final potential energy was 18.9 J. However, when the ball was dropped from 100cm, its final potential energy was 37.7 J.
The trend here is that as the height from which the ball dropped increases, the more its potential energy will be. This therefore leads to the height of the bounce to be greater. This trend proves my hypothesis.
Conclusion
A bouncing ball constantly changes between kinetic energy and potential energy. When it is dropped, it slowly loses its potential energy which is converted into kinetic energy. When the ball hits the ground, it loses some of its energy in the form of heat and sound which therefore causes its overall energy to drop. Because of this energy drop, we can safely conclude that the ball cannot reach the same height as which it was dropped from due to the loss of some of its energy and therefore the speed at which it leaves the ground after the bounce will be less.
As the law of conservation states that energy cannot be created nor destroyed and therefore the initial potential energy of the ball is equal to the sum of the potential energy of the ball after the bounce, the heat given off by the ball and the sound energy created by the ball.
I also learnt that the higher the height that the ball is dropped from, the more its velocity will be when it hits the ground and therefore the amount of kinetic energy will be higher. (Velocity is directly proportional to Kinetic energy through the equation:
http://i.ajdesigner.com/energy/kenetic_energy_equation.png
I have come to the conclusion that as the height at which the ball dropped increases, the corresponding height of the bounce will be higher. However I think that eventually the height of the bounced ball becomes constant as the height at which the ball is dropped increases. This occurs when the ball reaches terminal velocity. This implies that no matter what height the ball is dropped from, the bounce height will remain constant. However this is only noticed after a certain height because the ball takes some time to reach its terminal velocity and therefore a height of approximately 100cm won’t enable the ball to reach its terminal velocity.
Evaluation
I think my procedure and successful as my measurements were quite accurate, I ensured that I had no systematic error and tried to minimize the chances of having a random error by repeating each experiment 5 times which showed that I carried out my investigation well.
I found it challenging to record the exact height of the bounced ball because it only occurs for a split second. This was the reason that I carried out the experiment 5 times, so as to ensure that my results would be reliable and accurate. In order to improve the accuracy of my results, I could have performed the experiment with a friend. Whilst one of us could have dropped the ball, the other could have recorded the height of the bounce. This could have possibly minimized error. However, my results still managed to prove my hypothesis and they were sufficient enough to make a conclusion.
Another way in which I could have improved the accuracy of my results was through using a camera. If I used a camera to take a video of the experiment, I could have obtained very accurate results as the exact height of the bounce could be obtained through the use of the slow motion feature on the camera.
I would have liked trying the same experiment from higher heights as well as working with energy transfers within a ball to find out how energy transfers vary as the height from which the ball is dropped changes. This would have enabled be to form a more conclusive conclusion.
On the whole, I found my experiment to be successful and helped me gather a deeper understanding of the different factors that affect the bounce of a ball coupled with the various energy transfers that take place in a bouncing ball.