Surface: the margarine tub will be sliding along the same piece of floor for every experiment. This is because if I changed the surface that it moved over, it could create more or less friction (if the surface was smoother then less friction, if it was rougher, then more friction) which would affect the stopping distance of the tub and affect my results.
EPE: In order to make sure that the catapulted tub has the same amount of KE every time it is catapulted, I will pull the elastic band back the same distance (22cm) each time. This will ensure that the margarine tub has the same KE for every experiment. If I did not measure how far I pulled the elastic band back, it would affect my results because the elastic band would have different amounts of EPE each time. The EPE turns into the KE which propels the tub forwards, EPE so if the EPE changed, then the KE would do so as well. If the EPE changed each time, then so would the KE. The margarine tub would have different levels of KE pushing it forwards and so would have a varying sd. accordingly. Therefore, by using a fixed value of EPE, I am also using a fixed value of KE.
Air resistance: the amount of air resistance acting on an object varies according to the objects surface area. A larger surface area means a bigger amount of air resistance, which means that the objects stopping distance will lessen. In order to make sure that the air resistance does not change at all in this experiment and cannot affect my results, I will use the same margarine tub for every experiment.
Slope of surface: The margarine tub will be moving along a flat floor every time- and just in case there is some tiny slope to the floor, I will use the same patch of floor for each experiment. This is because if the margarine tub was on a sloped surface, going down, then the same amount of EPE and KE would take it further than it would on a flat surface because the KE would turn into GPE (Gravitational Potential Energy) which would pull the tub down the slope and work with the KE, not against it. However, if the tub was moving up the slope, the same amount of EPE and KE would take it less of a distance up the slope because the GPE would not help pull it down and forwards, it would pull it down and backwards, and work against the KE.
I will collect three sets of results for each mass of tub that I use, so that I can find an average, and see if there are any anomalous results. This will help ensure that the experiment is fair.
The factor that I will change for my experiment is the mass of the margarine tub. The mass of the margarine tub will affect its stopping distance. This is because if the tub has a larger mass then there will be more gravity acting on it. The gravity causes more friction, which unbalances the forces that move the tub and restrain it. If there is more friction working against the tubs movement than there is KE moving the tub, then the tub will slow down and stop more quickly, which lessens the sd. (stopping distance). Therefore I predict that as the mass of the tub increases, the stopping distance will decrease.
As preparation for this experiment, and to assist me with my predictions, I have done preliminary work on a simulation software program called ‘Science Investigations 5’. I looked at how mass of an object affects its starting speed. The starting speed was found by measuring the time it took for a 10cm piece of card stuck on top of a car to pass through a light gate. The car was catapulted, similar to the way that I will catapult my margarine tub in this experiment, so I had to stretch the elastic the same amount every time in order to ensure that that the trolley had the same amount of EPE every time. The software enabled me to change the mass of the car and collect results for different masses. The program also has built-in software which changed the results slightly, which meant that it was more realistic and I could get some anomalous results. I collected five sets of results (see results table A) for each mass and then found the average speed. However, when I plotted this on a graph, with a line of best fit, it produced a curve (see chart A), showing that there was no strict rule between the mass and the average speed. However, I played around with the results and found that if I plotted one divided by speed squared against the mass of the trolley, I got a straight line graph that bisected the origin (see chart B). This told me that mass is directly proportional to one divided by speed squared (1/speed^2).
That experiment also showed me that as the mass of the trolley increased, the starting speed decreased. If the starting speed is lower, then there is less Kinetic Energy that the friction has to turn into heat energy, meaning that the trolley (or in my case, the tub) stops more quickly. Therefore, this information supports my prediction.
There was another simulation program on ‘Science Investigations 5’ which looked at how starting speed (ss.) affects stopping distance (sd.). This followed on from the following experiment which looked at how mass affected ss.
On this program, I could change the height of a ramp that the trolley was on, and investigate the stopping distances for different heights; from two to nine centimetres, moving up one centimetre every time. Changing the angle of the ramp meant that the starting speed changed as well, because according to the height and slant of the ramp, the trolley would have more or less GPE (more if the ramp was higher, less if the ramp was lower). Once again, because the program had built-in error software, I took three sets of results for each height of the ramp and found the average. When I plotted this on a graph, the line of best fit was a straight line (see results table B and Chart C) although a few points were scattered slightly off of the line, the overall scatter was very close to the line. This shows that ss. is directly proportional to sd, meaning that as the starting speed (ss) increases, the stopping distance (sd) increases at the same rate; if the ss. doubles, then the sd will double, and so forth.
The results of these preliminary experiments support my prediction. The first preliminary experiment showed that as the mass increases, the starting speed decreases (and that mass is directly proportional to one divided by speed squared). Because in the second preliminary experiment that I did I found out that the starting speed and stopping distance are directly proportional to one another, this means that when the mass increases, making the ss. decrease, the sd. decreases at the same rate as the ss, so an increase in mass makes the sd. decrease.
Therefore, I can also predict the shape of a graph drawn of stopping distance against mass; it would look much like the graph that I got for Chart A, because if starting speed against mass produced a graph like this :
and speed is directly proportional to stopping distance, then a graph of sd against mass would look much the same. This means that I also predict that if I plotted a graph of one divided by sd against mass, it would be a straight line graph bisecting the origin, because if mass is directly proportional to one over ss, and ss is directly proportional to sd, then mass must be directly proportional to one divided by sd as well.
Method:
My apparatus will be set up as above. I will draw a line on the floor to mark where the margarine tub should be placed so it begins and is measured from exactly the same place every time. I will also use a metre stick so that I can accurately measure the distance that the tub has travelled in centimetres. Firstly, I will set up the apparatus as above (although I will not use any weights inside the tub for the first experiment).I will pull back the elastic band 22cm from where the margarine tub is positioned, and then let go so that it catapults the margarine tub. Using a metre stick, I will measure the distance the margarine tub has travelled, and then repeat the experiment twice more so that my results are reliable.
Then I will add one hundred grams weight to the margarine tub and collect three sets of results for that mass. I will continue adding 100g weights and collecting three sets of results until I reach a mass of six hundred grams.
Results:
Analysis and conclusion:
As the mass of the tub increases, the stopping distance decreases, as you can see from both my results and my graph (see Graph 1). The graph is, as I predicted, a curve similar to the one produced when, in my preliminaries, I plotted speed against mass. The curve is quite smooth, and only two out of seven points are not on it, and even they are very close to it. This graph fits my prediction very well.
In my prediction, I suggested that if I drew a graph of one divided by the stopping distance squared, I would have a straight line graph that bisected the origin, because if mass is directly proportional to one over ss, and ss is directly proportional to sd, then mass must be directly proportional to one divided by sd as well. In order to prove or disprove this theory, I added an extra column to my results table, of one divided by sd squared, and drew the appropriate graph (see Graph 2) :
As you can see, this graph fits my prediction quite well. It is a straight line bisecting the origin, and although some of the results are quite far away from the line of best fit, there is a clear trend in my graph, proving that mass is directly proportional to one divided by stopping distance squared.
From these results, I think that my results strongly support my prediction.
Evaluation:
The data that I collected was quite reliable, as there was a clear pattern visible on the graphs that I drew, so I think that I can draw a reasonably safe and reliable conclusion for the different masses that I tested.
To keep my experiment fair I kept the following factors constant:
The surface that the margarine tub was sliding along: I used the same piece of floor for every experiment. This is because if I changed the surface that it moved over, it could create more or less friction (if the surface was smoother then less friction, if it was rougher, then more friction) which would have affected the stopping distance of the tub and affect my results.
In order to make sure that the catapulted tub has the same amount of KE every time it is catapulted, I pulled the elastic band back the same distance (22cm) each time. This ensured that the margarine tub had the same KE for every experiment. If I had not measured how far I pulled the elastic band back, it would have affected my results because the elastic band would have different amounts of EPE each time. The EPE turns into the KE which propels the tub forwards, EPE so if the EPE changed, then the KE would do so as well. If the EPE changed each time, then so would the KE. The margarine tub would have different levels of KE pushing it forwards and so would have a varying sd. accordingly. Therefore, by using a fixed value of EPE, I am also using a fixed value of KE.
The amount of air resistance that acts on an object varies according to the objects surface area. A larger surface area means a bigger amount of air resistance, which means that the objects stopping distance will lessen. In order to make sure that the air resistance didn’t change at all in this experiment and couldn’t affect my results, I used the same margarine tub for every experiment, so it had the same surface area each time and did not have differing amounts of air resistance acting on it.
The margarine tub was moving along a flat floor every time- and just in case there was some tiny slope to the floor, I used the same patch of floor for each experiment. This is because if the margarine tub was on a sloped surface, going down, then the same amount of EPE and KE would take it further than it would on a flat surface because the KE would turn into GPE (Gravitational Potential Energy) which would pull the tub down the slope and work with the KE, not against it. However, if the tub was moving up the slope, the same amount of EPE and KE would take it less of a distance up the slope because the GPE would not help pull it down and forwards, it would pull it down and backwards, and work against the KE.
I collected three sets of results for each mass of tub that I used, so that I could find an average, and check for any anomalous results. This will helped to ensure that the experiment was kept very fair.
There are some anomalous data points on my graphs – on Graph 1, the most noticeable anomaly is the results for the 200 gram mass of margarine tub, and on Graph 2, the points for 100, 200 and 600 are quite a noticeable distance from my line of best fit. In Graph 2 there is a marginally wider scatter of points around the line of best fit, whereas for my first graph, the scatter is very slight and only includes two points. These anomalies could have been caused by several different factors: if the elastic band was pulled back even slightly too far or not far enough, then that would affect my results. If I did not measure very carefully and accurately how far I pulled the elastic band back, it would affect my results because the elastic band would have different amounts of Elastic Potential Energy each time. The EPE turns into the Kinetic Energy which propels the tub forwards, so if the EPE changed, then the KE would do so as well. If the EPE changed each time, then so would the KE. The margarine tub would have different levels of KE pushing it forwards and so would have a varying sd. accordingly. In order to prevent this from happening, a way of pulling the band back more accurately would be to place a board or clamp stand on the 22cm mark and clip the elastic to it so that to release it, all I have to do would be to open the clip or peg.
Although I attached the elastic band to chair legs and even asked someone to sit on the chair to keep it steady whilst doing the experiment, it is possible that the chair could have moved, which would affect not only the elastic bands position but also where the margarine tub was catapulted from. If the chair legs moved forwards and the margarine tub started by being slightly in front of the line it was supposed to start on this would affect the results because if it travelled (for example) one metre but had started from two centimetres over the mark, then the results would have recorded it as having gone one point two metres. This problem could be overcome if the elastic band was attached to a more solid, immovable object- for example, table legs.
It would have been better if the tub could have been propelled over a more regular surface, as the floor I used had dents and slight bumps in it. If the margarine tub had hit one of these, it would not only have created more friction and slowed the tub down, but also could have affected the tubs direction of movement and given it a slight diagonal slant so that although it moved just as far, it did so slightly sideways, and therefore the distance it travelled to the side would not have been measured.
Inaccurate measuring could also have caused the anomalies. A ideal way to fix this would be to have a giant grid on the surface that the tub was propelled along, so that with a ruler or metre stick, the line that the tub was on could be followed straight to the side and an accurate measurement could be found. However, this could be rather impractical.