Background Information
A pendulum is a device which consists of an object (pendulum bob) suspended from a fixed point that swings back and forth, with certain forces acting on it. These forces make the bob swing back and forth.
Formula
This formula allows the period of a pendulum to be calculated:
T = 2∏ √ (L/g)
- T is the period of oscillation of the pendulum (in seconds).
- L is the length of the pendulum (in meters).
- G is the acceleration of gravity (on Earth this is 9.8 m/s).
-
∏ has the value of 3.14159...etc
Using this, I will now predict the times for the different lengths of string on my results table.
For example, for 10cm I would do:
- divide 9.8 = 0.010204081
Then I would square root it to get 0.101015254
- x pi = 6.283185307
6.283185307 x 0.101015254 = 0.63 (to 2 decimal places)
Apparatus
- Long Ruler- To measure the length of the string.
- String – To have a pendulum
- Clamp Stand – To hold everything in place
- Weight (Bob) – To make the pendulum actually work
- Wooden blocks (2) – To hold the protractor and string
- Stopwatch – To time how long the swings take
- Protractor- To measure what the release angle of the string will be
- Tape – To stick the protractor to the wooden blocks
Theory
When the pendulum is at the peak of its swing, it becomes motionless for a very short period of time. At this point it has zero kinetic energy and maximum gravitational potential energy. When the pendulum falls though, the energy transfer that takes place here is:
Gravitational Potential energy → Kinetic energy
As the amount of kinetic energy produced increases, so does the speed. This therefore leaves us with a maximum amount of kinetic energy when the pendulum is at the bottom, and a minimum amount of gravitational potential energy. As the pendulum makes it way back up however, the kinetic energy gets transferred back into gravitational energy, and when the pendulum reaches its peak, and is momentarily stationary, the gravitational potential energy is at its maximum, and no kinetic energy is present. When the pendulum falls again, the process starts again and will carry on until the pendulum completely stops moving.
Because of the effect of air resistance, a small amount of energy is lost each time the pendulum swings. This makes every swing of the pendulum slightly shorter than the one before.
The pendulum bob has two forces acting on it. Gravity is the first, and this tries to pull the bob downwards, but the second force, the tension in the swing, resists this. Because there are only two forces, they can only be balanced when they are in opposite directions. In the pendulum this only happens when it is the middle of its swing. The rest of the time the forces are unbalanced; hence the reason why the bob swings back and fourth.
Here the two forces are opposite and equal. This means there is no resultant force acting on the bob. When the forces are like this, the pendulum is either stationary, or in the middle of its swing.
Here the two forces are not balanced. This means there is a resultant force on the bob to the right. If the bob is moving to the right then the force makes it accelerate and the speed increases as it moves to the centre. If the bob moves to the left then the force decelerates the pendulum and slows it down.
Prediction
I predict that the longer the string, the more time it will take for the pendulum to swing. I predict this because when the string is shorter the distance it needs to travel is also shorter, therefore reducing the time.
I will also need to draw a graph in the latter stages of this investigation. I think that the graph will look like this:
Method
First to complete the investigation I will need to get all my apparatus. When I have collected this I will need to set it up in the correct way so that my investigation will be a fair and accurate one. I will get a clamp stand and clamp 2 blocks of wood together. In between the two blocks of wood a piece of string, attached to it a weight (the bob), will be present. This string will be moved up and down so that I can use different lengths. Some tape will be wrapped around a protractor, which will be attached to the two wooden blocks. When the experiment is set up in the correct manner, the investigation can be performed.
I will time ten swings for each length of string, and will right the results down in the results table. The bob and the angle that the pendulum starts its osolation at will stay the same. For more accurate results, I will time 3 lots of 10 swings for each length, and I will work out the average. That way if I do get miscellaneous results then it does not need to be included in the average.
Also I will work out the average for 1 swing. I will do this by dividing my average 10 swings number by ten.
Blank Results Table
I will time 10 swings, and find out the average, for more accurate results.
Results Table
Being displayed here are the results from the pendulum experiment that I did, where I was trying to find out how the length of string affected the pendulum swing.
These results display what length of string was used, how long it took to complete 1 oscillation and 10 oscillations, and I also worked out the averages for these.
Conclusion
The results that I have collected and the graph a have drawn suggest a few things. For one, the results show that the longer the piece of string is, the longer it took for the pendulum to oscillate. For example, at 10cm, it took the pendulum an average of 0.97 seconds to swing once, compared to at 30cm, it took an average of 1.56 seconds to swing once. This statement was made in my prediction, and therefore I was correct. The results I have collected are also very close to my predicted results, which suggest that they were consistent and they were reliable.
The graph that I had produced showed a close link between the predicted results and the actual results. This proves the formula that was mentioned in the plan actually works, and shows the consistency of my results. Also because there were no eccentric or anomalous results, I can say that the reliability of the results again must have been good.
Evaluation
The experiment that was carried out was educational and enjoyable. But there were a few things that I found difficult, and a few things that could have been improved.
Measuring out the results was not as difficult as I had thought it would be. Getting the accuracy on the measurements did require some concentration, but was completed with little difficulty. Something that I found difficult was trying to get the correct release angle, as I was incorrectly setting it; I was putting the protractor in the wrong position. This problem was overcome by some assistance from the teacher.
Timing the pendulum exactly was another problem that I encountered, as my reaction time isn’t that great, but I believe that the results were accurate enough and didn’t affect any of the conclusions. Although this is the case, my results could be incorrect to up to 0.5 seconds.
The reliability of the results was very good, as the predicted results and actual results were close together. The only results that may be queried is the first one, at string length 5cm. This result is quite out, and I think it is because the pendulum was swinging very fast, so it was difficult to record the time exactly.
Although the experiment was a success in finding correct conclusions, certain improvements could be made. Longer lengths could be tried, up to whatever maximum could be obtained. With a suitable location a length of several metres could be obtained. It would be a good idea to try shorter lengths although a limit would be reached when the pendulum moves too quickly to be accurately counted. It could be possible to have a light gate to accurately measure the times. An alternative might be a very high speed digital video camera that could accurately record the position of the bob, and the exact time.
More repeats could have been done, as the experiment was only repeated three times. If more repeats were used, then I would have more accurate results. Even though this would be a good idea, I do not believe it would affect the actual conclusions, it would only make the results more reliable.
The measurement of the string could also be improved. More precision in measuring lengths could be used for more accuracy in the results. Again, I do not believe this will affect the outcome of the final conclusion.
The equipment that was used could also be improved. More updated, better conditioned equipment would help to the accuracy of the results.
If the experiment could be extended, I would try a few other things. I would test the other variables; for example the release angle and mass of the bob, and see how they affect the oscillation of the pendulum. I would also try out further lengths of string. This would improve my experiment by making it more reliable and more accurate. Sticking with the string, I would test different materials to see if the material of the string affected the pendulum oscillation. One other thing that I may do is see if there is another way to swing the pendulum, for example instead of swinging the pendulum backwards and forwards I would try and swing it in a horizontal circular path (conical pendulum), and compare those results with these ones.
