The constants are as follows:-
- Material ball is composed of
- Weight of ball
- Type of string used
- Room Temperature
- Height above sea level
- Air movement
I will keep the material of the ball and weight of the ball constant by using the same weight in every reading I take. I will also use the same type of string in every reading I take to ensure that this does not affect the results. I will ensure that all my readings are taken at the same height above sea level but a slight change in this factor would cause little to no change to my results as I am not able to vary the altitude I perform my experiment at by such a figure, the same is true with air movement as in closed conditions this should not play much of a role in the validity of my results.
APPARATUS FOR PRELIMINARY EXPERIMENT
- Stand and Clamp
- A spherical weight with a hook
- A stopwatch
- A ruler
- Different lengths of String
PRELIMINARY EXPERIMENT RESULTS
PRELIMINARY EXPERIMENT CONCLUSION
From the results from my preliminary experiment I conclude that the angle of release has no affect on the time period of a pendulum. This is because, for example, the average time rate for a pendulum that is 20cm in length and has been released from an angle of 45 degrees is 9.26 seconds and the average time period for a 20cm long pendulum that has been dropped from an angle of 90 degrees in length is 9.26 seconds. This means that the angle of release is no longer a factor in this experiment and I will implement this finding into my final experiment (i.e. I will discard the angle of release as a factor that will not affect my results in my main experiment).
My results also confirm to me that my original prediction was correct, because as the length of the pendulum increases, as does the time period of that pendulum and this is proven in my table of results, for example the average time period for a pendulum with a length of 10cm is 6.83 seconds and the average time period for a pendulum with a length of 20cm is 9.26 seconds, this shows an obvious increase in the time period of the pendulum by approximately three seconds.
My results concur numerically with my original data also as I predicted that the time period (using the formula) for a pendulum of length 20cm would be 8.96 seconds and the average time period turned out to be 9.26 seconds. This is a difference of 0.3 of a second and this difference was most likely caused my human error (i.e. reaction times) than a fault in my experiment.
My graph further reinforces evidence that my original prediction should technically be correct as
MAIN EXPERIMENT
APPARATUS
- Stand and Clamp
- A spherical weight with a hook
- A stopwatch
- A ruler
- Different lengths of String
METHOD
- Firstly I set up the clamp and stand with the pendulum set up in the clamp at the correct height for my first reading.
- Secondly I released the pendulum at any angle as I have already discarded the angle of release as irrelevant. At the moment of releasing the pendulum I started the stopwatch.
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I counted ten oscillations of the pendulum, an oscillation being when the pendulum passes the centre of the clamp stand every 2nd time, after ten oscillations I stop the stopwatch and then repeated 3 times using the same string. I did this for 8 different lengths of string.
Before I publish my results I will put on a table of perfect results which should be the exact times taken for any given length of pendulum. The formula I will use is (T = 2∏ (√L/G)) where T is the time period of the pendulum, L is the length of the pendulum and G is acceleration due to gravity.
PERFECT SET OF RESULTS
These results are the ideal set of results for my experiment, I will now publish my results and examine whether my evidence supports or undermines these results and to test the accuracy of my results.
MY RESULTS
These results show that my experiment was a fair test as the results are all fairly constant and there are no glaring anomalous results.
CONCLUSION OF MAIN EXPERIMENT
From this experiment I have concluded that as the length of a pendulum increases, so does the time period of the pendulum. This conclusion is proven through my table of results and my graph.
My results concur with the results I obtained from using an equation instead of practical means to draw results and my graph proves that the curve of both these sets of results are very similar, adding further credibility to my conclusion.
My conclusions also numerically concur with my earlier prediction. This prediction being that if a pendulum had a length of 20cm the time period for ten swings of that pendulum would be 8.96 seconds, this was calculated using the formula for the time period of a pendulum (T = 2∏ (√L/G)). My actual result for that length of pendulum was 9.28 seconds which is very close to the prediction hence, my results have numerically confirmed my initial prediction.
My graph also shows me that as the length of the pendulum increases the time period of that pendulum increases but at an increasing rate. This graph could possibly become an exponential curve because the difference between the time periods of pendulums with 5cm differences between their lengths was shortening at an increasing rate as is shown by my graph, but I did not have the time during this experiment to further investigate this hypothesis.
The reason that a pendulum has a higher time period as it gets longer is because it has a further distance to travel to reach the central measuring point, as it rotates in a circular motion, as the length of the pendulum increases, the circumference of the circle created would also be increased, therefore the pendulum would take a longer time to complete one oscillation. My results have proven this to me.
EVALUATION
My results that I have obtained are fairly accurate but which is surprising because of the method and conditions we operated under. For example, my experimental results are very close to that of the results I obtained using the formula for the time period of a pendulum, this shows that my results were actually quite accurate.
I also feel that the experiment that I conducted was flawed in many ways; therefore I am surprised to have such accurate results. For example, the factor that would have distorted my results the greatest was the reaction times of the person who was timing the pendulum, as reaction times could be flawed by around 0.6 seconds per reading at the minimum and yet at a length of 20cm that pendulum should technically have a time period of 10.04 seconds (through using the formula), and my experimental result was 9.78 seconds, approximately 0.2 seconds inaccurate which is quite an achievement. This leads me to conclude my experiment was more accurate than I had at first thought; hence, the evidence obtained from this experiment is reliable.
My graph shows to me that I have produced two anomalous results in my experiment. These anomalies are quite small though and are not significant due to this fact; they are most probably down to a slightly longer reaction time or a trivial fact along those lines and hold no bearing the validity of these results.
I feel that this experiment has been a fair test for numerous reasons. Firstly, because, in order to cancel out the effect of reaction times on the final results our group used the same person to release the pendulum and start and stop the stopwatch and as we used the same person per reading, this would certainly improve the validity of our results.
We also ensured that the factors that we had the ability to keep as constant were kept as constants. For example, we used the same type of string for each pendulum swing and we used the same ball for each reading, therefore none of these factors could affect our experiment and cause it to be a fairer test.
The evidence that I have obtained is more than sufficient to draw a firm conclusion, I could have most probably drawn a firm conclusion from my preliminary results as the conclusion is so obvious. I am able to conclude that as the length of the pendulum increases, the time period of that pendulum decreases because this is proven through my tables and graphs and through my background knowledge and also through the formula for the time period of a pendulum.
A way that I could extend this investigation would be by investigating another factor and it’s affect on the time rate of a pendulum. I could for example; test whether changing the weight of the bob at the end of a pendulum had any affect on the time period of that pendulum.
The way I would go about conducting this experiment would be to keep the length of the pendulum constant and to use different weights of bobs on the end of the pendulum. I would conduct that experiment in a similar fashion as to how I have conducted this experiment. For example
- Firstly I would set up the clamp and stand with the pendulum set up in the clamp at the correct height for my first reading.
- Secondly I would release the pendulum. At the moment of releasing the pendulum I would start the stopwatch.
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I would count ten oscillations of the pendulum, an oscillation being when the pendulum passes the centre of the clamp stand every 2nd time, after ten oscillations I stop the stopwatch and then repeated 3 times using the same string. I would do this for 8 different weights of bobs on the end of a pendulum.
- I would record my results and analyse them in order to draw a conclusion.
I feel that if this experiment were to take place then the conclusion drawn would be that the heavier the bob would be, then the time period would actually increase.
I predict this because if a pendulum is heavier, the pendulum would have a larger momentum and would have a lot more energy than a lighter pendulum and hence would be able to swing faster and therefore would have a shorter time period.
