Preliminary Three: Diameter of Bob
Results Table
This graph also shows a positive correlation between variable and the period of the pendulum, meaning that as the diameter is increased, the time it takes the pendulum to complete one oscillation also increases. The gradient of the line of best fit on this graph is 1. This preliminary has yielded results that has a steeper gradient than my first preliminary, which means this is also ideal for my main investigation.
Preliminary Four: Type of Bob
Results Table
According to this graph, there is a positive correlation between the type of bob used and period. The gradient of this graph is 0.9143. This gradient falls behind the ‘Length of String’ and ‘Diameter of Bob’ gradients, so it’s unlikely that I will use this for my main investigation, also, in terms of practicality, there wasn’t a large variety of materials to choose from.
Main Investigation: Length of String
I decided to choose Length of String for my investigation, because, my results for that preliminary had the one of most noticeable relationships between the independent and the dependent variable as well as the fact that there were no outliers.
I didn’t choose ‘Type of Bob, because ‘Type of Bob’ is an example of a discrete independent variable, in that it doesn’t have a numerical value that can be plotted on a graph. As well as this, even though there does appear to be a relationship between ‘Type of Bob’ and the period, there was another independent variable which was changed, which was the mass of each bob.
Although ‘Diameter of Bob’ was also ideal to be tested in my main investigation, it lost out to ‘Length of String’ simply because there was not a wide enough range of metal bobs that were made of the same material but had different diameter. So, although I predict it would’ve yielded noticeable results, Length of String is more practical to do, as well as the fact that the length of the string is easy to manipulate.
Method
- Collect all required equipment.
- Measure out each length of string to be used in the investigation, leaving an 8cm excess to allow for knot tying.
- Tie bob to length of string to be tested securely
- Set up clamp stand on the edge of the table to allow room for the pendulum
- The person in charge of dropping the bob holds it up taut so that the bob is parallel to the clamp stand, or the length of string is perpendicular to the clamp stand and checks that the angle is 90° with the protractor.
- Person in charge of the stopwatch signals when to drop the bob and measures the period with the stopwatch
- Third person records results in a table
- Retrial each length five times so as to that the results are as accurate as possible.
Results
Pendulum Equation (PE):
Time of Period=2π
Interpretation:
On the graph, there is positive correlation, according to my line of best fit. It appears as though the longer the string, the more time it takes for the bob to complete its oscillation.
This can be explained because when the bob swings, it swings from a high position to its lowest position (the midpoint of the swing, also where the bob will come to rest when it reaches dynamic equilibrium). The change in height is caused by Earth’s gravitational acceleration or the change in velocity over time caused by gravity acting on the bob. If the length of the string is longer, the distance to swing from the highest point to lowest will be greater (as the distance travelled is the length of an arc, we can calculate the length of the arc using the equation 2πr x θ/360, where θ is the angle from which the bob was dropped from), therefore it would take a longer amount of time to fall to lowest point of the swing.
Of course, gravity isn’t the only factor that affects the period, other forces such as air resistance and friction help to eventually slow down the bob, and the mass of the string, although slight, affects the force needed to swing the pendulum back and forth.
Evaluation
The main investigation went well, however there are many areas which could be improved in order to get more accurate results. For example, the method wasn’t very reliable because quite a few aspects of the investigation had to be carried out by humans, as well as the fact that the results which were recorded down were up to the judgement of the person who controlled the stopwatch when the bob completed its oscillation. This means that some of the results could be off by a few milliseconds or even seconds. Despite this, my group did try to keep the results as reliable as possible by making sure the same person was used to control the stopwatch and drop the bob, so that the factor of different people’s reaction times were limited. I could improve my experiment by:
- Using a computer and a laser to release and measure the bob, for instance, if at its starting the point, the bob was intercepting a laser/beam of light, so that when it was dropped, the computer could measure the time it takes for the bob to re-intercept the beam again, i.e. complete its oscillation completely.
- Using a lighter sturdier form for the pendulum shaft instead of string, as the string had a tendency to bend throughout the oscillation, which could’ve affected the results
- Have a release that was positioned parallel to the clamp stand so that the angle from which the bob was dropped from each time was the same
- Having a way to hook the pendulum length/string to the clamp and the bob without having to tie knots so the length of the string that would swing was more accurate
Other than that, I believe my equipment was as accurate as I needed them to be, so I wouldn’t change any of the equipment I was using to carry out the experiment. I think that my results are reliable because the range bars are all relatively small on my graph, however in comparison to the Pendulum Equation; the results are too big and are in turn not scientifically accurate. I’ve calculated the average difference between my Averages and the Pendulum Equation line and have found it to be up to 0.4 of a second in difference. In conclusion, I believe that the length of string does affect the period of a pendulum, despite the inaccuracy of my results as my investigation proved that this factor still theoretically affects it.
