- Measuring the surface area of contact when the ball is dropped.
By measuring the surface area of contact of the ball when it falls, you should be able to notice a difference in size indicating how much energy was absorbed by the ball when it bounced. When the ball hits the ground the ball will deform slightly as it collides with the hard surface. Therefore, the bigger the surface area of contact, the greater the energy the ball has absorbed because the ball has squashed more.
The problem with this experiment is that it is very difficult to measure the surface area of contact of the ball when it hits the hard surface.
- Measuring the time taken for one bounce.
Here I could investigate whether the time difference is the same or different at different initial heights. However, this could also be difficult to measure as you have to have good reflexes to be able to start and stop the stop watch at the correct points of where the ball falls and rebounds.
Outline Method
In this experiment I will drop a tennis ball at various heights and calculate the fraction of energy absorbed by each bounce. From my results I will then be able to plot a graph and identify whether there is a relationship. In order to calculate the fraction of energy absorbed, I have already mentioned that I need to know the potential energy and kinetic energy, so with each result I will work out a value for the potential and kinetic energy at that height also.
Apparatus
- 1 Metre Ruler – I will use the metre ruler to measure the initial and rebound height of the ball for each set of results. The metre ruler is accurate to 1mm. This, usually, is not considered to be very precise but for the results that I am going to take I think that the metre ruler should be really precise.
- 1 ball (tennis ball) – I decided to use a tennis ball for my experiment because it was easily available to use in the science laboratory. Also, I knew that the ball is able to bounce and so I knew that I would obtain some results, whether they were what I expected or not.
- 1 Balance – I will use the balance to measure the mass of each of the balls. I need to measure the mass of the ball so that I can calculate the potential and kinetic energy of the ball at the initial height and the rebound height. The balance that I will be using is accurate to 2 decimal places. This will make my measurements very precise which will be good so that I can get an accurate, reliable reading for the fraction of energy absorbed the ball at different heights.
Variables
Here is a list of all the possible variables that could have an effect on my results in the experiment:
- Height of the ball,
- Size/Mass of the ball,
- Material of the ball,
- The surface that the ball is bounced onto,
- Pressure inside the ball.
As I am going to be looking at the relationship between the fraction of energy absorbed by the ball and the initial height, I will be varying the initial height that the ball is to be dropped from.
The size and mass of the ball will remain constant because I will only be using one ball. I will use the same ball for each set of experiments that I carry out so that my experiment will be fair and so that I will obtain reliable results.
The material of the ball will therefore also be the same throughout as I am not going to be changing the ball that I use.
I will drop the ball onto the same hard surface each time. I am dropping the ball onto a hard surface so that it will bounce.
Again, as the ball I am using is not going to change, the pressure inside the ball will therefore remain constant.
It is important that I keep as many of the variables constant as possible so that my experiment is fair and so that I can receive reliable results to conclude from.
Risk Assessment
When carrying out my experiments I have to be aware of any risks that are involved. In this particular experiment I don’t really think there are many risks as I am not using any chemicals.
However, I will have to be careful with the tennis ball that I am using. I will have to make sure that I do not leave the tennis ball lying around on the floor as anyone could easily slip and trip on the ball. As it is only a tennis ball, it is not as noticeable as a larger ball.
When carrying around the metre ruler I must make sure not to swing it around as someone may be behind me and get hit.
Developed Method
I had initially planned to drop a tennis ball at various heights and record the fraction of energy absorbed. Therefore I gathered all of the equipment that I needed to carry out the experiment and set it up as in the diagram above.
I will ensure that when setting up my experiments that there is a hard surface underneath for the ball to bounce on otherwise if there is a soft surface the ball will not bounce and so I will not be able to get the results that I need. To make each experiment fair I will therefore use the same area each time so that there are no other factors that will affect my results.
Firstly, I will measure the mass of the tennis ball by using the balance. I am recording the value of the mass of the ball because I will need it later when working calculating the value of potential and kinetic energy. I will lift up the tennis ball to the first initial height, 1metre. I will drop the ball and then record the rebound height by reading of the appropriate value on the metre ruler.
When trying to read off the rebound height on the metre ruler I did find it hard to read off an exact value because the ball will only be at the highest position for a split second. To come over this I tried to think of an alternative method of reading off the height. With some though I decided to continue carrying out the experiment how I intended but in addition I will use a video camera and a piece of squared/graph paper.
I will use the video camera to record the experiment so that later I can replay the video tape in slow motion and therefore read off the correct, accurate value of the rebound height. To squared paper will be used as a background against the metre ruler so that I can mark the highest point on the paper where the ball bounced and then read along to the appropriate height on the metre ruler. By using the video camera and the squared paper as a guideline, hopefully I will be able to read off accurate values of the rebound height.
Once I have recorded this accurate value of the rebound height, I will then continue to carry out the experiment in the same way but changing the starting height of the tennis ball. I will record results up to 1 metre every 10cm.
Looking at my results I then decided to get a few more recordings by taking readings up to 1.5 metres. I decided to do this so that I had a good range of results to plot on my graph and to make conclusions from. The more results that I would have taken, the more reliable my results would be because I have more to analyse.
As I had completed getting all of the necessary results needed for the tennis ball I then wondered whether different sized balls with a different mass would have an effect on the fraction of energy absorbed in a bounce. So to investigate this further I decided to take some more sets of results but with other balls.
The other balls that I used were a basket ball and a ping pong ball. I decided to use these other two balls so that I can obtain results from a different material and compare the fraction of energy absorbed. I specifically chose these other two types of ball because each one is different in size, material and in mass to the tennis ball I originally investigated. All of these different properties could well changes the fraction of energy absorbed when it bounces.
As I was now looking at two other balls as well, I had to also record the mass of the basket ball and ping pong ball using the balance. I recorded my results for these two balls in the same way as with the tennis ball by using the video camera and squared paper as a guideline. I also recorded the results for the same heights as with the tennis ball so that I could later compare the differences when I had worked out the fraction of energy absorbed.
Hopefully, by recording some extra set of data with these different sized and mass balls, I will improve the reliability of my results because I can look at a few balls overall rather than just focussing on the one tennis ball. To also improve the reliability of my results I took repeat recordings for each of my experiments.
Results
Here are the results of my experiments with; 1. A tennis ball,
2. A basket ball,
3. A ping-pong ball.
* See results sheet
I have displayed my results in Microsoft Excel because it allows me to use formulas and work out calculations easily. In each table I have displayed my worked calculations for the potential and kinetic energy from the heights that I have recorded. To calculate the potential and kinetic energy I have used the average of my sets of results so that I can obtain a general value for each height.
Graphs
I have decided to draw graphs of the initial height of the ball against the rebound height to show the relationship between the two. I have also decided to plot a graph of the initial height and the fraction of energy absorbed by the ball after the bounce. Each graph will help me to identify any possible relationships between the data. For both graphs I have plotted my results for each ball onto the same graph so that I can clearly distinguish any possible relationships and make comparisons.
Analysis and Evaluation
From my results I have been able to work out the fraction of energy absorbed by a ball as it falls from a certain initial height. From my results of the calculations of the fraction of energy absorbed I would have expected the percentage to have been more as all of the values were below 1%. But overall, the fraction of energy absorbed varies. I think that the value of the fraction of energy absorbed will depend on the ball and its properties, what it is made from, size and mass.
The first graph that I decided to plot was of the initial height of the ball when dropped and the rebound height of the ball. The graphs for all three of the balls clearly show a positive relationship between the values. If I were to plot a trend line onto the graphs, the line would be linear. The general patterns show that the bigger the initial height of the ball then the bigger the rebound height.
The results of the ping pong ball are much greater than those of the tennis ball and the basket ball. This would be because of its size, mass and the material it is made from. The ping pong ball had a very light mass and was the smallest of the balls that I sampled. Therefore, this shows that the smaller and lighter the ball, the bigger the rebound height.
Both the basket ball and tennis ball results are in the same range. The results are both lower than the ping pong ball results as they have a bigger mass and are bigger in size. The basket ball results are slightly bigger than those of the tennis ball. I think that this is because the basket ball is made out of a rubbery material which allows it to bounce more, despite it being a bigger ball than the tennis ball. The tennis ball is also made from a rubber but it is covered in a felt/carpet material which does not allow it to bounce as high.
The second graph is of the initial height of the ball and the fraction of energy absorbed in the bounce. There is also a relationship between these results too. It looks as though the bigger the initial height, the smaller the fraction of energy absorbed. Although in the middle of the results the graph is fairly level. Each of the graphs looks the same in that the fraction of energy absorbed is high at the lower heights but then as the initial height increases, the fraction of energy absorbed seems to level out. Perhaps this is due to the material of the balls. The material may have absorbed as much of the energy that it is capable of doing when dropped at these heights.
The overall results of the ping pong ball are lower than those of the basket ball and the tennis ball. I think that this is also to do with it being a smaller ball and having a smaller mass. As the ball is smaller it will fall towards the ground with a smaller force than a ball with a big mass.
The results of the tennis ball and the basket ball are similar in this graph as well. The results overlap towards the higher initial heights.
There are a few obvious anomalies in each of the graphs and they can be seen clearly. In the first graph, initial height against rebound height, there are a few anomalies for each of the balls when the initial height is highest. Perhaps this could be due to the fact that the ball balls faster to the ground and so will rebound faster making it harder to record the exact value for the rebound height. To improve the reliability of these results I could take a few more readings at these heights only so that I can take an overall average to use on the graph at these points.
The few anomalies on the second graph are also at the highest initial height region. This would be because I used the other results to work out these results, the fraction of energy absorbed by the bouncing ball. The error would therefore have been carried through into the calculation. There are also a few other anomalies at the other region of results, at the low initial heights. I think that this could be because at the smaller heights there is not much difference between the initial height and the rebound height so this will make it harder to read off an accurate value too. Again, to improve the reliability of these results I would take a few more readings in each of the high and low initial height regions.
One thing that I may have improved was how I released the ball from the initial height because it is not very accurate by dropping it by hand. Perhaps I could do this by placing the ball onto a ledge and then using a release mechanism to remove the ledge so that the ball will fall from the exact height.
I could also look at the effect of using a different surface that the ball will bounce on. This may improve my results if I find a surface that the balls will bounce on really well.
I could also investigate the effect of the initial height on the surface area of contact of the ball on each bounce.
I think that I could also look to see what effect the pressure inside the ball has on the fraction of energy absorbed by the balls and the rebound height of the ball.
I think that the results that I obtained are fairly reliable because they show the general relationship between the data. Also, I think that they are reliable because I have no major anomalies. Those anomalies that I do have, I have commented on and tried to explain why they occurred.
I think that another reason for the anomalies, apart from those already mentioned in my analysis is how the ball fell to the ground. How could I make sure that the ball did fall to the ground straight and not at an angle? This could have been a limiting factor of the experiment.
Other limitations are to do with the precision of the equipment. Although I thought that a metre ruler would be accurate enough for my results, I think that if I was able to take more accurate readings then I could improve the overall reliability of the results as the results and calculations will be more accurate.
Although my results are not as accurate as they could have been, I think that I have still been able to show that there is a relationship between the initial height and the rebound height, as well as the fraction of energy absorbed by the ball as it hit the ground. I have therefore been able to answer my question that I set myself at the beginning of the experiment.
References
- ‘Practical Physics at A-Level’, by Trevor Cross – p105