Prediction
For this experiment I predict that the length of the pendulum will have a great affect on the length of time for a swing, in the way that the longer the pendulum is the longer the time for one swing. I also predict that the size of the pendulums swing will have no effect on the time. Also the mass of the pendulum will have no effect on the time per swing unless the pendulum is lighter than the string, if this is so the pendulum would not really swing and experiment would not really work.
Method
- Mould pendulum out of plasticine.
- Attach pendulum to length of string.
- Adjust length of string to the correct length and measure length from center of pendulum to the point where the pendulum is attached or weigh pendulum and add or take away plasticine to make up correct weight.
- Tie pendulum to hook attached to ceiling.
- Pull back pendulum to angle of release for the size of the swing [displacement] keeping the string taunt.
- Release pendulum.
- As pendulum is releases start stop clock and time the amount of time it takes for the pendulum to swing back and forth 20 times. Count the swing every time the pendulum returns to its original release point
- Record results in table.
- In each pre test carry out the two variations and in main test measure length from 30cm to 230cm at 20cm intervals and carry out each experiment three times to work out an average result.
Apparatus
Other Apparatus
Metre rulers, Stop clock and weighing scales
Pre Test
- Changing the mass of the pendulum.
- Changing the length of the pendulum.
- Changing the size of the swing [displacement]
- Changing the air resistance of the pendulum.
This does have a small effect on the pendulum’s time per swing, however this would be very hard to study without using very large pendulums and very accurate timing equipment. Therefore I will not be testing air resistance in this
experiment.
After studying my results from the pre-test I have decided to test the length of the pendulum and not the mass or the size of the swing. I have chosen to do this as this has the greatest affect on the pendulum’s period. In my main experiment to keep the test fair I will be keeping the mass and the size of the swing the same throughout the experiment even though this will have no affect on the time
Risk Assessment
There are no real safety risks in this experiment.
Conclusion
Results Table
[Graphs on separate sheets]
Graph 1
This graph shows how the length affects the time per swing of the pendulum. The gradient of the graph decreases as the length becomes longer. This shows that the rate of increase slows down as the length increases. This tells me that if I were to test very long pendulums the rate of increase would slow down so much that the length would hardly affect the pendulum at all. I predict that this would occur on pendulums over about 600cm but to be sure about this I would have to carry out much more testing.
Graph 2
This graph shows how the time per swing of the pendulum is affected by the square root of the length of the pendulum. Because I have used the square root of the length the results have formed a straight-line graph and because this is a straight-line graph through the origin its equation is:
Y = MX
To find the gradient of this graph
3.1 = 0.20
15.2
The equation of this graph is:
Time = 0.20 x square root of length
I have found that the time for one swing of the pendulum is directly proportional to the square root of the length of the pendulum. Most of the points on my graph form a straight line, however I do have one anomaly which can be seen on both graph one and graph two, this probably occurred due to a minor error in timing. I believe that this trend in the graph should also apply to longer and shorter lengths than I have already tested. However as it would be very difficult to time very short pendulums I would need to use more accurate equipment like a light sensor and a computer counting device if I were to obtain valid results. I also would need a much larger space and a higher ceiling to measure very long lengths. My prediction was proved correct as the time per swing did increase with the length, however I did not predict that the square root of the length would be proportional to the time per swing.
Evaluation
My results for this experiment were fairly accurate. The main problems proved to be measuring the length accurately and measuring the time accurately. The main problem in measuring the length was finding were the centre of the pendulum was in order to measure the string and the centre of the pendulum. However this did only cause a small error that hardly affected the results if at all. My other problem in measuring was that to measure lengths like 230cm I had to use two metre rulers so this probably also caused a small error.
As I stated before timing was also an aspect that caused minor errors, this is because although the stop clock is very accurate the timing was affected by the reaction time of the person operating it. To keep the experiment fair the same person operated the stop clock throughout the experiment. Even with these errors I do feel that my results are reliable enough as they do form a firm conclusion.
To improve my experiment I feel that it would prove worthwhile to find a method to make the pendulum perfectly round to a correct size so that its diameter and radius can be found. This would make the measuring more accurate as we would know exactly where the centre of the pendulum is. Also the string can stretch under the weight of the pendulum slightly so I feel to improve this we could use a more rigid type of string that doesn’t stretch at all.
To extend the investigation I could test the air resistance to prove that this does have an effect on the time per swing. To do this I would have to use much longer string and very big pendulums to easily notice a variation in the results.
Another way of extending the investigation would be instead of having the pendulum swinging I could have it attached to an elastic cord so that it would spring up and down vertically. I would test how the length of the cord and the distance the cord is stretched before release affects the amount of time it takes for the pendulum to rise and fall above the arm it is attached to.