Plan
- Firstly I will collect all the apparatus I will need to use to carry out the investigation. This includes cup cake containers, a timer, stand and clamp and two 1 metre rulers. With the cup cake containers, when increasing the surface area, I will need to staple the cup cake containers together. This means that as I increase the surface area, I will also be increasing the weight during each test. Therefore I will need to even out the weight of each try. I will carry this out by placing the correct amount of cup cake containers into another container to even out the weight to produce a fair test. For example, as I will be testing five different sizes of surface area, during my first try, testing the surface area of only one cup cake container, I will place another four extra cup cake containers into that one container. When testing the surface area of two cup cake containers, I will place two extra containers in one of the stapled containers and another into the other container. This is the fairest way to even out the weight of the containers. Each cup cake container/s will be used by being dropped at the beginning of each experiment at the specified height. The timer will be used by starting it as the cup cake container reaches the 1 metre height and then stopping it as the cup cake container touches the ground. I will be starting the cup cake container at this height so I am sure that the cup cake container has reached its terminal velocity. I will set up the stand and clamp and will clamp a 1 metre ruler to the stand and clamp, making sure the bottom of this ruler is exactly 1 metre from the ground to make a 2 metre height.
- I will then drop one cup cake container, containing 4 extra cup cake containers, from the top of the 2 metre height. When the cup cake container reaches the 1 metre height I will be sure that it has reached its terminal velocity and I will start the timer. As the cup cake container touches the ground it will have fallen at its terminal velocity for at a length of 1 metre and I will then stop the timer. I will then repeat this 2 more times to get an average and also to make sure that if I get any anomalous results, I will also have back-up results. I will then repeat this test but each time I will increase the surface area by stapling on an extra cup cake container. I will then even out the weight by adding enough cup cake containers to equal the weight of 5 cup cake containers.
- Altogether I will take a range of 15 measurements to show the effect of the input variable. I will be taking 5 separate measurements for each size of surface are, but then I will be taking an extra 2 to reach an average result.
- I will be using 5 cup cake containers during each test, each time adding 1 of these cup cake containers to the side of the previous cup cake container to achieve the chosen surface area.
- I will be measuring change in the test each time the cup cake container/s touch the floor from falling. I will measure this by using a timer.
- I will be taking these measurements each time I drop a cup cake container and when it touches the ground by using the timer. I will need to measure this as accurately as possible because I will need to have the correct times to prove my prediction made at the beginning of this investigation.
- I will not need to make many precautions before carrying out this investigation as I will not be using a lot of apparatus. The only hazard I will need to watch out for is the chance of the stamp falling causing the clamp and ruler to fall which may injure me. This can be made safe by making sure the stand and clamp is well out of the way of others so it cannot be touched which will stop it from falling.
- When I have collected my data I will process it by making calculations. Firstly I will need to calculate the surface area of each amount of cup cake containers and for this I will use the equation for surface areas of circles: area = πr² (r = radius). To calculate the rate of fall, I will use the equation distance ÷ time = speed (rate of fall. I will then calculate the average rate of fall from each set of 3 tests by calculating the sum of each set of 3 tests and then dividing this number by 3. By finding the average I will have the most accurate result for each test.
Preliminary Work
Before I begin my investigation I will need to carry out some preliminary work and trial runs to make sure I am using the correct apparatus and achieving accurate results.
After carrying out my preliminary work I found that the apparatus I selected is suitable and works. The cup cake containers provided me with the fairest and most reliable source for what I am trying to find out and the timer was also the most reliable piece of apparatus for this investigation. The stand, clamp and ruler also supplied with steady and stable apparatus for measuring.
From this I can see that I will not need to adjust any of my apparatus as my results are already appropriate. Below is a small version of a results table of the results I collected during my test run.
From these results I can clearly see that the results are consistent and are as predicted. Therefore I will not need to rearrange my investigation to find out my previous prediction.
Results Table
(Continues on next page)
Processing My Results
To provide my results table with the calculations of surface area of cup cake containers, rate of fall of cup cake container and average rate of fall of cup cake container I used the equations shown in section 8 of my plan.
To show what I have found out, I have drawn a graph of my results.
Analysis
From investigating the affect of surface area of a cup cake container on its rate of fall, I have found that by increasing the surface area of a cup cake container, the slower the rate of fall and by decreasing the surface area of a cup cake container, the faster the rate of fall. My graph supports this finding. This is exactly what I predicted at the beginning of my investigation and so compares extremely well to my prediction.
In my results, I can see that as I increase the surface area of the cup cake container, the rate of fall and the average rate of fall decreases and vice versa. The smallest surface area I investigated was 50.27cm² and this gave me my highest value for the rate of fall: 3.42. The largest surface area I investigated was 251.35 and this provided me with my lowest value for the rate of fall: 1.05. With the first couple of surface areas of cup cake containers I investigated, the time taken started to double as I increased the surface area. Therefore the rate of fall of the cup cake container started to half. This doubling and halving started to lessen as I began to increase the surface areas of the cup cake containers. This could have been a cause of a small lack of accuracy: when the cup cake containers are stapled together, parts of the surface area of each container sit side by side and therefore these parts of the surface area will not cause effect to the rate of fall. As I increase the surface with more containers, slightly less of the surface area is being resistant each time and therefore this will cause the rate of fall not to be halved anymore. This is only a small problem but causes the doubling of the time taken to fall and the halving of the rate of fall to gradually fade out, but it does not make a difference to my prediction.
I got these results from my investigation because of air resistance. As a cup cake container falls, the rate of fall depends on the amount of air resistance: when the container falls, particles in the air hit the base of the container which constricts its speed of fall. This air resistance slows the container down from reaching the floor. When a cup cake container with a larger surface area is dropped, there is a larger area for the particles in the surrounding area to hit the area. More particles in the area can hit this surface, and with more particles this causes the container to slow down even more. The air particles hitting the surface causes air resistance and this causes the rate of fall to decrease. Therefore, when the cup cake container has a smaller surface area, there are fewer particles in the air to hit the surface of the container. This means that there is less air resistance to restrict the container from falling and therefore the container can fall faster causing a bigger rate of fall.
Evaluation
My results match the trend in my results very accurately. From my graph, you can see that there is a strong trend where the larger the surface area of the cup cake container, the lower the average rate of fall and vice versa. You can also see in the graph that all the results fit into a pattern. The amount of variation in my data is not very big and this means that my results are good enough to support my conclusion.
Although my results do not fit into a completely perfect pattern, it is plain to see that they all do fit into the trend. There are no anomalous results. Although you can see a clear pattern in my graph and results, you can also see that the pattern does not continue perfectly. When carrying out my investigation, I did not feel the need to change my investigation to completely clear this problem because my results still confirmed my prediction and still provided me with a firm conclusion.
Some of the factors which could have limited the accuracy of the experiment could have been the problem which I stated in my analysis. This was that when stapling the cup cake containers together, some of the surface area is restricted and therefore it is possible for the amount of air resistance to be less than expected. If I were to do the experiment again, I could use another way of joining the cup cake containers together at the very top of the container to make sure I have full use of each container. I could also try making the containers flatter to make sure that the whole of the surface area is used during the investigation.
Other investigations I could try to thoroughly investigate the problem of surface area is to try my previous idea: I could try flattening the cup cake containers out which would allow full use of the surface area and would also provide larger surface which could provide more effective results.
