An Investigation into the Length of the String on the Time of Swing for a Pendulum
An Investigation into the Length of the String on the Time of Swing for a Pendulum
Theory
A pendulum is a body, suspended by string or similar, which swings from side to side.
The pendulum only works when the bob is raised at an angle from point at which it is vertically suspended at rest. By raising the bob, the pendulum gains Gravitation Potential Energy (GPE), because when it is raised, it is held above its point of natural suspension and so is acting against gravity. Once the bob is released, gravity is able to act on it, pulling it downwards towards its original hanging point. As it is released, the GPE is converted into Kinetic Energy (KE), which makes the pendulum to swing. Once the bob returns to its original point of suspension, the GPE has been totally converted into KE, causing the bob to continue moving past its pivot and up to a height roughly equal to the height it was released at. However, it never reaches the exact height it was released from, because some energy is lost as heat through friction (on the pivot, which can be eradicated depending on how it suspended, and on the air).
The same factors affect the pendulum on its reverse swing - GPE gained after reaching its highest point in its swing is converted into KE needed for it to return back to its natural point of suspension. Due to this continuous motion, the bob creates an arc shaped swing.
Calculation for the Time of Swing for a Pendulum
T =
l = length of string
g = acceleration under gravity
We can see in the equation that there is no mention of weight; therefore I do not consider weight an affecting factor.
Predictions
I predict the time of swing will increase with the length of the string, in a straight line.
My prediction is best explained with the use of a diagram;
Factors
* Length of String - Controlled
This is measured from the pivot to the ...
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Calculation for the Time of Swing for a Pendulum
T =
l = length of string
g = acceleration under gravity
We can see in the equation that there is no mention of weight; therefore I do not consider weight an affecting factor.
Predictions
I predict the time of swing will increase with the length of the string, in a straight line.
My prediction is best explained with the use of a diagram;
Factors
* Length of String - Controlled
This is measured from the pivot to the center of gravity of the bob.
* Gravity - Constant
* Time of Swing - Measured
Equipment
* clamp stand
* boss
* clamp
* pendulum (40g)
* 120mm of string
* stopwatch
* protractor
Preliminary Work
Based on the preliminary work, I have decided not to use a greater length than 100mm, as this presents a danger to other people, due to the height at which it would have to be released, and thus the height it would swing to. Also, the height of the clamp stand is only about 80cm, so any lengths longer than this will have to dangle off the edge of the bench.
Method
. Suspend a pendulum weight from a clamp stand, by a boss and clamp, using a piece of string.
2. Measure the string out to the desired length.
3. Holding the pendulum at the maximum length of the string, release it at an angle of elevation from the clamp stand (vertical) of 40º.
4. Record the time pendulum to swing away, and then back, stopping the clock when the pendulum is just starting to swing away for the second time.
5. Repeat the experiment twice, to ensure accurate results, and minimise anomalies.
When I carry out the experiment, I will obtain a time for each of the nine lengths of string I will be using, and I will carry out the experiment three times in total. I will take an average from the groups of three results, and these averages will be the values I will use in my graphs, and comment on later.
The readings will be taken with a digital stopwatch, though due to human reaction times, 0.2 seconds will be added to the average times. This value was found by testing as part of the preliminary work.
A 'no go' area of 2 metres will be enforced, in order to protect other pupils in the vicinity.
To make the test fair, the same person will take all the time readings.
All of these precautions will make my final results more reliable and keep anomalies at a minimum, thus making the entire investigation fair, as well as safe.
Results
Experiment
Theory
Using the results from my table, I drew a graph to show the results obtained from the experiment. The points are slightly scattered, but none of the results are more than 0.2 seconds out. The line of best fit is a straight line with a positive gradient, which shows that as the length of the string is increased, the time of swing will increase.
My other results, calculated using the equation, were very similar to the results produced from the experiment, showing that my experiment was successful.
My findings indicate that the time of swing varies in proportion to the length of the string.
Evaluation
The evidence obtained from my experiment supported my prediction that as
the length of the pendulum increases, the period increases.
These results were very close to those I predicted and those given by the equation, therefore showing that my method was fairly accurate, and contained few errors.
Though some of the results were not as accurate as others, appearing off the line of the best fit, the majority of my results were no more than a few hundredths of a second away from the formula results and, therefore, I consider them reliable.
The procedure was reliable, and went according to the plan. However, there were some small errors in the results, possibly due to;
* An error in the measurement of angle of elevation. The angle was difficult to measure accurately, as it was done by eye, using a protractor attached to the stand.
* Human reaction time. Depending on human reaction time, the times could have been measured inaccurately, due to slow reactions when setting the stop-clock etc. This could be improved by using two people to time the pendulum, to get a more accurate reaction time.
I believe the procedure is fine as it is, except I would have liked to have used a light gate and timer to record the time of swing more accurately, without the inconsistencies related to recording them manually, using a stopwatch. This could have solved the minor discrepancies in the data.
I believe I can safely say that my evidence is sufficient to support my conclusion that; the only factor which affects the time of swing of a simple pendulum, is its length, and that the longer the string, the longer the swing.
If I were to continue my investigation, I would collect additional results, to improve the accuracy of my current results, and to give a broader range of values, to back up my conclusion further. I would also consider using a light gate and timer to record the time of swing more accurately, without the inconsistencies related to recording them manually, using a stopwatch.
Bibliography
* Key Science Physics, Jim Breithaupt, 1994
* Microsoft Word and Excel 2000
* Microsoft Encarta Encyclopaedia 2001 Deluxe
2/11/2002 Andrew Smith 11e
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