With this higher internal pressure the ball won’t deform as much as it normally would when it hits the surface and it will also recover its original shape faster. If only a small amount of deformation occurs then only a small amount of energy will be wasted on changing the shape. Also, if the ball has more energy, then it will recover it’s shape faster thus pushing itself of the ground with greater force.
Safety:
To prevent injury from the hot water in the baths I will ensure care is taken to keep them well away from the edge of the bench. I will also use tongs to place and remove the balls from the hot water. To prevent burning fingers on the hot balls gloves will be worn.
Experiment
I performed my experiment using the above plan. No changes were made, except the ruler wasn’t held by a stand and grips. Instead one of my peers held it upright for me and it was at right angles to the bench.
I used three different bounce heights to give me a broader range of results. The different heights and temperatures will help me see if the pattern of results is similar. I repeated each bounce three times to enable me to see a pattern or make certain any anomalous results weren’t the norm.
The bounces were conducted in under a minute to ensure that minimum cooling occurred, so the temperature will be accurate to within a degree. The values in the temperature column were taken from the hot water bath, not the ball.
When bouncing the ball I discovered that the results would be inaccurate if I didn’t move my eyes to a position opposite to where the ball rebounded. This is called parallax error and it is where perspective effects what you can see, for example if I was looking down at the ball whilst recording its height the height I would see would be different to the height achieved by the top of the ball.
The height I recorded was the height achieved by the top of the ball.
Table of Results:
As you can see there are three columns, one for each bounce height. The height achieved by the ball is beneath the heading ‘bounced from’. I decided that putting them under another heading would be confusing. The heights are rounded to the nearest centimetre.
The table shows the raw data collected from my investigation. One trend is immediately obvious; the rebound height increases with temperature.
Analysis
I feel that the table above is inappropriate for displaying my results so I’m going to process them into new tables. To achieve this I will change the results into averages as this should make any trends or anomalies stand out. The statistical average I will use is mean and the workings are shown below.
For bounced from 20cm;
300C=(4+6+6)/3=5.3cm
400C=(7+8+9)/3=8cm
500C=(10+11+11)/3=10.7cm
600C=(13+12+14)/3=13cm
800C=(15+15+14)=14.7cm
900C=(16+17+13)=16.3cm
For bounced from 40cm;
300C=(9+9+11)/3=9.7
400C=(14+16+16)/3=15.3
500C=(16+17+19)/317.3
600C=(22+26+24)/3=24
800C=(28+30+27)/3=28.3
900C=(31+32+32)/3=31.7
Table of Mean Results:
The above shows all my results for each bounce height and each temperature collected into averages. The rebound height is under the columns headed ‘bounced from’ and is in cm.
As my results for each bounce a similar pattern I am going to change them into one average. This will give me one bounce and so I will have just one variable, temperature. If you would like to see graphs displaying the individual data then please refer to appendix one.
Second table of Mean Results:
Bounced from 40cm
This table shows all my results turned into a mean using the same method as I did on my first mean table.
Graph of Mean Results: (refers to a separate sheet)
The graph shows a clear relationship between height achieved and temperature. As the temperature is increased the bounce height increases also. At a low temperature the squash ball doesn’t bounce very high, but the rebound gets greater and greater, steadily increasing with temperature. The curve steadily gets less steep until at 900C it veers up again. This is an anomalous result and I will explain it my evaluation.
I have drawn a dotted line down to x=30 and y=0 the sense of drawing such a line is in doubt. I know that at a certain temperature the ball will rebound very little (it will be almost completely plastic or frozen). I also know that at thirty degrees Celcius the ball rebounds to 10cm. So by drawing a line down to the x-axis I can indicate that the bounce of the ball does lessen, but I can’t indicate the temperature at which this occurs because I have no results. It is because I have no results below 300C that the sense of the line is in doubt (I cannot prove it is so). I will, however, leave it in to show the bounce does lessen (as has been proved by physicists).
Conclusion
My results show a clear correlation between temperature increase and the height achieved when bounced (refer to graph of mean results). This is in accordance with my prediction, which stated that the bounce height would increase with temperature. So this means that heating the ball does give it more energy than it originally had. The sort of energy must be kinetic energy, in the molecules of the rubber and air. Heat energy is also present.
Intermolecular forces of attraction hold solid matter together. These forces can be described to be like springs holding the elastic material together. When a squash ball hits a surface these springs are compressed and stretched. The stretching and compressing of the springs stores the kinetic energy of the ball as potential elastic energy (p.e.e). When all the kinetic energy has been stored the spring will release the p.e.e. back into k.e. by returning to their original shape. Some of the kinetic energy is lost during this transition and it becomes heat energy (warming up the springs). So the ball doesn’t bounce back to its original height.
The higher the temperature of the rubber the greater the vibration of the springs and if the temperature becomes hot enough the material melts or leaves as a gas and the springs are broken and the material is no longer elastic but becomes a fluid or gas. Also many elastic materials such as rubber become very brittle at extremly cold temperatures and loose their elasticity and will shatter like glass if they are dropped. This means that the behaviour of the springs holding the matter together is strongly affected by temperature.
Matter in a gas is not held together by intermolecular forces of attraction but is the opposite. The molecules are whizzing about at speed, because they have so much energy that they have broken the intermolecular forces of attraction. In gases the hotter they are the more kinetic energy they have in the form of the molecules moving with more speed.
When a gas is moving at high speed there are more opportunities for it to collide with other molecules. Also as a result of going faster the collisions will have more force. Heating a gas has a dramatic effect on the pressure; in fact there is a law, which states that, in a container of constant volume, Pressure is proportional to Temperature. So if you up the temp you up the pressure.
I conclude that it is mainly the increased pressure of the air within the ball that leads to an increase in bounce efficiency. I can assume that the ball is a container of constant volume, as it is sealed, so the pressure would increase if the temperature were increased. The increase in pressure means that the air molecules inside the ball will be hitting the internal surface more often, which will give the ball more kinetic energy. When the ball deforms it is pushed back into shape by the air. As the air has more kinetic energy the ball will be pushed back into shape faster than it otherwise would. A faster recovery of the original shape means that the ball will push itself off the surface faster and with more force than it otherwise would. Such an occurrence means that the bounce height of the ball will be increased.
The rubber itself also has more energy, which can be found in the molecules making it up. The energy is expressed by the greater vibration of the molecules, stretching and compressing the springs holding it together (felt as heat). When the ball impacts with the surface the springs are stretched and compressed. So the heat of the ball must augment the rebound in the sense that the molecules already have kinetic energy. This also increases bounce efficiency.
Evaluation
The experiment on the whole was a success in the sense that I obtained a large range of results. The repeat results were very close together, which is good because I can assume there were no other significant variables involved. The amount of readings I have taken, 54 in total, ensures that any pattern is easily detected. The results are reliable because I took such a large range of readings. My evidence easily supports the conclusion I have come to. Still there are some improvements I would make if I were to repeat the experiment.
There was one anomalous result in the experiment, which is immediately obvious when you look at the graph of mean results. All the results up to 800C follow a pattern, which gradually gets less steep, but when 900C is reached suddenly the curve gets steeper, veering from the course it was on. The problem can be traced back to the original table of mean results, at a temperature of 900C for ‘bounced from 60cm’. It is here that the result suddenly leaps from 36.3cm (for 800C) to 43cm (for 900C); whereas all the other bounce heights and temperatures follow a clearly defined pattern.
This could just be a strange anomaly that occurs at 900C for a bounce height of 60cm. The result cannot be ignored, however, for I got the same reading three times. If I had the result after that reading then I would be able to see if the curve went back down or if it continued on that steepness or balanced out there after. For know all I can say is that it could be a mistake of the reading on my part. Or it could be a strange property of the ball that at a certain temperature and bounce height its bounce efficiency suddenly increases dramatically (which I doubt). I am going to put the result down to human error because the other two bounce heights don’t display the same property at that temperature.
Such an anomalous result as this doesn’t undermine my conclusion because it still follows the same pattern of bounce increasing with temperature. It does put the effectiveness of my method and the reliability of my evidence into doubt simply because it is ‘out of the norm’.
Improvements:
There are some improvements I would like to make to my method to improve the reliability of my results. Firstly, after taking the first reading I would place the ball back in the bath for a minute to ensure that the temperature stays fixed for each height. Secondly, I would do some higher and lower temperatures to see if there is a maximum bounce height or if the bounce height gets higher and higher until the ball melts. I would also like to repeat the whole experiment at least three times to ensure maximum reliability.
Further Work:
Other experiments would involve testing the balls internal pressure at different temperatures. This would offer more support for the theory that the balls pressure does go up with temperature. Another thing I could do is to pump more air (thus raising the internal pressure) into the ball and see if this makes a difference to the height achieved when bounced.
I would also like to test the elasticity of other solids (ones without air inside) and see if their bounce efficiency went up with temperature.