H α x (H is proportional to x)
This tells us that the height at which the roller is rolled from is proportional to its stopping distance.
However, we have also established that G (angle of the ramp) is constant, which means that:
H α D (H is proportional to D)
(H = Height, D = distance up ramp)
I worked this out using the following equation:
∴ H = Sin G × D
So, if we take out G which is constant we are left with:
H α D
Finally, using what we found out earlier: H α x, we can substitute D into the equation giving us the following:
D α x (D is proportional to x)
The previous calculations, show that what I predicted is in theory correct, as it worked out that D α x (Distance of the roller up the ramp is proportional to its stopping distance).
This is a testable relationship for a fixed angle, fixed mass roller, fixed carpet.
There are numerous ways in which to test this prediction. To test it, I will record the stopping distance of rollers at different distances up a ramp, then, to check if the stopping distance is proportional to the distance of the roller up the ramp, I will plot a graph. This graph, if the predictions are correct, will be a straight line.
Preliminary Short Tests
Before proceeding with the experiment, it is necessary for us to carry out a few small tests in order to find out the range of variables to be used. For example, we need to know the number of distances up the ramp we are going to be using for each roller so that we can make the results accurate and fair. Also, we need to know what range of distances up the ramp we are going to be using for the rollers (this will differ for each roller, as they are different in weight). Once we have done these preliminary tests we can go on to the actual experiment.
How we did the preliminary tests
To do these tests we needed the following apparatus: 50cm ruler, ramp, carpet and rollers (small, medium and large). With this apparatus, we then needed to find the minimum distance and maximum distance of each roller. Doing this was simple, firstly, we set a sensible starting point as the minimum distance up the ramp for the roller. Then, we had to find the maximum distance up the ramp the roller could be put to, before rolling off the carpet. This was easily done, all we had to do was put the roller on the ramp and let it roll: if it went off the carpet, we would put it slightly lower down the ramp. This process was repeated until the maximum distance the roller could be put up the ramp was found. Once it was found, we measured how far up the ramp it was using the ruler and recorder this value. Throughout these tests, we kept the carpet constant (never changed it) and the angle of the ramp (notch at which it was set) fixed. We then did this for each roller and the ranges were recorded as follows:
In order to make it fair, we needed to split up the range into different intervals as to give us approximately the same number of results from each roller. For example, we decided that for each roller, we wanted 10 sets of results, this meant that for the large roller, it would be rolled at 3cm intervals whereas the medium roller would be rolled at 4cm intervals and the small one at 5cm intervals.
Obtaining Accurate Results
If we are to get accurate results, we must take note of natural human error. It is obvious that during this experiment we are not going to acquire completely accurate results, in fact, it is inevitable the results are going to be slightly inaccurate. However, so as to decrease the error of the results, it will be essential to repeat results. This means, that for every distance from which we roll the roller, we cannot simply take down the first result we get, but instead, repeat it a few times and then take an average. We decided, that to get the most accurate results, we should repeat the results 6 times for each distance up the ramp, thus giving us an average more likely to be accurate.
Also, another thing which will help us to get accurate results is our choice of apparatus. To measure the stopping distance of the roller more accurately, we are using a set square. We will measure the roller from its centre of mass each time. In doing so, our results will be consistent. The reason for measuring the roller from its centre of mass is simple, because, when the roller stops, it is not always going to be straight - sometimes it will stop and will be at an odd angle to measure. We will use the set square along with a 1m ruler which will be by the side of the carpet.
Recording Our Results
During the experiment, when we are taking measurements, we will record them into a table, so that they are clear and accurate. The table will like this:
Obtaining the Evidence
Recording the Results
With the table set out as shown in the plan, we began to take measurements. Before recording the stopping distances for a roller, we weighed it, and recorded this value. We started with the large roller, and began recording its stopping distance with the range 3-27cm, which we worked out in the preliminary tests. We recorded the results into the table and repeated each result 6 times. We repeated this process for each of the 3 rollers, which gave us three tables of results. Once we had obtained the results containing the stopping distances, we worked out the averages to 1 decimal place. Working them out to one decimal place gave us results which were accurate enough, and which we could easily plot onto a graph.
The following results were obtained:
(Results Continued Overleaf)
Analysing The Evidence
The Graphs
I have chosen to represent my results in the form of a line graph, using a line of best fit. This shows the data best, and can be compared well to my prediction. On three of the individual graphs, they show an approximate straight line.
What the Results Show
Patterns
You can see an obvious pattern In the results in that all the graphs show a straight line. This can be seen on one of the graphs which compares the three results, showing that they are very similar.
Also, by studying the graphs carefully, you can see, that the heavier the roller, the further it travels. For example, a heavier roller rolled from a distance like 20cm up a ramp would roll further than a lighter roller rolled from 20cm. This can be seen on the comparison of results graph. This therefore means that the range should be bigger with a smaller roller, and that also is true, this can also be seen on the graph comparing results (the smaller roller has the highest line - indicating a big range of distances up a ramp).
Relationship of Results with Theory
The results fit with theory and show that the distance of the roller up the ramp is proportional to the stopping distance. This can be seen in the graphs, which show the straight lines, meaning the variables are proportional. Because they are proportional, it means that it is possible to estimate things. Like, for example, you could estimate, using the graphs, that if you put a large roller on a ramp set to the fourth notch at a distance of 33cm up, its stopping distance would be approximately 85cm.
Conclusion
I can conclude, from my results, that my prediction was correct, and the distance of roller up the ramp is proportional to the stopping distance. The science of this was explained in the earlier part of this, in the planning, where I predicted it.
Evaluating The Evidence
Reliability of Results
I think that the results I obtained were reliable enough to draw a valid conclusion. They were not as accurate as they could have been, but allowed me to contrast and compare them with the predictions I made earlier. If I had not repeated results the amount of times I did, then the results would have been very scattered, and I may not have been able to make the conclusion I did. Also, the graphs are fairly accurate due to the precision of the results, and you can see on them that there is a clear straight line. All in all, I am satisfied with the reliability of the results, as they have enabled me to analyse and do what I need with them. However, as with any experiment there are the occasional anomalous results which I got, but this did not hinder any of my work, and can be explained.
It is for sure that my results are not so reliable that I would get them again if I were to do the experiment again, but there is nothing I can do which would actually completely nullify human error, but instead there are methods to decrease the chance of human error.
How well do the Results Correlate with Theory?
The results correlate very well with the theory. As I predicted, the distance of the roller up the ramp was proportional to the stopping distance. But, I did not predict all that I could have. As I found, that the heavier the roller, the further it rolls, compared to lighter rollers, which have a bigger range, due to the fact that they do not roll as far.
Improvements
There are many improvements I could make to enhance the reliability of the results, and produce a more accurate and precise experiment if I were to repeat it:
Practical Work
I was satisfied by the method I used to obtain results from measurements, however, there are ways I could have used to increase its accuracy. For instance, the ramp which I used was not perfect - it was most probably slightly bumpy in places and quite rough. To change this I would sand it down to make it smooth, making the test more fair. Also, if I were to repeat the experiment then I would probably include a larger range of results, and have a smaller interval between the distances of the roller up the ramp. Also to take away more of the natural human error, I would repeat each result many more times, this way the average would be more accurate, and the results would be more consistent. Also, learning from this experiment, I would take more care in placing the rollers at the higher distances on the ramp, as I found that this was the main reason for the anomalous results I got. In addition to these improvements, I could also take more care in the actual recording of the results. Instead of recording the results to 1 tenth of a centimetre as I did with this experiment, I could record them to 1 hundredth of a centimetre, to make it more precise. If it is not possible to do this by eye, then I could use magnifying tools to make it easier. However, if I recorded results to that degree of accuracy, then it would not be possible to plot an accurate graph, so instead of doing graphs by hand, I could input the data into a computer which would plot a very accurate graph.
Further Work
There are quite a few other things I could do extend this investigation. The combinations of which are endless. In this experiment I used aluminium rollers, a wooden ramp, and carpet. If I were to extend this experiment, I could just change some of these fixed variables around. For instance, instead of doing the experiment with aluminium rollers, I could do it with iron rollers, or wooden rollers. I could switch things around, like I could have an aluminium ramp and wooden rollers. I could change the surface from carpet to wood. If I had do one thing to investigate further I would change the rollers from aluminium to iron rollers and see what happens. This again would most probably produce very similar results to this project.
Another thing which I could do to get more evidence, would be to change the angle of the ramp to get more results which would strengthen the proof of my conclusion that the distance of the roller up the ramp is proportional to the stopping distance.
Overview
Overall, I think that the experiment was conducted systematically, and produced enough results with reasonable precision, which allowed me to show my prediction to be true. It correlated well with the theory and there were not too many unexpected results.
Anomalous Results
The results I produced from the experiment were on the whole fairly accurate enough to allow me to analyse them and find patterns. However, on the graphs there are a few anomalous results. These can be explained. You can see that in general, these anomalous results appear at the end of the graph, and are usually the last points plotted. This is because, when you roll the roller from higher up the ramp, the stopping distance can be greatly affected by the accuracy with which you place it on the ramp. In other words, what I am saying is that, if you place it 1mm out of place at a distance of 50 cm up the ramp, the stopping distance will be more greatly affected than if you place it 1mm out of place at 5 cm up the ramp. This can be shown in the graph on the next page, which shows that the results were more consistent at a lower distance up the ramp than a higher distance up the ramp (explaining the reason for anomalous results).
