Whilst carrying out this experiment you have to realise some safety issues that are to do with the equipment we are using. The pendulum must be set up away from other people as it could hit them and hurt them. Also secure the stand with some G- clamps to make sure it doesn’t fall on you or anybody else.
My prediction is that as you increase the length of the string the period too will go up. But I do not think this will be a very big change, just large enough for it to be noticed as a trend. I think this as longer swing is closer to the ground and so has less gravitational potential energy than a shorter string, and so it takes longer to complete one full swing. I shall account for any anomalous results from preliminary experiments to make sure the same problems are not repeated. If these anomalous results do re-occur I will suggest ways of overcoming them and what might be the probable cause of them.
Equipment:
- Stand
- Arm clamp
- Cork
- Lead bob with string
- Metre rule
- Stop watch
- Paper
- Scales
- G clamp
The stand will be placed on the table and secured with a G-clamp, as it is a safety hazard. Then I will thread the string and bob through the cork and then clamp the cork in position. I will measure the correct length of string with the wooden rule. The string will be checked and the bob will be released. Then it will swing for a few periods so I can get used to the speed and timing and then I will start the stopwatch. After 10 periods I will then stop the stopwatch and record the result.
Obtaining Evidence
My results and table:
I used the method that I talked about in my earlier plan, and took readings three separate times times. I did not divide my time for 10 periods by 10 to average time for one complete period because I didn’t know if the first 5 periods went faster than the second set of 5 periods. So I didn’t want to assume anything. I was careful that I did not forget about any of the safety procedures. I also paid careful attention in making sure that I measured string lengths perfectly and accurately each time I took a set of readings. This was just in case the string did slip on the weight of the bob and made it an unfair test. I took 7 results which I felt is a larger enough range looking at my graph and repeated them 3 times so that I could get an average.
Analysis
My graphs show a number of things. My first graph does not show a direct relationship between the time of a period and the length of the pendulum, therefore I tried to work out what would make it have a direct relationship. First I tried the average time of ten periods and half of the length but this did not work, as there was not a direct correlation. I then plotted the relationship between length against the average length squared the line of best fit for this graph was a straight line and the line passed through the origin. This meant that the time of period is directly proportional to the length of the string squared. Not all the points are exactly along the line of best fit, which is because my experiment could not have been perfect. A number of things could have changed the result, for example, the weight of the bob many have pulled the string down a bit or my reaction times interfered with results. The curve of the graph of the relationship between length and ten periods suggests than as length gets longer the increase of time gradually gets slightly smaller the higher it gets. Every graph will pass through the origin because if the length of the string were 0 cm then the period would be 0 cm too.
As I predicted earlier on the results seem to show that as the length of the string increases so does the time for one period. I believe that this has happened as when the pendulum gets longer the pendulum gets lower to the ground with the bob at the lowest point, so has less gravitational potential energy than a pendulum that is shorter and so higher up. The higher that something is the more gravitational potential energy that it has, and so using that principle the shorter the string the more potential energy it will have. When the ball gets released the gravitational potential energy is converted to kinetic energy and so making the pendulum fall. When the pendulum reaches the bottom and begins to climb to the opposite side of where it started it will regain most of its gravitational potential energy but not quite the same as it loses energy through heat and other things. And so the pendulum will not rise to the same point/ height that it began from as it will have less energy. This pattern continues back to the other side where the period finishes. No matter where in the period that a pendulum is, if they are started at the same time the shorter pendulum will always finish a period faster than a long pendulum.
But I do not still think that as the length of the pendulum is longer the longer length that it will have to travel will affect the period is correct. This is because if a long pendulum were to be released from two different positions, its period would be the same as at the start of the experiment. This is due to the fact that I proved that the starting amplitude does not matter. If a pendulum were to start from a wider angle its travelling a further distance than if it was started from a tighter angle yet the period of both would be the same time.
Evaluation
It is easy to see how good my results were in accuracy, as all you have to do is see how well they fit my line of best fit. The points fit the graph that goes through the origin very well and so I can conclude that I carried out a reliable experiment. However as I have stated I am will definitely have lost accuracy due to my reaction times when starting and stopping the watch. It would be best if we could use a system that did no rely on human reactions, as they are always wrong. By measuring 10 periods I have made this time a smaller fraction of the total time, although the more periods would make the inaccuracies less, so maybe to improve the experiment I could time 15 periods.
To improve my experiment and to make it have a lot higher accuracy I could have used light gates so I know when the pendulum has completed one period. However I would still have the inaccuracy of stopping and starting the stopwatch and could only measure one period as the pendulum does not always reach the same height, gradually it decreases. My graphs show that seven points are enough to draw an accurate line of best fit, the problem with more points is that there are more points that could be wrong, and so I have concluded that I had just the right amount of points on my graph. I could have taken a larger range of lengths however, by going up to 150cm long, and by doing this I could have proven whether eventually the relationship between period and length eventually levelled of or got very close to doing so. This could not have been done for this experiment, as there was a maximum length you could use until the experiment became too big and unsafe. To be sure that where I started from the same place I could have used a protractor to start at the same angle every time. But as my previous experiment showed there would be little point in doing this.
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