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# Pendulum Experiment

by

## Sebastian King

on 22 August 2013

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#### Transcript of Pendulum Experiment

Pendulum Experiment
Sebastian King
Planning Log
The experiment I have chosen to conduct is whether the mass swinging on a pendulum affects the period (the time it takes to swing). I read a claim that there is no effect on the period but it was unsubstantiated, so I took it upon myself to determine whether this was true or not. The experiment seemed simple enough to complete, with some research being necessary and certain precautions taken. I would construct a pendulum from basic house hold materials and test the hypothesis through a fair experiment and hopefully end with quantitative data, proving or disproving
the hypothesis.
Background Research
The experiment was selected after reading an article where it was stated that the period would not be affected if the mass of the pendulum was changed. This was not substantiated however and I felt that it would be an appropriate investigation to complete. I then researched further into pendulums and their periods, as well as attempting to discover an ideal angle of release, with no success. There did not seem to be a most common, or best, angle to complete the experiment at, so I decided to release the pendulum at an angle of 45 degrees. It seemed logical to use that angle as 90 would be too great and as 45 is half of 90; it was
also convenient and easy to measure precisely.
Discussion
Possible real life application of this experiments results are that in a trapeze act in a circus more weight on the trapeze may suggest more speed would be acquired during flight. This would be wrong however, and may cause a serious injury if they wrongly attempted to compensate for the change in weight. Acts may look to an experiment such as this with a formal lay out to give strong evidence and information on what to do in the situation.

Experimental Record
Hypothesis: The mass swinging on the end of a pendulum will NOT affect the period outside of the margin of error.

Aim: To determine whether changing the mass on a pendulum has a discernible effect on the period

Variables
The independent variable would be the mass, which
I would change in determined increments.

The dependent variable would be the length of the chord. The experiment may benefit from having more dependent variables to increase accuracy, or a
series of controlled variables.

Controls, Risk Assessment,
Experimental controls would include the drop angle, which would have to remain constant, as well as the force applied to the drop (some sort of system will have to be devised to regulate this). Other controls would include the force of the release, which would be kept constant by dropping the weight each time, as opposed to forcing it.
Background Research
I then researched what materials should be used in the construction
of the Pendulum and it was clear that there were many different ways to create one, all using readily available materials. I decided on using a light gauge of string to attach the bob on one end, and to anchor at the other. The anchor would be a small metal pipe held in place by a piece of tape. The bob (weight or mass that swings) was determined to be large metal nuts. This was chosen because the weight could be changed accurately by removing or adding the nuts of a known weight onto the end of the string. The string will be 45cm long, and that will remain constant for the entirety of the experiment.
Background Research
To maintain the exact angle of release I will place a protractor against the string, to line up the taught string with 45 degrees before dropping it each time. Researching methods of release also indicated that, simply dropping, rather than forcing the mass, will yield more accurate results, and be far simpler to conduct. When researching methods of how to time the experiment, I discovered that timing a full back and forth motion (or more), is far easier than timing half of that (from the start of the swing to the other side). This seemed logical and was highly recommended, so I decided to complete my experiment by timing each weight increment in groups of 5.
Results
NOTE: The nuts weighed 2 grams each, so the
total of each increment was placed next to the number of nuts in the results table for convenience and reference.
Equipment
- Metal Nuts
- Metal Pipe
- String
- Flat surface
- Tape
- Stopwatch

Method
1) A metal pipe was taped down onto a flat surface
above the ground (with clearance for the pendulum
to swing freely).
2) A piece of string was then
tied firmly around the circumference
of the pipe one on end and on the
other end a nut was tied, so that
there was a distance of 45cm
between the two whilst taught.
3) A protractor was set up so that
the string could be aligned with the
correct angle to accurately measure
the angle it was released from.
4) The weight was then released
and a stopwatch used to time 5 back
and forth movements (period).
(<-- Video)

5) The previous step was completed
3 times
6) In increments of 2, additional nuts were tied onto the end of the string and for each increment of nuts; steps 4 and 5 were repeated.

Reflection
A significant problem that I first had when releasing the pendulum, was that the string would rotate on the pipe and the free hanging section of string would end up on one side of the pipe and therefore higher than where I began, creating another plane of movement that altered the results. This was fixed by taping the string into place and the string remained stationary during its swing.
String rotated String Centred
Conclusion
The results acquired produced data that was clear and displayed an obvious pattern. All the time values were extremely close for the large differences in the pendulum masses. The small differences can be attributed to human error, and the level of precision that was used. The averages differ in 30ms, a negligible difference, meaning that the original hypothesis ‘The mass swinging on the end of a pendulum will NOT affect the period outside of the margin of error’, has been proved true as the results show.
Conclusion
The hypothesis can also be proved true by the formula;
T = (2 x Pi) x √(l/g)

Where
- T = Period (seconds)
- L = Length of the string (metres)
- G = Acceleration due to gravity (9.8m/s)
- √ = Square Root

In no place in this equation is mass used, therefore one could change the mass in any way they chose and the period would remain unaffected.

Discussion
Another possible application of these results is with pendulum clocks. The weight on the end of the pendulum does not matter or affect the period, which in this case is very important. This knowledge may help reduce the price of the clocks, if it was believed that a large weight was needed to keep the swing going for longer or more accurately.
Reflection
Another problem that occurred was my accuracy. It took a few attempts of timing the period as ONE back and forth movement unsuccessfully until I research indicated that timing 5 back and forth movements would be much easier. This made the experiment far easier to conduct, as well as more accurate and reliable. I also timed the pendulum swings 3-5 times without noting the time down to attempt and hone my timing accuracy, with the first 1 and 2 times being far out from the others due to my inexperience. After this ‘practice’ time the timing became consistent and reliable.
Reflection
The main problem, however, with the experiment was the timing aspect of it. The weight was all controlled extremely precisely, because the nuts are all built identically, but the discrepancies in timing could be rectified given another opportunity to complete the experiment. Timers that use infrared beams to start and end the timing sequence could be used to great effect here. You could drop the string through the beam to start the timer and it would return through it (on the first period at least) to stop the timer, thus giving incredibly accurate times and discovering if there was a difference
when the weight changed, however small.
An example of the infrared timer
Does the weight of a pendulum have
an affect on time it takes to swing?

Validity
To ensure that the final sets of data were valid and useful, the string was changed each time the weight was changed so the string did not stress and stretch and therefore change the results in an unwanted way. In the event that a large outlier was obtained, that particular swing was redone and the previous value discarded. An outlying result in an experiment such as this was unlikely but a contingency for one was made, as to ensure the most accurate and valid data. Repeating the experiment while taking into account each of the precautions listed in this section and the reliability section ensured valid and usable data.
Variables
The independent variable in this experiment was the mass
(bob) swinging on the end of the pendulum. I required this variable to be changed accurately to give me quantitative data and reliable results. The dependant variable in my experiment was the length of string. This factor had to remain constant; otherwise the experiment would become invalid due to discrepancies from different string lengths. Other variables that were controlled included the force of release. This was regulated by not forcing or throwing the weight at all, and releasing the weight and letting it swing under its own momentum. The second controlled variable was the angle of release. This was kept constant by the use of a protractor to correctly align the string with the designated
angle of 45 degrees.
Variables
Another variable that had to be controlled was the human error involved in the experiment. The timing specifically, and this was controlled as best I could by timing 5 back and forth motions, increasing the margin of error for the experiment to a point where human error is negligible. Meaning, human discrepancies were still factored in, but the longer period meant that the small changes would have less of an effect, as opposed to the larger effect they would have on a shorter period.
Reliability
Reliability was ensured in a number of ways. The experiment did not have
a large number of points where the data could be invalidated, but there were some, so precautionary steps had to be taken. Reliable data was achieved by controlling the afore mentioned variables. The swing was not forced, but released, to ensure that the same amount of force was applied to each swing and that any differences in the data were because of the change in mass. The method for timing the periods was a person with a stopwatch, timing by hand, as the margin of error was large enough to accommodate the small discrepancies that would occur. The string was also changed for each weight, but the length and way it was tied was kept the same, to ensure reliable results with different weights. The experiment was also completed 3 times for each weight, ensuring that the results achieved were reliable and repeatable. The experiment was completed exactly the same for each swing to ensure reliable results. To complete the experiment in a reliable way the procedures above were followed very closely. To add further to this, only one independent and dependent variables were used to keep the experiment simple.
Risk Assessment
Risks in this experiment were few in number and not notably harmful. The pendulum itself would be swinging at waist height, making it impossible to be hit in the head with the bob and basic intuition would also tell the person conducting it not to stand in the way of the weight. Apart from this there is no observable safety hazard, except dropping the relatively light weight onto your foot. This is unlikely but still possible so the experiment was conducted with enclosed shoes on to prevent injury in that area.
Validity and Reliability
To ensure validity and reliability certain precautionary steps should be taken. I would make sure the drop height, angle and force are all constant throughout the experiment. If the chord was showing signs of stress, it may need to be changed at some point, so the length does not change by stretching slightly. Each weight increment will also be completed 3 times to ensure the results are consistent and fair.
Bibliography
Name of Website, Author, Title of article, Date visited, URL

1. Wiki How, Jeffrey Burrdo, How to build and use a pendulum, last visited 19/08/13, http://www.wikihow.com/Build-and-Use-a-Pendulum
2. Internet Science Institute, Author N/A, Pendulum Experiment, last visited 19/08/13, http://isi.loyola.edu/lab/pendulum/pen1a.html
3. School for Champions, Ron Kurtis, Simple Pendulum Equations, last visited 18/08/13, http://www.school-for-champions.com/science/pendulum_equations.htm
4. Hyperphysics, Author N/A, Simple Pendulum, last visited 15/08/13, http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html

Scatter graph displaying every throw and averages for each, showing the relatively small changes in time. 
Graph
Graph
Graph displaying the average throws with values of 1-10 seconds on the Y-axis showing the minute differences. This lent hand to the original hypothesis
Full transcript