Aim of the investigation
The aim of the pendulum investigation is to see what will happen if I change a variable whilst I swing a pendulum and see the effect which it has on the pendulums time to complete one whole swing (from where it starts, to the opposite end, and back again). This will give me an insight into what will effect the time of the swinging of the pendulum, be it weight, string length, the angle, or the swinging point.
Planning my investigation
I will set up my investigation by having a 30cm length of string. This will be cut six times as I am measuring six different lengths of string. These will include lengths of: 30, 25, 20, 15, 10 and 5 centimeters. To make my results reliable I will test them three times each, at all the lengths, and average them out, to give a more accurate measurement. I think that I can produce reliable, precise results, using this information and plan. I will have enough data to spot “misfit” results too.
For safety, I will use a pair of safety goggles. This is because whilst the pendulum is swinging, it may hit me in my eyes, as the pendulum is at a similar level of height to my head.
I will also clear all the chairs, coats and bags from the vicinity as they may cause obstruction to me, other people who I work with, or people passing who may be injured.
After taking these measures into account, I was able to proceed to the next stage of the gathering of results.
I will make my testing as fair as I can by firstly, making sure that the windows are closed so there are no elements affecting my pendulum, before I begin the investigation. Secondly, I will then measure the piece of 30cm string and the weight of the pendulum to double check on my first readings. Thirdly, I will use a protractor to measure exactly 90º of where to swing the pendulum from. And finally, I will measure ten swings and the time it takes to complete them. This is because it is easier to count the length of ten swings than it is to count the length of one swing. I will then divide my answer by ten to show the result for the length of one swing.
My prediction of the test results
I believe that the events which will occur are that the longer the piece of string which holds the weight, the longer the time it takes the pendulum to complete one whole swing. So the shorter the string length, the faster the time for the pendulum to fully complete a full swing, as it has less distance to attain.
For my investigation I will use:
– One piece or 30cm string – to be used as the length of the pendulum
– One 17g piece of plaster-scene – as a weight, to swing the pendulum
– A Stand – to hold all of the equipment on
– A G-clamp – to hold the stand in place
– Safety goggles – to protect my eyes
– A stopwatch – to record the swing length of the pendulum
The key factors which are involved in this experiment are the swinging angle of the pendulum, the swinging height which the pendulum will be released from on each experiment and the weight which will go on the end of the string to form the complete pendulum. The other effects such as wind are negligible and will not affect the experiment in any noticeable way.
Factors I will change
The variable which I will change is the length of the string which holds the pendulum. I will change the length of the string from 30, 25, 20, 15, 10 and 5 centimeters. This will give me a good indication of what effects the length of time which a pendulum takes to make one complete swing, and a reasonably large range of results to analyse.
I will control most of the factors (string length, height dropped from, weight and the swinging angle). The factors which I will not control are the effects of gravity on the pendulum and the resistance of the air on the swinging.
Factors involved in predicting
I will take into account the string length and the weight of the pendulum. These two factors will be the basis of my prediction. This is because the longer the string, the longer the distance is to complete the full swing of the pendulum.
The weight of the pendulum will also affect the time for the pendulum to complete a full swing. This is because the less the weight, the faster something will move through the air and the heavier it is, the more resistance it creates.
Range of results
My range of results are gathered by using a string of a variable lengths from 5cm – 30cm. The test will be repeated three times to obtain a more accurate reading. I will swing the pendulum from an angle of 90º which I will measure using a protractor. This will give a constant variable of the angle which it is swung from so one time the pendulum is not swung from a higher point or lower point to the others.
In order to record these results accurately, I have recorded the amount of time it takes for ten swings, rather than one swing, as it is easier to count ten swings if each swing is only a half a second long, so I will just divide the total of ten swings by ten to give me the result of one swing. These results are recorded in the table below:
String Length Test 1 Test 2 Test 3
30cm 1.3 1.3 1.4
25cm 1.2 1.1 1.5
20cm 1.0 0.9 1.1
15cm 0.9 0.7 1.0
10cm 0.7 0.6 08
5cm 0.5 0.5 0.6
The results are shown for one complete swing of the pendulum. The values for each test are stated in seconds.
There is one unusual result (highlighted on the results table) which is inconsistent with the rest of the results, as it is of larger value than the previous result. This result can be dismissed as it is clearly out of place and I can put this down as a testing error. This result should be around 1.2 rather than 1.5 seconds.
This result is included on the graph but when I drew my “line of best fit” I have neglected to include it as a feasible result to use. This is because I believe it to be a misfit. So the graph would be wrong if I included it as the line of best fit’s course would be altered by the result, so high above the other two results.
Analysing my results
I have found out that the longer the string (longest was 30cm) the longer it takes for the pendulum to complete one total swing. This is because it has a longer distance to travel (see diagrams in: “Factors involved in predicting”). The shorter the swing, the less distance the pendulum has to travel. I came to this conclusion with this theory at the beginning of my investigation.
The graph shows a general trend that when the string length is shorter then the time taken is less. For example: the test a 5cm length of string took under 0.8 seconds at the most to complete a full swing. Yet the test of the string length of 30cm took over 1.2 seconds to complete a full swing from one point to opposite and back again.
I think that the graph (above) and the result analysis table (previous page) contain enough information for me to form my conclusion, based on these results. I have tested adequate lengths of string ranging from 5cm – 30cm.
My results were also recorded three times so they will be more reliable and it should be easier to see if there are any in-conclusive results within my readings.
I believe that my method was good enough to be able to come to this conclusion as I tested my results thoroughly, three times. I also timed the results to ten swings and then divided the answer by ten. This has good and bad points to it. The good point is that the results will be able to be read more easily as they give me more time to stop the watch if they are over a few seconds. As the results such as 5cm for one complete swing are around 0.8 of a second, they would be hard to time as it is extremely difficult to start and stop the watch accurately in that amount of time. So by timing ten and then dividing it. By ten I can take around 8 seconds to start and stop the watch which will make them more accurate.
The bad point is that by the time it takes to make ten swings the pendulum may be taking less time to complete full swings as it will not reach the same high, 90º point on the tenth swing of the investigation which it was released from at the start of the investigation.
I think I have an adequate amount of data which was collected during the test stages. I tested the pendulum’s string length at six individual points: 30, 25, 20, 15, 10 and finally 5 centimeters. This gave me six results. I then did each string length twice more to give me more results which I could compare my initial test with. I plotted all three of these on the graph in the result analysis section of this investigation. In total I have eighteen results. So I think this is adequate to form a conclusion on the string length factor which I changed.
My measurements were very accurate. I measured the string twice myself and had somebody else check the length too. This gave me a very accurate string length. I also weighed the plaster-scene weight on a digital weighing scale so it was very precise. I made sure that this scale was calibrated to zero before I began to take readings from the scale. I measured the angle which I swung the pendulum from with a protractor at an angle of 90º each time. Me and another person timed each test and averaged our results to give a more accurate reading for each test. Finally, I measured the average of ten swings to obtain my reading and then divided this by ten to give a very precise reading for a single swing. I consider my testing to be accurate, by taking into account all of these factors.
I think that my conclusion makes scientific sense, as the longer the string, the longer the pendulum takes to complete a full swing. For example, a 30cm piece of string takes 1.3 seconds on average to complete a whole swing. Another example of a smaller length string is that a 5cm piece takes on average 0.5 seconds to make a complete swing. This proves that the shorter the string, the less time it takes to complete a whole swing. These results make scientific sense.
There are ways of further investigating more factors in which I could test, such as the weight on the end of the pendulum etc. These would give me more information on how different types of factors effect the pendulum’s time to complete one full swing. It would be interesting to investigate these other factors and see if they have a similar effect. One way that would extend my current investigation on the factor of string length is by doing more tests at different lengths and at different heights. This would gain more data and I could produce a better understanding of how these new results effect the current data, either in a similar way or in a slightly different way to what I have discovered by doing this investigation.