FORMULA – Spearman’s Rank:
6∑d2 = 0
6 x 0 = 0
n(n2-1) = 3(32-1) => 24
= 1 – (0/24) = 1 <--- As the final answer is 1; this means that there is a strong correlation.
From this experiment, I found that the shorter the string the faster it took the ball bearing to complete one full oscillation. Regarding the reliability of results, I have tried to make to as accurate as possible by using elastic bands to fix the ruler to the retort so that measuring the length of the string was easier. However, there are limits to how accurate I can be with this experiment as there is human error to consider. The results could have been affected by reaction time as well, from the person timing the experiment.
Preliminary Test #2:
In this preliminary, I am investigating how changing the material and the weight of the ball bearing can affect the period. The independent variables here are the material and weight of the ball bearing and the control variables are the length of the string, size of the ball bearing, height of dropping the ball bearing and the person in charge of timing. These factors are kept the same to ensure that nothing other than the changing of ball bearings will affect the results.
METHOD:
- Weigh the different ball bearings using the electric scales and record the material and weight.
- Measure as accurately as possible 30cm of string, not forgetting to leave a bit more to make a loop to attach the ball bearing.
- Attach the string and ball bearing to the retort.
- Get a partner to help with dropping the ball bearing, and using a protractor, check that the angle of dropping is 180°.
- Make sure that your partner drops the ball bearing the same time you start the stopwatch.
- Stop the stopwatch as soon as one oscillation is over.
- Once all the different ball bearings have been tested, repeat the test once more to see if the results are similar.
Looking at the results for this preliminary, I do not think these results are reliable. I assumed that the results would show that the heavier the ball bearing, the less time I would take to complete one oscillation. However it seems that the results are almost similar, and it also includes 2 outliers. A possible cause of the similar results may be due to human error, as an error could have been made when timing and the reaction of both the time keeper and the person dropping the ball bearing. Furthermore, an error could have been made when weighing the ball bearings, as the scales were slightly faulty this would have affected the accuracy of the weighing.
Preliminary Test #3:
In this preliminary I am testing to see how changing the angle for dropping the ball bearing will affect the time taken for the ball bearing to complete one oscillation. The independent variable in this test is the angle and the control variables are the length of the string, the material of the ball bearing and the stopwatch keeper.
METHOD:
- Choose a ball bearing of any material.
- Measure 30cm of string, not forgetting to leave a bit extra to make a loop for the ball bearing then attach it to the retort.
- Get the protractor and attach it to the retort with cello tape, so it makes it easier as well as improving accuracy.
- Get a partner to help you drop the ball bearing.
- Check that you start the stopwatch as soon as your partner drops the ball bearing.
- Stop the stopwatch as soon as the ball bearing makes one oscillation.
- Once all the angle changes have been tested, repeat the test again to make the results more reliable.
FORMULA – Spearman’s Rank:
6∑d2 = 0
6 x 0 = 0
n(n2-1) = 5(52-1) => 120
= 1 – (0/120) = 1 <--- As the final answer is 1; this means that there is a strong correlation.
For this preliminary I chose to use the iron ball bearing, weighing 39.58g. The results shown do show that as the angle decreases, the time taken for the ball bearing to make one complete oscillation was faster. But the results may not be as accurate as I want them to be as there were some flaws with the way the experiment was carried out. First of all with attaching the protractor to the retort, that may have been accurate but the person who dropped the ball bearing may have misread the protractor by a few degrees, which would affect the final results. There are also several outliers here, due to the stopwatch keeper’s reaction.
SUMMARY FROM PRELIMINARIES:
From the results gathered from the preliminaries, I think the results are fairly reliable, even though there were a few outliers. From the Spearman’s Rank calculation for the first preliminary, it shows that there is correlation between the independent and the control variable, as well as suggesting that the method used to test is the correct method. However, some minor changes may have to be made to the method for the main experiment such as improving the equipment used. The retort, for example, may have had a small affect to the results as the one I used for the preliminaries was slightly faulty because it moved as the ball bearing was swinging. But by repeating the experiment twice, this improved the reliability of the results.
HOW THE PRELIMINARIES APPLY TO MY MAIN EXPERIMENT:
For my main experiment I chose to experiment further on how changing the length of the string can affect the period of the pendulum. I chose to test this variable based on the preliminary as it showed a strong correlation as well as being quite a simple experiment to carry out. Making this experiment as accurate as possible is also accomplishable, as only 2 people are needed; one to keep the time and the other to drop the ball bearing. By keeping the same people to the same task throughout the experiment, this would minimize human error and the results would be more reliable.
THE MAIN EXPERIMENT:
Hypothesis: I think that the length of the string will have an effect on the period of the ball bearing, so the shorter the string, the faster it takes for the ball bearing to complete one oscillation.
Collecting Data: In all experiments there is always human error, so I have to consider that for this experiment as well. Everyone has different reactions so to make it a fair test as well as making it as accurate as possible, having the same person in charge of the stopwatch and the same person in charge of the ball bearing.
EQUIPMENT:
- String (cut into 50cm, 45cm, 40cm, 35cm, 30cm, 25cm, 20cm, 15cm, 10cm, 5cm)
- 1 retort stand
- 1 aluminium ball bearing: 66.55g
- Protractor
- Stop watch
- Electronic scales
- 30cm ruler
- Elastic bands
- Cello tape
- Scissors
METHOD:
- Measure out the string as accurately as possible using the 30cm ruler, not forgetting to leave some spare string to make a loop for the ball bearing.
- Use the elastic bands and attach the ruler to the retort, making sure that it is the right way up.
- Attach the string and ball bearing to the retort, and using a protractor, check to see if the angle for dropping the ball bearing is 180°.
- Get a partner to hold the ball bearing and make sure that when you start the stopwatch your partner lets go of the ball bearing at the same time.
- Stop timing as soon as one oscillation is over.
- Record the time down and proceed to test other angles. After testing, find the average from all the times and round it off to 2 decimal places.
6∑d2 = 0
6 x 0 = 0
n(n2-1) = 9(92-1) => 720
= 1 – (0/720) = 1 <--- As the final answer is 1; this means that there is a strong correlation.
INTERPRETING AND EVALUATION:
From the results, you can see that my hypothesis was correct: the shorter the string the shorter the time it took. The range of measurements in this experiment covered more than the preliminaries, so the interpretation would be easier. The lengths of string have been tested more in this main experiment than the preliminary so it would show a clear relationship between the length of the string and the time taken. I would say that the results are quite reliable as there is only one outlier, and that could be due to the reaction of the time keeper, as the string was getting shorter so the time keeper needed to have a good reaction time because the ball bearing would finish the oscillation very quickly.
If I were to do this main experiment again, I would consider about the equipment again as they do affect the reliability and accuracy of the results. I had used the same electronic scales as in the preliminary, and they were the faulty scales, so the weight of the ball bearing may have been wrong by a few grams.
IMPROVEMENTS:
The main concern regarding improvements is the equipment again. The stopwatch is one of the pieces of equipment that could be improved. A quicker responding timing device would have increased the accuracy of the experiment, as sometimes the start button would jam, therefore delaying the time and affecting the test.
Furthermore, the measuring of the lengths of string could also be improved. By using a ruler marked with millimetres as well as centimetres would improve the accuracy of the experiment as it would enable us to cut the string to the perfect length.
Even with such small improvements to the method and the equipment, I think it would make the results even more accurate, and possibly to get results with no outliers included.
CONCLUSION:
To conclude what I have discovered in carrying out this experiment, I found that my hypothesis was proved and that length of the string affected the ball bearing a lot, but it would also be even better if the results were even more accurate and if there was no outliers at all. I also realised that not only did the length of the string affect the period of the ball bearing, but other factors such as the equipment also affected the results.
If it were possible, I think I would do one more experiment, changing another factor to see which variable affected the time the most, that way a more solid conclusion could be drawn.