PV = constant
The elasticity of the ball derives from the fact that the air inside the ball tries to return to the lowest possible pressure, i.e. a spherical form.
Greater range of heights at which the balls are being dropped. Also I will do repeats because I will have more time available. Just like the preliminary experiment one person will drop the ball and the other person will record how high the ball returns. Measurements will be taken from the bottom of the ball by sight against a ruler.
I think that there will be a certain percentage of the height that the ball will return to. This is because the higher you drop the ball from; the more the ball is deformed. The more the ball is deformed, the more energy is lost due to vibrations in the ball and the surface (as heat and sound).
As a lot more energy will be used to deform the ball, the ball’s elastic energy will be increased. When the ball stops being deformed, it will try and spring back to its original shape, converting the elastic energy into kinetic energy again. The energy used to do this will increase as the height that the ball is dropped from increases, and so the height that the ball returns to will increase as well.
Also more energy will be lost as heat due to friction from the air as the ball will be dropping a greater distance.
I predict that the height that the ball is dropped from will be directly proportional to the height that it returns to. I think that the graph will look like this. The rubber ball doesn’t lose a lot of energy so I think that the height returned will be slightly lower than the height dropped.
Height ball
returned to
(m)
Height ball dropped from
(m)
Ball - It has more elastic energy and therefore loses less energy and might be more reliable. Also it is easier to measure at which height it returned to, as it is smaller than the tennis ball.
2 metre rulers - This is so the ball can be dropped from a larger range of heights producing more accurate results.
Consistent floor - I will use the floor in the classroom (flat, hard) for a fair test
- Set up equipment as shown in the diagram.
- Drop ball from 0.25 metres.
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Repeat step 2 for 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 metres. This is a large number and range readings so results should be accurate and reliable. 2 metres is the highest dropping point as it is hard to easily reach any higher with just a stool.
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Repeat steps 2-3 twice so that you get an average and so can detect any anomalies. This makes the results more reliable.
Controls
- The ball used must always remain the same because if there was a change in volume, material or mass then the elasticity would be different and so it wouldn’t be a fair test.
- Always drop the ball onto the same surface because if you used a different surface then the ball may bounce back higher or lower depending on how hard and smooth the surface is. The surface isn’t used as independent variable as it isn’t continuous.
- The temperature of the ball and surface must remain the same. This is because if they were made hotter then they would have more energy and so would bounce back higher. This isn’t the independent variable because it would be difficult to keep the balls at exactly the right temperature and would be a bit impractical.
- The pressure outside the balls must remain the same because otherwise if the pressure increased then the ball would deform more when it bounced and so wouldn’t rise back as high up.
- The person dropping the ball and the person measuring the height that the ball returns to must remain the same, because different people might judge the ball to have bounced up at different heights.
Independent
- The independent is the height that the ball is dropped from. It is continuous data and will cover a large range of heights to obtain more accurate and reliable results.
Dependent
- The dependent will be the height that the ball returns to.
- Make sure that the rulers are secure so that they don’t fall onto someone’s head.
- Be careful as the balls are very bouncy and could hit someone in the eye.
These are the only anomalies I found.
From the graph I can see that the height that the ball is dropped is proportional to the average height that it returned. The reason I think that the ball is not doubled because tennis balls have a tendency to lose energy when they have been bounced too much.
This occurred because the higher the distance is that you drop the ball from, the greater the ball is deformed (i.e. squashed) at the bottom and so more energy is lost due to vibrations in the ball and the surface, as heat and sound. As the height increases there is also a greater distance over which heat will be lost due to friction by the air. This increase in distance lost would be directly proportional.
The correlation between the original height that the ball was dropped from and the height it returned to, was very strong and all of the plots were quite tight the line of best fit. Also this line went straight through (0,0) which further proves that the measurements are correct because theoretically if the ball were dropped from 0m it would bounce back up to 0m.
From my results I can conclude that the energy lost is directly proportional to the height that it was dropped from. This is because as the height at which the ball is dropped from increases, the amount of energy lost due to vibrations in the ball and surface by the air and the ground increases.
The amount of energy transferred into kinetic energy after the bounce increases as the height increases, and this percentage is always the same for each ball.
In my planning I predicted that the ball would return to a certain percentage of the height it was dropped from was. This is because the higher you drop the ball the more the ball squashes and therefore there is more friction and so more heat and sound energy is lost. A larger amount of energy is lost due to vibrations in the surface and the ball, due to the ball deforming more. As it deforms more, a greater amount of energy is lost as the ball tries to spring back into its original spherical form. Also a greater amount of energy is lost as heat due to friction from the air.
I think that my results support my prediction as the values are in a very strong positive correlation.
I think that my results are very accurate and reliable as the method was very good. I used a wide range of results (from 0.25m – 2m) and did two repeats on every measurement that I took. Also, as the correlation between the height that the ball was dropped from and the height that the ball returned to was very strong this shows that my results were accurate and therefore reliable. I think that my results are good enough to firmly support my conclusion.
To make sure it was a fair test I always used the same ball because if I used a different ball then the elasticity, mass, etc. would all be different and so the height that the ball returned to wouldn’t be altered. To make sure the experiment was fair, it was always the same person who used the dropped the ball and the same person who judged how high the ball returned. Different people might judge the ball to bounce back up to different heights and so the experiment would have many anomalous results, making the investigation less reliable and less accurate.
There bottom few were anomalous results. These were when the ball was dropped from 2m. For the 2m drop the second reading was 0.98m, 0.95m and 0.99m. These anomalous results were probably due to me dropping the ball from too low down or incorrectly measuring the height at which the ball returned. As the height increased it became harder to measure the height at which the ball returned. This is because it was bouncing back up at greater speeds and so it was harder to tell exactly how high the ball reached. The reason I think that the ball is not doubled because tennis balls have a tendency to lose energy when they have been bounced too much because the pressure inside the ball goes down.
Although I did get a wide range of results, I could have improved the method and extended the experiment further and increased the range in which I took measurements, of up to 2.25m or 2.5m, to make the results even more reliable. To do this I would have to stand on a stool though and it would make the experiment less safe and would take more time.
I think that the pattern (of a positive correlation) isn’t only true for the range of values that I used. This pattern would probably continue if the height dropped from were increased because the correlation is strong and because my results are very reliable. I could develop my investigation to confirm this by testing for a larger range of heights.
I could expand my investigation in a number of ways and do further experiments to give more evidence that my conclusion is correct.
One thing I could do is investigate whether the mass of the balls affect the height that the ball returns to. I would do the same experiment but use different mass balls. I would use a range of about 7 balls with different masses. The independent would still be the height that the ball was dropped from and the dependent would still be the height at which the ball returned to. If the size of the ball remained the same (i.e. volume), then I predict that as the mass increased so would the height that the ball returned to. This is because a higher percentage of energy would be transferred into kinetic energy after the bounce, because it would be harder to deform the ball if it was denser as less energy would be lost, and so the height returned percentage would be higher because:
Height reached % = Energy transferred into KE %
Doing this experiment would confirm that the percentage of energy lost when a ball bounces is always the same regardless what ball you use.
